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STRATEGIC FINANCIAL MANAGEMENT for

C. A. FINAL INDEX

Sr. No. Chapter Name Page No.

1 Equity Valuation 01 to 15

2 Valuation of Bonds 16 to26

3 Foreign Exchange 27 to 53

4 International Financial Management 54 to 57

5 Derivatives – Futures & Options Derivatives – Interest Rate Risk Management

58 to 72 73 to 79

6 Portfolio Management 80 to 98

7 Mutual Funds 99 to 106

8 Mergers & Acquisition 107 to 117

9 Value At Risk (VAR) 118 to 120

“At Khetan Education, people come as students but carry lifelong experience.”

- Prof. Archana Khetan

KHETAN EDUCATION EQUITY VALUATION

...................................................................... 1 ..............................................................

EQUITY VALUATION I. VALUATION • The Value of an Equity or Stock is the present value of expected future cash flows

discounted at investor’s required rate of return → ROR. • In order to compute the value or intrinsic value or should be value of an equity, we can

use various theoretical Models suggested by experts. As required by the Model, we would use various parameters relevant to valuation. • The Models to be used to study the chapter can be segregated as follows: Discounted (C) Comparable (D) Residual (E) Net Approach Firms Valuation Asset Approach Approach Method (A) Dividend (B) Free Cash Discount Flow Model Approach (FCFF/FCFE) II. DISCOUNTED APPROACH (A) DIVIDEND DISCOUNT MODEL : This model has been suggested by ‘Gordon’. As per this model, the price or value of a stock should be the present value of expected future dividends discounted at investor’s required rate of return. The DDM can be segregated into three types depending on the growth involved within an enterprise i.e. No growth, Constant growth and Multiple growth. The value of the stock can be computed using either of the models –

No Growth Model Constant Growth Model Multiple Growth Model

SFM EXPRESS KHETAN EDUCATION

...................................................................... 2 ..............................................................

NO GROWTH MODEL

P0 = 1

e

DK

CONSTANT GROWTH MODEL

P0 = 01

e e

D (1 + gc)D = K - gc K - gc

MULTIPLE GROWTH MODEL P0 = Value in gs + Value in gc D0 = Dividend per share at t = 0 D1 = Dividend per share at t = 1/ Expected Dividend Ke = Cost of Equity gc = Constant growth rate 1. X Ltd reported an EPS of ` 12 for the year just ended and a pay-out ratio of 40%.

The earnings are expected to grow at 30% p.a. for the next 4 years. Beyond the 4th year, growth rate would be 6% p.a. forever. Find out the intrinsic value of the share if ROR is 18% p.a.

Ans. EPS = ` 12 Payout = 40% gs = 30% till 4 years gc = 6% beyond 4 years ROR = 18% DPS = ` 12 × 40% = ` 4.80 P0 = Value in gs + Value in gs While using Dividend Discount Model, we primarily assume two points :

• The dividends grow at the same rate as EPS • The payout ratio does not change across maturity

Value in 𝐠𝐠𝐬𝐬 (assuming Payout does not change i.e. DPS will grow each year by

growth rate) Year DPS ` PV @ 18% PV

1 4.8 + 30% = 6.240 0.847 5.29 2 6.24 + 30% = 8.112 0.718 5.82 3 8.112 + 30% = 10.550 0.609 6.42 4 10.55 + 30% = 13.710 0.516 7.07

TOTAL ` 24.60 ⇒ YEAR 0


...................................................................... 3 ..............................................................

Value in 𝒈𝒈𝒄𝒄

P4 = 5

e

DK - gc

= 4 c

e

D (1 + g )K - gc

= 13.71 (1.06)0.18 - 0.06

= ` 121.105 ⇒ Year 4 Present Value of P4 @ t = 0

= ` 121.105 × 41

(1.18)

= ` 121.105 × 0.516 = ` 62.49 P0 = ` 24.60 + ` 62.49 = ` 87.09 2. Consider a firm which paid a dividend of ` 17.0/- share. This is expected to grow @

60% p.a. for the next 3 years. Beyond the 3rd year, the growth rate will start falling in a linear fashion so as to become 4% p.a. from the 7th year onwards and stay at that level forever. Find out the intrinsic value of the share if ROR is 20% p.a.

Ans.

60% 60% 60% 46% 32% 18% 4% 4% 4%

Linear form D0 = ` 17 gs = 60% for 3 years gs = 4% p.a. from 7th year ROR = 20%

Fall in the growth rate per anum = 60% - 4%7 years - 3 years

= 14%

P0 = Value in gs + Value in gc


...................................................................... 4 ..............................................................

Value in gs

Year DPS PV @ 20% PV 1 17.00 + 60% = 27.20 0.833 22.66 2 27.20 + 60% = 43.52 0.694 30.20 3 43.52 + 60% = 69.63 0.579 40.32 4 69.63 + 46% = 101.66 0.482 49.00 5 101.66 + 32% = 134.195 0.402 53.95 6 134.195 + 18% = 158.35 0.335 53.05 7 158.35 + 4% = 164.68 0.279 45.95

TOTAL ` 295.13 Value in gc

P7 = 8

e c

DK - g

= 7 c

e c

D (1 + g )K - g

= 164.68 + 4%0.20 - 0.04

= 171.2672

0.16 = ` 1,070.42

Present Value of ` 1,070.42 @ t = 0

= ` 1070.42 × 71

(1.20)

= ` 1070.42 × 0.279 = ` 298.73 ∴ P0 = Value in gs + Value in ge = ` 295.13 + ` 298.73 = ` 593.86

(B) FREE CASH FLOW APPROACH The free cash flow model is based on the view that the value of a business is the present value of expected future cash flows left out after meeting all the operational expenses and growth related expenses. This model can be segregated into two:

a. Free Cash flow to the firm (FCFF) b. Free Cash flow to the equity (FCFE)

FCFF = EBIT (1-T) + DEPRECIATION – CAPEX – CHANGE IN WORKING CAPITAL

OR FCFF = EBIT (1-T) – ( CAPEX - DEPRECIATION ) – CHANGE IN WORKING CAPITAL The value of the firm can be computed using either of the models – No Growth Model Constant Growth Model Multiple Growth Model


...................................................................... 5 ..............................................................

NO GROWTH MODEL

V0F0 = 1

C

FCFFK


V0F0 = 01

c c

FCFF (1 + gc)FCFF = K - gc K - gc

MULTIPLE GROWTH MODEL V0F0 = Value in gs + Value in gc Value of Equity (VOE) = Market value of Firm (VOF) – Market Value of Debt

Price Per Share = VOENOS

3. The following details are available with regard to the projected operations of

Pragati Limited. Years 1 2 3 4 5

Sales 120 132 145 159 175 Operating expenses 53 58 62 67 73 Depreciation 11 10 10 12 12

Years 1 2 3 4 5

Investment in current assets at the beginning of the year

6 5 6 7 5

Investment in fixed assets at the beginning of the year

30 20 10 0 0

Year Post tax non- operating cash flows

1 12 3 8 5 22

The company has long-term debt carrying an interest rate of 12.5% and has some non- interest bearing current liabilities. The cost of equity capital is 16%. The company does not have any other long-term sources of finance. The market value of equity is ` 50 lakhs and the market value of debt is ` 30 lakhs. The effective tax rate applicable to the company is 36%. From the sixth year onwards the free cash flow of the company is expected to grow at the rate of 8% p.a.

You are required to calculate the value of company using the discounted cash flow approach.


...................................................................... 6 ..............................................................

Ans. WORKING NOTE : Computation of Kc Kc = WdKd (1 - t) + WeKe

= 30

50 + 30 × 12.5 (1 - 36%) +

5050 + 30

× 16

= 13% Computation of value in explicit forecast period is gs

Particulars (`) 1 2 3 4 5 Sales 120 132 145 159 175 Less: Operating Expenses (53) (58) (62) (67) (73) EBDIT 67 74 83 92 102 Less: Depreciation (11) (10) (10) (12) (12) EBIT 56 64 73 80 90 EBIT (1 - T) 35.84[56 (1 - 36%)] 40.96 46.72 51.2 57.6 +Depreciation 11 10 10 12 12

Capex (30) (20) (10) 0 0 ∆ in WC (6) (5) (6) (7) (5) Operating FCFF 10.84 25.96 40.72 56.2 64.6 +Non-Operating Cashflow 12 - 8 - 22 FCFF 22.84 25.96 48.72 56.2 86.6

Year Cashflow(`) PV @ 13% PV

1 22.84 0.885 20.21 2 25.96 0.783 20.33 3 48.72 0.693 33.76 4 56.20 0.613 34.45 5 86.60 0.543 47.02

TOTAL ` 155.77 Value in gc

VOF5 = 6

c c

FCFFK - g

= 5 c

c c

FCFF (1 + g )K - g

= [86.6 - 22]1.08

0.13 - 0.08 = ` 1,395.36

P.V. of VOF5 = 1,395.36 × 51

(1.13) = ` 757.68

Value of firm = 155.78 + 757.68 = ` 913.46


...................................................................... 7 ..............................................................

NOTE: While computing FCFF6, we did not take non- operating cashflow component as it seems like a non-recurring item. 4. Following information is given in respect of WXY Ltd., which is expected to grow

at a rate of 20% p.a. for the next three year after which the growth rate will stabilize at 8% p.a. normal level, in perpetuity.

For the year ended March 31, 2014 ` in Crores

Revenues 7, 500 Cost of Goods Sold (COGS) 3,000 Operating Expenses 2,250 Capital Expenditure 750 Depreciation (included in COGS & Operating Expenses) 600

During high growth period, revenues & Earnings before Interest & Tax (EBIT) will grow at 20% p.a. and capital expenditure net of depreciation will grow at 15% p.a. From year 4 onwards, i.e. normal growth period revenues and EBIT will grow at 8% p.a. and incremental capital expenditure will be offset by the depreciation. During both high growth & normal growth period, net working capital requirement will be 25% of revenues.

The Weighted Average Cost of Capital (WACC) of WXY Ltd. is 15%. Corporate Income Tax rate will be 30%.

REQUIRED : Estimate the value of WXY Ltd. using Free Cash Flows to Firm (FCFF) & WACC methodology.

The PVIF @ 15 % for the three years are as below: Year T1 T2 T3 PVIF 0.8696 0.7561 0.6575

Ans. Given: gs = 20% p.a. for next 3 years gc = 8% p.a. Kc = 15%

Particulars (`) 1 2 3 4 EBIT [Sales – COGS – Operating Expenses] i.e. (7,500 – 3,000 - 2,250) at t = 0

2,700 (2,250+20%)

3,240 3,888 4,199.04

EBIT(1-T) 1,890 2,268 2,721.6 2,939.328 Less: Capex- Dep. (750 – 600 = 150) at t = 0

(172.5) (150+15%)

(198.38) (228.13) -

Less: ∆ in W.C. (375) (450) (540) (259.2) ∴ FCFF 1,342.5 1,619.62 1,953.47 2,680.128


...................................................................... 8 ..............................................................

WN : Computation of W.C. Year 0 1 2 3 4

W.C. 1,875 2,250 2,700 3,240 3,499.2

∆ in W.C. - 375 450 540 259.2

Year Cashflow PV @ 15% PV 1 1,342.50 0.870 1,167.98 2 1,619.62 0.756 1,224.43 3 1,953.47 0.658 1,285.38

TOTAL 3,677.79 Cr Value in gc

VOF3 = 4

c c

FCFFK - g

= 2,680.13

0.15 - 0.08 = ` 38,287.57

P.V. of VOF3 = 38,287.57 × 31

(1.15) = ` 25,193.22

VOF = 3,677.79 + 25,193.22 = ` 28,871.01Cr

(C) RELATIVE VALUATION MODEL/COMPARABLE FIRMS APPROACH 5. XY Ltd. A cement manufacturing company has hired you as a financial consultant

of the company. The Cement industry has been very stable for sometime and the cement companies SK Ltd & AS Ltd are similar in size and have similar product market mix characteristic. Use comparable method to value the equity of XYZ Ltd.

In performing analysis, use the following ratios: 1. Market to book value 2. Market to replacement cost 3. Market to sales 4. Market to net income

The following data are available for your analysis: (Amount in `) SK Ltd AS Ltd XY Ltd Market value 450 400 Book value 400 300 250 Replacement cost 600 550 500 Sales 550 450 500 Net Income 18 16 14


...................................................................... 9 ..............................................................

Ans. Particulars SK AS Average Mkt / B.V 450

400 = 1.125

400300

= 1.33 1.2275

Mkt / R.C 450600

= 0.75 400550

= 0.73 0.7400

Mkt / sales 450550

= 0.82 400450

= 0.89 0.8550

Mkt / PAT 45018

= 25.0 40016

= 25.0 25.0000

→ 1.2275× 250 = 306.875 → 0.74 × 500 = 370 Average = ` 363.59 Lakhs → 0.855 × 500 = 427.5 → 25 × 14 = 350 (D) RESIDUAL VALUATION MODEL/ EVA & MVA : As per the above mentioned model, if a firm is capable of generating extra cash flows post meeting all operating expenses and stakeholders requirements, it calls for a higher valuation. The cash left out is called ‘Residual Income’ or ‘Economic Value Added’. The present value of all EVA’s discounted at an appropriate discounting factor is called ‘Market Value Added’ EVA = EBIT (1 - T) - Kc × Capital employed Where, EBIT (1 - T) = NOPAT Kc = WACC Capital employed = Debt and Equity ⇒ Present Value of EVA is Called MVA Present value can be computed with the help of either of the models – The PRESENT VALUE OF EVA can be computed using either of the models – No Growth Model Constant Growth Model Multiple Growth Model NO GROWTH MODEL

MVA0 = 1EVAKc


...................................................................... 10 ..............................................................


MVA0 = 01 EVA (1 + gc)EVA = Kc - gc Kc - gc

MULTIPLE GROWTH MODEL

MVA0 = Value in gs + Value in gc VOF = BOOK VALUE OF THE FIRM + MVA Value of Equity (VOE) = Market value of Firm (VOF) – Market Value of Debt Price Per Share = VOE/ NOS

6. Consider a firm with the following capital structure – Net worth= 500 Lakhs 15%

long term debt 500 lakhs. The firm is subject to tax rate of 40% and its cost of equity is 17%. For the next year the firm is expected to generate an EBIT of 250 lakhs. Compute EVA and find out the intrinsic values of the share :

Case I : Assuming EVA to be perpetual. Case II : Assuming EVA to be subject to a perpetual growth rate of 5% p.a. No of

shares = 10 lakhs. Ans. Kc = WdKd (1 - T) + WeKe

Kc = 500

1000 × 15 (1 - 0.40) +

5001000

× 17

= 13% a. If EVA is perpetual:

MVA = 1

c

EVAK

Where EVA = [EBIT (1 - t) - Kc × Capital employed] = 250 (1 - 40%) - 13% × ` 1,000 L= ` 20 L

∴ MVA = 20L0.13

`= ` 153.85 L

Hence, Value of firm = Book Value + MVA = ` 1,000 L + ` 153.85 L = ` 1,153.85 L ∴ Value of equity = VOF - Debt = 1,153.85 - 500 = ` 653.85L

∴ Price/ Share = VOE

No. of shares =

653.85L10L

`= ` 65.385 /-

b. If EVA grows by 5% p.a.

MVA = 1

c c

EVAK - g

= 20L

0.13 - 0.05`

= ` 250 L

VOF = 1000 + 250 = ` 1,250 L VOE = 1250 – 500 = ` 750 L

∴ Price/share = VOE

No. of shares =

750L10L

` = ` 75 /-


...................................................................... 11 ..............................................................

MISCELLANEOUS TOPICS: A. RIGHT ISSUE

No. of new shares = Desired fundsSubscription price

No. of rights = Existing shares

New shares

Ex-right price = MN + SR

N R+

Where; MN = No. of existing shares × Current MPS SR = New Shares × Subscription Price N = No. of existing Shares R = Right Shares 7. Mega soft Ltd plans to expand its operations and estimates the total cost of

expansion to be ` 24 crore. The same is proposed to be financed by internal accruals of ` 9 crore and the balance through a rights Issue. The current share capital of the company is ` 2.40 crore. The shares of the company are currently quoting at ` 345. The company proposes to price the Rights at ` 250.

Based on the above information: a. Compute the ratio of the Rights. b. Calculate the value of Rights c. Determine the gain/loss of a shareholder, if he

• Exercises his Rights in the Rights issue • Allows his Rights to expire

Ans. Total cost of expansion = ` 24Crores Internal accruals Amount to be raised ` 9 crores ` 15 crores ⇒ Amount of funds to be raised through Rights = 24 - 9 = 15 crores Current share capital = ` 2.4 Crores Face Value ` 10 (Assumed) ⇒ No. of existing shares = 24L

⇒ No. of shares to be raised as Rights = 15 crores

250`

` = 6 Lakhs

a. Ratio of Rights = 6L: 24L = 1:4

b. Ex-Right price = 4 × 345 + 1 × 250

4 + 1 = ` 326 /-

Value of right = Ex - right price - subscription price

N =

326 - 2504

= ` 19


...................................................................... 12 ..............................................................

c. ⇒ Accept the Rights Wealth before : 4 × 345 = `1,380 Wealth after : Value of total shares = 5 × 326 = 1,630 Cost of Rights share = 1 × 250 = (250) ` 1,380 ⇒ Allows Rights to expire Wealth Before = 4 × 345 = ` 1,380 Wealth After = 4 × 326 = ` 1,304 ∴ Loss = ` 76

B. TECHNICAL ANALYSIS - SMA & EMA There are two types of equity analysis method: a. Fundamental analysis : Uses the financial data of a company assuming the value

is dependent on the cashflow generating ability. b. Technical analysis : It uses past prices and volume behavior with the assumption

that the market and investors follow certain behavioural pattern. This technique is about reading these patterns.

8. Closing values of SSE Sensex from 6th to 17th day of the month of January of the

year 2001 were as follows: Day Date Day Sensex

1 6 Thu 14,522 2 7 Fri 14,925 3 8 Sat No Trading 4 9 Sun No Trading 5 10 Mon 15,222 6 11 Tue 16,000 7 12 Wed 16,400 8 13 Thu 17,000 9 14 Fri No Trading

10 15 Sat No Trading 11 16 Sun No Trading 12 17 Mon 18,000

Calculate Exponential Moving Average (EMA) of Sensex during the above period. The 30 days simple moving average of Sensex can be assumed as 15,000. The value


...................................................................... 13 ..............................................................

of exponent for 30 days EMA is 0.062. Give detailed analysis on the basis of your calculations.

Ans. α = 0.062 Prices Opening EMA 1 - 2 3 × α (0.062) Closing EMA 14,522 15,000 (given) -478.00 -29.64 15,000 - 29.64=14,970.37 14,925 14,970.37 -45.36 -2.81 14,967.55 15,222 14,967.55 254.45 15.78 14,983.33 16,000 14,983.33 1,016.67 63.033 15,046.36 16,400 15,046.36 1,353.64 83.93 15,130.29 17,000 15,130.29 1,869.71 115.92 15,246.21 18,000 15,246.21 2,753.70 170.73 15,416.93

C. VALUATION OF A NON LISTED ORGANISATION 9. X ltd. presently operates in a cement industry with a debt equity ratio of 2:1. Its

cost of debt and equity are 13% and 17% respectively. It is subject to a tax rate of 30%. It feels that the growth rate in the cement business is going to be low or moderate. It therefore decides to strategically diversify into the new emerging bio- technology sector. The projected cash flows from the long term funds point of view for this new biotech projects are shown below:

0 1 2 3 4 (170) 50 60 40 60

The amount of ` 170 crores is to be financed by a debt equity ratio of 3:1. Debt would be by way of a four year term loan from ICICI at an interest rate of 16% p.a. To understand the risk of equity in the biotech business, two proxy firms i.e. Bharat Biotech Ltd. And granular Biotech Ltd. has been identified. Their details are given below:

Company D. E. Ratio Tax Rate Equity beta Bharat Biotech Ltd. 2.5 35% 2.2 Granular Biotech Ltd. 4 32% 1.9

Based on the similarity of the assets it is considered prudent to assign 70% weight to B and 30% weight to G. Rf = 8% and market risk premium = 7%. Find out the NPV of the biotech projects?

Ans. DE

= 3:1,

Kd = 16% In order to compute NPV, we require Kc for biotech business. As given, Kc = WdKd (1 - t) + WeKe

Wd = 34

, We = 14


...................................................................... 14 ..............................................................

Kd = 16%, tax =30% ⇒We require Ke for computing Kc In order to do that, we would follow CAPM Ke = Rf + (Rm – Rf) β The sum provides Rf and (Rm - Rf), we need to compute Beta with the help of asset

beta concept. Deleveraging of Proxy Beta: For Bharat,

Βe = βA [ 1 + D (1 - t)]E

2.2 = βA [1 + 2.51

(1 - 35%)]

∴ βA = 0.84 For Granular,

Βe = βA [ 1 + D (1 - t)]E

1.9 = βA [1+ 41

(1 - 32%)]

∴ βA = 0.51 Average βA = (0.70 × 0.84) + (0.3 × 0.51) = 0.74 βe for X Ltd,

βe = 0.74 [ 1 + 3 (1 - 30%)]1

βe = 2.29 Ke = 8 + 7 × 2.29 = 24.03

∴ Kc = 34

× 16 × (1-30%) + 14

× 24.03 = 14.41

Year Cashflow PV @ 14.41% PV 1 50 0.874 43.70 2 60 0.764 45.84 3 40 0.668 26.72 4 60 0.584 35.04

Total ` 151.30 Cr ∴ NPV = ` 151.30 Cr - ` 170 Cr = (` 18.70 Cr)


...................................................................... 15 ..............................................................

D. CONVERTIBLE SECURITIES 10. The data given below relates to a convertible bond: Face value ` 250 Coupon rate 12% No. of shares per bond 20 Market price of share ` 12 Straight value of bond ` 235 Market price of convertible bond ` 265 Calculate: i. Stock value of bond. ii. The percentage of downside risk. iii. The conversion premium iv. The conversion parity price of the stock Ans. a. Stock Value of Bond = No. of shares × MPS = 20 × ` 12 = ` 240

b. % downside risk = Market price of bond - Investment value

Investment value × 100

= 265 - 235

235 × 100

= 12.77% c. Conversion Premium = Market Price of Bond - Conversion value/ Stock Value = 265 - 240 = ` 25

Conversion Premium (%) = 265 - 240

240 × 100 = 10.42%

d. Conversion Parity Price = Market price of bond ÷ No. of shares

= 26520

`

= ` 13.25


...................................................................... 16 ..............................................................

VALUATION OF BONDS

I. COMPUTING THE FAIR VALUE OF A BOND. The value or price of a bond is the present value of expected coupons and redemption amount discounted at investors required rate of return. V0 = C × PVA(r,n) + R.A. × PVIF(r,n)

1. Consider a three year corporate bond of Face value of ` 1000 and coupon rate =

12% p.a. payable annually. The bond is redeemable at par at the end of three years. The bond is presently selling at ` 957. If the required rate of return is 13%, find out the intrinsic value and give your investment advice.

Ans. V0 = 120 × PVA(13%,3) + 1000 × PVIF(13%,3) V0 = 120 ×2.3612 + 1000 × 0.693 = 976.344

Since the actual value of the bond is < intrinsic value, the bond is relatively undervalued and we suggest to buy the bond.

II. TYPES OF YIELD MEASURE

The return to a bond investor can be measured in terms of the following. a. CURRENT YIELD (C.Y.)

C.Y. = CouponPrice

× 100

b. YIELD TO MATURITY (Y.T.M) There are two methods for computing YTM:

⇒ Approximation Method/ Shortcut method:

YTM =

F - PC + n

F + P2

× 100

Where, C = Coupon F = Redemption amount P = Price N = No. of years i.e. maturity

In order to use above mentioned equation – • The coupon rate must be fixed • The principal repayment should be one shot

KHETAN EDUCATION VALUATION OF BONDS

...................................................................... 17 ..............................................................

If either of the conditions are not met or both are not met, we cannot use Short Cut Method. Rather we need to use ‘Trial and Error method’ or IRR method.

YTM is actually IRR of Bond. It considers coupon income, capital gain and interest on reinvested coupon.

V0 = C × PVA(r,n) + R.A. × PVIF(r,n)

Here, solving for YTM means solving for ‘r’ in the above mentioned equation. So, a YTM indicates that rate at which the present value of inflows from the bonds

equates the outflow (Price). 2. Consider the following data regarding the bonds issued by Neha Ltd. On March

15, 2003 to be redeemed on March 15, 2010. Face value of the bond ` 100 issued at a discount 10% Redeemable at a premium of 10% Interest payable Semi-annually 8% p.a. Current market price as on March 15, 2005 ` 95. Compute: • YTM • BEY • EAY

Ans. YTM =

C F - P + m n × m

F + P2

× 100 (m = frequency of coupon payment)

=

8 110 - 95 + 2 5 × 2

110 + 952

× 100

= 5.37%/semester BEY = 5.37% × 2 = 10.74% EAY = [(1 + 0.0537)2 - 1] × 100 = 11.03% p.a. III. COMPUTATION OF DURATION AND MODIFIED DURATION

• Duration of a bond measures the weighted average time which elapses before all the cashflows are received. Since the concept was first introduced by Macaulay, duration as defined above is also called Macaulay’s duration.

• Duration can also be defined as ‘holding period for which interest rate risk disappears’.

• The sensitivity of Bond price to change in interest rate is called Bond Price Volatility and it can be measured by “Modified Duration”.


...................................................................... 18 ..............................................................

2. The following data is available for a bond: Face Value ` 1000 Coupon rate 16% Years to maturity 6 Redemption value ` 1000 Yield to maturity 17% What is the current market price, duration and volatility of this bond? Calculate

the expected market price, if there is an increase in required yield by 75 basis points.

Ans. Current Market price = 160 × PVA (17%,6) + 1000 × PVIF (17%,6) = ` 964.10 a. DURATION OF THE BOND =

Year C.F. PV @ 17% PV Wi.xi 1 160 0.855 136.80 136.80 2 160 0.731 116.96 233.92 3 160 0.624 99.84 299.52 4 160 0.534 85.44 341.76 5 160 0.456 72.96 364.80 6 1160 0.390 452.40 2,714.40

Total ` 964.40 ` 4,091.20

• Duration = 4091.2 964.40

`

` = 4.24 years

• Volatility of the bond = Modified duration = D1 + YTM

= 4.241.17

= 3.63

This means if interest rate change by 100 bps or 1%, price of the bond would change by 3.63% in the opposite direction.

• The expected market price if yield increases by 75bps So, if interest increases by 75 bps or 0.75%, the price of the bond should change by 3.63 × 0.75 = 2.7225% New price = ` 964.40 - 2.7225% = ` 938.14

OR, New YTM = 17.0 + 0.75 =17.75% ∴ New Price = 160 × PVA (17.75%,6) + 1000 × PVIF (17.75%,6) = ` 938.40

IV. INTEREST RATE ANTICIPATION AND PORTFOLIO CHURNING Bond prices and interest rates have inverse relationship. If interest rates go up prices of

bonds go down and when rates go down, the prices go up. An added property says that, when rates go down, prices of all bonds go up , but they go up more for longer maturity


...................................................................... 19 ..............................................................

bonds in comparison to short maturity bonds. Similarly when rates go up, all bonds go down, but long maturity bonds loose value relatively more. This property is exploited by fund managers for portfolio churning.

3. The Investment portfolio of a bank is as follows:

Government Bond

Coupon Rate (%) Purchase rate (FV= ` 100/ bond)

Duration (years)

G.O.I. 2006 11.68 106.50 3.50 G.O.I. 2010 7.55 105.00 6.50 G.O.I. 2015 7.38 105.00 7.50 G.O.I. 2022 8.35 110.00 8.75 G.O.I. 2032 7.95 101.00 13.00

Face value of total investment is ` 5 crores in each bond. a. Calculate actual investment in Portfolio. b. What is a suitable action to churn out investment portfolio in the following

scenario? i. Case I : Interest rates are expected to lower by 25 basis points. ii. Case II : Interest rates are expected to rise by 75 basis points. Also calculate

the revised duration of investment portfolio in each scenario. Ans. a. Face value of each bond = ` 100

∴ No. of bonds in each category = 5 crore 100

`

` = 5 lakhs

Bonds Rate ` Investment(Wi) ` In lakhs

Di Wi*Di ` In lakhs

GOI 2006 106.50 532.5 [5L × ` 106.50]

3.50 1,863.75

GOI2010 105.00 525.0 6.50 3,412.50 GOI2015 105.00 525.0 7.50 3,937.50 GOI2022 110.00 550.0 8.75 4,812.50

GOI2032 101.00 505.0 13.00 6,565.00 Total 2,637.5 20,591.25

Actual investment in the portfolio = ` 2,637.5 L

b. Present Duration of the portfolio = 20,591.252,637.5

= 7.81 years


...................................................................... 20 ..............................................................

i. If interest rates lower by 25bps, the prices of all bonds will go up but they will go up more for longer maturity bonds. The fund manager can shift short term bonds to long term in order to maximise gains.

We can shift 2006 bonds to 2032 bonds and there are many more options available. However, we follow the procedure followed by PM. One such sample would be to shift GOI 2010 to GOI 2032.

Revised Dp = 20591.25 - 3412.5 + 525 × 132637.5

= 9.10 years

ii. If interest rates go up by 75 bps, the prices of the bonds will go down, but they will go down more for longer maturity bonds.

The fund manager can shift long term bonds to short term in order to avoid losses. One such sample would be to shift GOI 2032 to GOI 2010.

Revised Dp = 20591.25 - 6565 + 505 × 6.52637.5

= 6.56 years

V. DISCOUNTED SECURITIES

There are two ways of computing yields or returns: a. ADD ON METHOD: When a security is issued with a basic denomination i.e. face value which is used for

computing coupon amount is called Add on Method. E.g. A coupon paying bond or Debenture b. DISCOUNTED METHOD: When a security is issued much below its price and is redeemed at par, it is called as

Discounted Method. The difference between issue price and face value is the interest component.

E.g. A T-bill or ZCB. The discounted securities can be segregated into two categories on the basis of their

maturity. i. LESS THAN OR MAXIMUM ONE YEAR:

There are a few securities which are issued at discount and redeemed at par, but the maturity does not exceed 1 year. The yield of such securities:

Yield = F - PP

× 100 × 12n

× 365n

Where, F = face value, P = price, n = maturity of the security If the equation is used to compute yield of a T-bill, the computed yield would be a good substitute for Rf. A T-bill is a short term security issued by RBI. It is issued at discount and redeemed at par. We have 91 days T-bill, 182 days T-bill, 364 days T-bill and so on.


...................................................................... 21 ..............................................................

A Commercial Paper or CP is a security issued by firms and organisations to meet their working capital requirements. They are again issued at discount and redeemed at par with a maximum maturity of one year.

ii. MORE THAN ONE YEAR:

The securities which are issued at discount and redeemed at par but the maturity is greater than one year. They are called zero coupons bonds or Deep discount bonds.

Price/Vo = nFV

(1 + r)

Where, r = IRR of ZCB. If ZCB is issued by Government, then r = Rf. • The duration of a ZCB is always equal to maturity.

VI. TERM STRUCTURE OF INTEREST RATES A yield curve is a line that plots the interest rates of the bonds having equal credit

quality but different maturity dates. E.g. We can plot a yield curve with the help of zero coupon sovereign bonds with

different maturities. The yields are plotted on Y-axis and No. of years to maturity can be plotted on X-axis.

There are 4 types of yield curves: i. Upward rising/ Normal ii. Inverted / Downward Sloping iii. Flat yield curve iv. Humped yield curve

VII. SPOT AND FORWARD RATES i.e. BOOTSTRAPPING The spot rate is the current yield for a given term. Market spot rates for certain terms are

equal to yield to maturity of ZCB with those terms. Generally, the spot rates increases as the term increases. Using these spot rates, we can

compute implicit forward rates. The method is called ‘Boot Strapping’. E.g. If we want to invest for two years, we can either invest directly for 2 years at

r02(spot rate for 2 year investment) or we can invest at r01 and reinvest for one more year.

The implicit rate between year 1 and 2 should be such that we are indifferent to two options.

(1 + r02)2 = (1 + r01)1 (1 + f12)1 Similarly for a 3 year investment, (1 + r03)3 = (1 + r02)2 (1 + f23)1 (1 + r03)3 = (1 + r01)1 (1 + f13)2


...................................................................... 22 ..............................................................

4. The Following is the yield structure of AAA rated debenture: Period Yield (%)

3 months 8.5

6 months 9.25

1 year 10.50

2 years 11.25

3 years and above 12.00

Based on the expectation theory calculate the implicit one year forward rates in year 2 and 3. If the interest rate increases by 50 basis points, what will be the percentage change in the price of the bond having a maturity of 5 years ? Assume bond is fairly priced at the moment at ` 1000.

Ans. One year forward rate in year 2 = f12

One year forward rate in year 3 = f23

⇒ (1 + r02)2 = (1 + r01)1 (1 + f12)1 (1.1125)2 = (1.105)1 (1 + f12)1

(1 + f12)1 = 1.23761.105

f12 = 12% (1 + r03)3 = (1 + r02)2 (1 + f23)1 (1.12)3 = (1.1125)2 (1 + f23)1 F23 = 13.52% b. Since the bond is fairly priced at ` 1,000 it means coupon rate = YTM = 12% If interest ↑ by 50 bps New YTM = 12% + 0.50 = 12.5% V0 = 120 × PVA(12.5%, 5) + 1000 × PVIF(12.5%,5) = 982.2 ∴ PV of future cashflows for 5 years discounted @ 12.5% = 982.2

∴ % ∆ in price = 982.2 - 1,0001,000

×100 = -1.78%

5. From the following data for Government securities, calculate the forward rates:

Face value (`) Interest rate Maturity (year) Current Price (`) 1,00,000 0% 1 91,500 1,00,000 10% 2 98,500 1,00,000 10.5% 3 99,000

Ans. a. Since the one year maturity is like ZCB.

∴ Price = nFV

(1 + r)


...................................................................... 23 ..............................................................

91,500 = n1,00,000(1 + r)

91,500 = 11,00,000(1 + r)

∴ r = 9.29% i.e. r01

b. 98,500 = 110,000

(1 + r01) + 2

1,10,000(1 + r02)

98,500 = 110,000

(1.0929) + 2

1,10,000(1 + r02)

98,500 = 9149.968 + 2110,000

(1 + r02)

2(1 + r02) = 1.23111

⇒ 2(1 + r02) = (1+r01)1 (1+f12)1

1.2311 = (1.0929)1 (1 + f12)1 f12 = 12.65%

c. 99,000 = 110,500

(1 + r01)+ 2

10,500(1 + r02)

+ 31,10,500(1 + r03)

99,000 = 110,500

(1.0929) + 2

10,500(1 + r02)

+ 31,10,500(1 + r03)

(1 + r03)3 = 1,10,50080,863.58

= 1.366

(1 + r03)3 = (1 + r02)2 (1 + f23)1 1.366 = (1.2311)1 (1 + f23)1 (1 + f23) = 1.1096 f23 = 10.96% VIII. CALLABLE BONDS AND PUTTABLE BONDS CALLABLE BONDS: The bonds which can be redeemed before maturity but after the lock in period are called Callable Bonds. This option is available to an issuer and these bonds are issued in case of falling interest rates. The schedule of redemption and call prices are mentioned beforehand in the Bond Deed. PUTTABLE BONDS: The bonds which can be redeemed before maturity but after the lock in period is called Puttable Bonds. This option is available to investor and can be exercised in the rising interest rate scenario.


...................................................................... 24 ..............................................................

IX. BOND REFUNDING 6. M/s Transindia Ltd. Is contemplating calling ` 3 crores of 30 year, ` 1,000 bond

issued 5 years ago with a coupon interest rate of 14%. The bonds have a call price of ` 1,140 and had initially collected proceeds of ` 2.91 crores due to a discount of ` 30 per bond. The initial floating cost was ` 3,60,000. The company intends to sell ` 3 crores of 12% coupon rate, 25 years bonds to raise funds for retiring the old bonds. It proposes to sell the new bonds at their par value of ` 1,000. The estimated floatation cost is ` 4,00,000. The company is paying 40% tax and its after tax cost of debt is 8%. As the new bonds must be sold and their proceeds, then used to retire old bonds, the company expects a two months period of overlapping interest during which interest must be paid on both old and new bonds. What is the feasibility of refunding bonds?

Ans. Computation of initial outflow Post Tax Premium Outflow = ` 25,20,000 + Floatation cost on new bond = ` 4,00,000 + Post tax interest expense on old bonds

` 3 Crores × 14% × 212

× (1-40%) = ` 4,20,000

-Tax benefit on unamortized portion of flotation cost

On old bonds = 360,00030 years

× 25 year × 40% = (` 1,20,000)

-Tax benefit on unamortized portion of discount

On old bonds = Rs. 30 30,00030 years

× × 25 year × 40% = (` 3,00,000)

Net outflow = ` 29,20,000 Computation of incremental savings

Particulars Old Bonds New Bonds Post Tax Interest Expense ` 3 crore

× 14%(1 - 40%) = (` 25,20,000)

` 3 crore × 12%(1 - 40%)

= ` 21,60,000 Tax benefit on floatation cost 3,60,000

30 years`

× 40% = (` 4,800)

4,00,00025 years

`

× 40% = (` 6,400)

Tax benefit on Discount 30 30,00030 years×`

× 40% = (` 12,000)

-

25,03,300 21,53,600


...................................................................... 25 ..............................................................

Savings p.a. = 3,49,600 ⟶ P.V. = 3,49,600 × PVA (8%, 25) = 3,49,600 × 10.675 = 37,31,980 NPV = ` 37,31,980 – 29,20,000. = 8,11,980 We recommend to retire the old bonds. X. CONVEXITY 7. Consider a bond with a face value of ` 100 and coupon = 10% p.a. The bond has a

maturity of 5 years and is trading at par. Compute: a. YTM of the bond b. Duration and Modified duration of the bond c. New price using P.V. Method if

• Interest rate increase 1% • Interest rate decrease 1%

d. Show that the relationship between interest rate and bond price is inverse and not linear.

e. Compute Convexity f. Compute convexity effect g. Compute the bond price using convexity if

• Interest rate increase 1% • Interest rate decrease 1%

Ans. Given : a. Coupon = 10% N = 5 years Since the bond is trading at par ⟶ Price = F.V = 1,000 Also, Coupon = YTM = 10% b. COMPUTATION OF DURATION

Year C.F. PV @ 10% PV Wixi 1 10 0.909 9.09 9.09 2 10 0.826 8.26 16.52 3 10 0.751 7.51 22.53 4 10 0.683 6.83 27.32 5 110 0.621 68.31 341.55 100.00 417.01

wixiwi

∑∑

Where, wi = Weight / PV of C.F. xi = No. of years


...................................................................... 26 ..............................................................

Duration = 417.01100

= 4.17 years

Modified duration = D1 + YTM

= 4.171.10

= 3.79

This means if interest rates change by 1% i.e. 100 bps, the bond price should change by 3.79% in the opposite direction.

For e.g.: If interest increases by 1% New YTM = 10 + 1 = 11% New Price = 100 - 3.79% = 96.21 If interest decreases by 1% New YTM = 10 – 1 = 9% New Price = 100 + 3.79% = 103.79 c. Interest Rate increase by 1% New YTM = 10 + 1 = 11% V0 = 10 × PVA (11%, 5) + 100 × PVIF (11%,5)

= 10 × 3.696 + 100 × 0.593. = 96.26 Interest Rate decrease by 1% New YTM = 10 – 1 = 9% V0 = 10 × PVA (9%, 5) + 100 × PVIF (9%,5) = 103.89 This calculation confirms the fact that relationship is inverse in nature. d. When interest rate increases by 100 bps i.e. 1% P0 = ` 100 P1 = ` 96.31

% change = 100 - 96.31100

= 3.69%

If interest rate decreases by 100 bps P0 = ` 100 P1 = ` 103.89

% change = 103.89 - 100100

= 3.89%

Average change = 3.69% + 3.89%2

= 3.79% which is equal to modified duration

e. Convexity = 2P1 + P2 - 2 × P0

2 × P0 × (ΔYTM) = 2

96.31 + 103.89 - 2 × 1002 × 100 × (0.01)

= 10

f. Convexity effect = convexity × (△ YTM)2 × 100 = 10 × (0.01)2 × 100 = 0.10 % g. If Interest rate increases by 1%, Price of the bond should go down by 3.79% - 0.10% = 3.69% If Interest rate decreases by 1%, Price of the bond should go down by 3.79% + 0.10% = 3.89% So, if rate increase, new price = 100 - 3.69% = 96.31 If rate decrease, new price = 100 + 3.89% = 103.89

KHETAN EDUCATION FOREIGN EXCHANGE

...................................................................... 27 ..............................................................

FOREIGN EXCHANGE 1. BASICS OF FOREIGN EXCHANGE a. DIRECT V/S INDIRECT QUOTE: When the quotation is such that some units of home currency is quoted against one unit

of foreign currency, it is known as Direct quote E.g.: ` 65.00/ $ When the quotation is such that some units of foreign currency is quoted against one

unit of home currency, it is known as Indirect quote. E.g. $ 0.01538/` b. TWO WAY QUOTATIONS: `/$ = 65.00/70.00 Bid Ask We buy at higher price and sell at lower price. c. SYNTHETIC QUOTATIONS:

E.g. : $ /` = 0.0196 / 0.0198 (Bid)/ (Ask) Synthetic rate: ` / $

= 1 1Ask Bid

= 1 10.0198 0.0196

`/$ = 50.51/51.02 d. RULES OF CONVERSION: E.g.: ` / $ = 60.00/65.00 X Y Bid Ask

Rule 1 → If we buy ‘Y’ → Ask rate If we sell ‘Y’ → Bid rate Rule 2 → If we move from ‘Y’ → ‘X’ → Multiply If we move from ‘X’ → ‘Y’ → Divide


...................................................................... 28 ..............................................................

e. Cross Currency Rates E.g. 1.

Mechanics → `/£ = × / × `/£ = 60.00 × 2.1056 / 65.00 × 2.1086 `/£ = 126.336/137.059 E.g. 2. If the common currency is not diagonally placed we can compute synthetic as required and follow × & × as e.g. 1

`/$ 60.00/65.00 £/$ 0.4560/0.4860

Synthetic $ / £ = 1 10.4860 0.4560

(∵ $ not in diagonal position)

∴ `/£ = 1 160 × 65 × 0.4860 0.4560

i.e.

= 123.46 / 142.54 f. THREE POINT ARBITRAGE: REFER TO QUESTION 2. g. SPOT MARKETS AND FORWARD MARKETS

→ When the transactions are entered into and squared off at the same point of time, it is known as spot market rate.

→ When the transactions are entered into now and squared off sometime in future, they are known as forward market rates.

On the basis of quoted spot and forward rates, we can compute premiums and discounts on currencies.

E.g. : Spot Rate (S) ⇒ `/$ = 60.00 (X /Y) Forward rate (F) ⇒ `/$ = 65.00 Maturity (n)

∴ Annualized premium on y against x = F - S 12 × 100 × S n

∴ Annualized premium on x =

1 1 - 12F S × 100 × 1 nS

= S - F 12 × 100 × F n

`/ $ . 60.00 / 65.00

$ /£ 2.1056 / 2.1086


...................................................................... 29 ..............................................................

h. SWAP POINTS Rule: Low / High ⇒ Add e.g. 30/40 High / Low ⇒ Deduct e.g. 40/30 E.g. Spot rate `/$ = 65.00/67.00 3 month swap = 40/60 6 month swap = 110/3 3 month forward rate : Spot rate `/$ = 65.00/67.00 3 month forward rate = + 00.40/00.60 65.40/67.60 6 month forward rate : Spot rate `/$ = 65.00/67.00

6 month forward rate = - 1.10/0.0363.90/66.97

(`/ $)

i. T.T. MARGIN/RETAIL MARGIN/EXCHANGE MARGIN ASK ⇒ Add BID ⇒ Deduct NOTE : If T.T. Margin is given, then all the rates are interbank rates (whole sale rate) and needs to be adjusted to make them “Retail Rates”. 1. Bank A in India quotes `/$ = 45.10/ 46.00

(a) An Indian firm has imported goods from US and needs to pay $ 10,00,000. What amount of ` would be required?

(b) An American student has to pay ` 5,00,000 for an Indian course. What amount of $ would be required?

(c) An Indian company has surplus funds of ` 40,00,000 and wants to invest in US. It therefore needs to convert Rupee into $. What amount of $ will it get?

Ans. `/$ = 45.10 / 46.00 X/Y = (Bid) / (Ask) (a) $ 10,00,000 × ` 46.00 = ` 4,60,00,000 (b) ` 5,00,000 ÷ ` 45.10/$ = $ 11,086.47 (c) ` 40,00,000 ÷ ` 46.00/$ = $ 86,956.52 2. Consider the following quotations by 3 banks. A $/ £ 2.1050/ 2.1090 B €/ £ 1.8950/ 1.9010 C $/ € 1.0150/1.0180 Check for 3 way arbitrage and carry out the same using £ 10,000.


...................................................................... 30 ..............................................................

Ans. Case I : (i) We sell £ 10,000 to Bank A @ $ 2.1050/£ = £ 10,000 × $ 2.1050/£ = $ 21,050 (ii) We sell $ 21050 to bank C i.e. buy £ @ $ 1.0180/€ = $ 21,050 ÷ $ 1.0180/€ = € 20,677.80 (iii) We sell € 20677.80 to Bank B i.e. buy @ € 1.9010/£ = € 20,677.80 ÷ € 1.9010 /£ = £ 10,877.32 CONCLUSION : Arbitrage Profit = £ 10,877.32 - £ 10,000 = £ 877.32 Case II : (1) We sell $ 10,000 to Bank C i.e. buy € @ $ 1.0180/€ = $ 10,000 ÷ $ 1.0180/€ = € 9,823.1827 (2) Well sell € 9823.18 to Bank B i.e. buy € @ € 1.9010/£ = € 9,823.18 ÷ € 1.9010/ £ = £ 5,167.3764 (3) We sell £ 5,167.3764 to bank A @ $ 2.1050 / £ = £ 5,167.376 × $ 2.1050/£ = $ 10,877.3275 CONCLUSION : Arbitrage Profit = £ 10,877.32 - £ 10,000 = £ 877.32 Case III : (1) We sell € 10,000 to Bank B i.e. buy £ @ € 1.9010/£ = € 10,000 ÷ € 1.9010 /£ = £ 5,260.3892 (2) We sell £ 5,260.38 to Bank A @ $ 2.1050/£ = £ 5,260.38 × $ 2.1050 /£ = $ 11,073.09


...................................................................... 31 ..............................................................

(3) We sell $ 11073.09 to Bank C i.e. buy € @ $ 1.0180 / € = $ 11073.09 ÷ $ 1.0180 / € = € 10,877.29 CONCLUSION : Arbitrage Profit = £ 10,877.29 - £ 10,000 = £ 877.29 2. Currency Of Borrowing & Investment. 3. An Indian company based at Mumbai needs short term funds of ` 50 million for a

period of 3 months. The company collected the following information from its banker:

`/$ `/ £ Spot 48.50/55 74.05/10 3-month Interest Rates p.a. 45/50 85/90

3-month Interest Rates p.a. ` 9% $ 4% £ 6%

You are required to calculate the annualized effective cost of borrowing, (a) If the company borrows in USD and

• Covers the exchange rate risk through forward market • Keeps the position open and the spot rate after 3 months turns out to be `/$ = 48.90/95.

(b) If the company borrows in pounds and • Covers the exchange rate risk through forward market • Keeps the position open and spot rate after 3 months turns out to be `/£ = 74.75/ 80.

Ans. (a) (i) BORROWING IN INDIA i` = 9% p.a. Amount = ` 50m

∴ Effective outflow = ` 50m + ` 50m × 9% × 312

= ` 51.125m

→ Effective cost 51.125m - 50m 12= × 100 × 50m 3

= 9% p.a.


...................................................................... 32 ..............................................................

(ii) $ BORROWING Equivalent amount of $ which need to sold in the spot market to get ` 50m

= 50m 48.50/$`

`

= $1.03093m $ outflow on maturity = $ 1.03093m + $ 1.03093 × 4% × 3/12 = $ 1.04124m NOTE: This means we need to find out those no, of $’s which if sold today would yield

` 50 m. Case 1 : Forward cover We buy $ 1.04124m 3m forward @ ` 48.55 + 0.50 = ` 49.05/$ Outflow of ` On maturity = $ 1.04124m × ` 49.05/$ = ` 51.073m

Effective cost of borrowing $ = 51.073m - 50m 12 × 100 × = 8.58% p.a50m 3

Case 2 : No Cover → If he doesn’t buy any cover and waits till maturity Outflow on maturity = $ 1.04124m × ` 48.95/$ = ` 50.969m

∴ Effective cost 50.969m - 50m 12= × 100 × = 7.752% p.a50m 3

(iii) £ BORROWING

Equivalent £’s to be borrowed = 50m £0.6752m 74.05/£

=`

`

Outflow of £ on maturity = £ 0.6752m + £ 0.6752m × 6% × 312

= £ 0.6853m Case 1 : Forward cover @ ` 74.10 + 0.90 = ` 75.00/£ Outflow of ` On maturity = £ 0.6853m × ` 75.00/£ = ` 51.3975m

Effective cost = 51.3975m - 50m 12 × 100 × = 11.18% p.a.50m 3

Case 2 : No Cover @ ` 74.80/ £


...................................................................... 33 ..............................................................

Outflow on maturity = £ 0.6853m × ` 74.80/£ = ` 51.26m

∴ Effective cost = 51.26m - 50m 12 × 100 × 50m 3

= 10.08 % p.a.

→ Though $ borrowing with no cover is the best alternative, yet the final decision would rest on the risk appetite of the organization.

3. EXCHANGE RATE DETERMINATION

Interest Rate Parity Theory Purchasing Power Parity Theory International Fisher Effect

INTEREST RATE PARITY THEORY : 4. Based on six month forward rate of ` 42.60, the annualised forward discount on $

happens to be 10%. Find out the spot rate. Ans. Given: 6 month forward rate = ` 42.60/$ Annualized forward discount on $ = 10 % p.a. Spot rate = ?

Annualized forward discount on $ F - S 12 × 100 × S 6

=

-10 42.60 - S 12= × 100 × S 6

Spot rate ⇒ `/$ = 44.8421 5. The following table shows interest rates for the United States dollar and French

francs. The spot exchange rate is 7.05 Francs per Dollars. Complete the missing entries:

3 Months 6 Months 1 Year Dollar Interest rate (Annually compounded)

11.5% 12.25% ?

Franc interest rate (Annually compounded)

19.5% ? 20%

Forward franc per dollar ? ? 7.5200 Forward discount per franc percent per year

? -6.3%

Ans. (A) Spot FFr 7.05/$ iA =19.5 % p.a. (annualized effective) iB = 11.5 % p.a. (annualized effective)


...................................................................... 34 ..............................................................

As per IRP

FS

1/4(1 + iA)= 1/4(1 + iB)

F7.05

1/ 4(1.195)1/ 4(1.115)

=

F7.05

1.0455= 1.0276

3 month forward FFr/$ = 7.17

(B) Premium on FFr S - F 12= × 100 × F n

Premium 7.05 - 7.17 12= × 100 × = -6.69%7.17 3

∴ Discount per Franc per annum = 6.69% (C) For 6 months Spot 7.05 FFr/$ iB = 12.25% p.a. → Premium on FFr = -6.30% p.a

→ Premium on FFr = S - F 12 × 100 × F n

-6.30 = 7.05 - F 12 100 F 6

× ×

6 month forward = FFr 7.28/$ (D) As per IRP

FS

= n(1 + iA)n(1 + iB)

7.287.05

= 1/2(1 + FFr)

1/2(1 + 0.1225)

1.0940 = (1.iFFr)1/2 1 + iFFr = (1.09405) 2 1+ iFFr = 1.1969 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 19.69 % p.a.


...................................................................... 35 ..............................................................

(E) For 1 year Spot FFr 7.05/$ iA = 20% 1 year forward FFr 7.5200/$ As per IRP

FS

n(1.iA)= n(1.B)

7.527.05

1(1.20)= 1(1 + iB)

i$ = 12.5% p.a. NOTE : As per the data provided, the sum looks like Annual compounding. *But as per the ICAI solution we get answer only if we go by quarterly / half yearly

compounding. COVERED INTEREST ARBITRAGE : 6. Given Spot rate ` 42.0/ $ 3 month forward rate ` 42.7/ $ Three month interest rate p.a. ` 12% $ 7% Check for IRP and carry out covered Interest arbitrage using $1,000 or ` 42,000. Ans. As per IRP,

FS

1 + niA= 1 + niB

IA = i` IB = i$

42.742

31 + × iA12= 31 + × 0.07

12

Should be iA = 13.78 % p.a. Actual iA = 12.00% p.a. On comparing Should be ‘iA’ and Actual ‘iA’, we find that Actual ‘iA’ is < than Should

be ‘iA’ which means i` is relatively undervalued and vice-versa i$ is relatively overvalued.

Hence, borrowing should take place in ` and investment should take place in $ to earn an arbitrage profit. Since, this situation is suitable to an Indian, we will earn an arbitrage profit if an Indian borrows in ` And invests in $.


...................................................................... 36 ..............................................................

(1) Borrow ` 42,000 @ 12% for 3 month

Outflow = ` 42,000 + ` 342,000 × × 12%

12

= ` 43,260 (2) Convert ` 42,000 @ ` 42.00/$ on the spot

42,000= 42.00/$

`

`

= $ 1,000 (3) Invest $ 1,000 @ 7% p.a. for 3 months

Inflow = $ 1,000 + $ 31,000 × × 7%12

= $ 1,017.5 (4) Convert $ 1,017.50 @ ` 42.7/$ = $ 1,017.50 × ` 42.7 / $ = ` 43,447.25 ∴ Arbitrage profit will be = ` 43,447.25 – ` 43,260 = ` 187.25 FORWARD COVER VS. MONEY MARKET COVER : 7. An Indian firm has $ 1,00,000 payable and £ 2,00,000 receivable 3 months from

now. Given spot `/$ 43.50/43.80 3 month swap points 20/30 Spot $/ £ 2.1045/ 2.1065 3 month swap points 110/90 3 month interest rates p.a. ` 10%/11% £ 7%/8% $ 4%/5% How should the firm hedge the payable and receivable – Forward Cover or Money

market Cover? Ans. Payable $ 100,000 Forward cover @ ` 43.80/$ + 0.30 ` 44.10 /$ Outflow of ` on maturity = $ 100,000 × ` 44.10/$ = ` 44,10,000


...................................................................... 37 ..............................................................

Money market cover ⟹ [Invest – buy – borrow] (1) Invest the present value of $ 1,00,000 @ 4% for 3 month

PV = $ 1,00,000 × 131 + 0.04 ×

12

= $ 99,009.90

(2) Buy $ 99,009.90 on the spot @ ` 43.80 /$ = $ 99,009.90 × ` 43.80 /$ = ` 43,36,633.62 (3) Borrow ` 43,36,633.62 @ 11% for 3 months

Outflow = ` 43, 36,633.62 + ` 343,33,633.62 × 11%

12

= ` 44, 55,891.04 → Forward cover is better since outflow is less. → Receivable £ 200,000 Since `/£ is not given directly, we have to compute cross currency rates Spot `/$ = 43.50 /43.80 3month forward `/$ = 43.50/43.80 + 0.20/0.30 43.70/44.10 Spot $ /£ = 2.1045 / 2.1065 3 month forward $ /£ = 2.1045/2.1065 -0.0110/-0.0090 2.0935/2.0975 Cross currency Rates ⇒ Spot `/£ = 43.50 × 2.1045/43.80 × 2.1065 = 91.546 /92.265 3 month forward `/£ = 43.70 × 2.0935/44.10 × 2.0975 = 91.486/92.500 (a) Forward cover Inflow = £ 200,000 × ` 91.486/£ = ` 1,82,97,200


...................................................................... 38 ..............................................................

(b) Money Market Cover ⇒ [Borrow – sell – invest] (i) Borrow the present valve of £ 2,00,000 @ 8% for 3 month

PV = £ 2,00,000 × 131 + 0.08 ×

12

= £ 1,96,078.43 (ii) Sell £ 1,96,078.43 on the spot @ ` 91.546/£ = £ 1,96,078.43 × ` 91.546/£ = ` 1,79,50,195.95 (iii) Invest ` 1,79,50,195.95 @ 10% for 3 months

= ` 1,79,50,195.95 + ` 31,79,50,195.95 × 10% ×

12

= ` 1,83,98,950.85 → Here, money market is better since inflow is more. SHORT TERM BORROWING & INVESTMENT 8. A US fund brought $ 1,00,000 into India at the beginning of the year, when the

exchange rate was ` 40.0/$. He invested the corresponding ` proceeds in the Nifty which was trading at 4,000. At the end of the year Nifty trades at 4,800. Find out the return to the US investor in dollar terms if

Case (i) Rupee appreciates by 8%. Case (ii) Rupee depreciates by 8%. Ans. Method 1 : RFI = [(1 + RFA)(1 + RFC) − 1] × 100

RFA = 4800 - 40004000

× 100 = 20%

Case 1 : if ` ↑ 8 % RFI = [(1.20) (1.08) -1] × 100 = 29.6 % Case 2 : If ` ↓ 8 % RFI = [(1.20) (0.92) -1] × 100 = 10.40 % Method 2 : Case 1 : (1) He converts $ 1,00,000 @ ` 40.00/$ on the spot = $ 100,000 × ` 40.0/$ = ` 40,00,000


...................................................................... 39 ..............................................................

(2) He invests ` 40,00,000 @ ` 4,000 in nifty No. of Nifty units = 1000 (3) He sells 1000 units @ ` 4,800 after 1 year Inflow = ` 48,00,000 (4) If `↑ 8 %

Synthetic rate `/$ = 140

= $ 0.025/`

Expected spot = $ 0.0250/` + 8 % = $ 0.0270/` Inflow of $ = $ 0.0270/` × ` 48,00,000 = $ 1,29,600

∴ Return in $ = 1,29,600 - 1,00,0001,00,000

× 100 = 29.60 %

Case 2 : Expected spot = $ 0.0250/` - 8% = $ 0.0230/` Inflow of $ = ` 48,00,000 × $ 0.0230 /` = $ 1,10,400 ∴ Return in $ = 10.40 % 9. An Indian firm needs funds for 1 year. It has the following 3 choices.

(a) Rupee borrowing - interest rate - 10% (b) Dollar borrowing - interest rate - 6% (c) Yen borrowing - interest rate - 20%

Assuming IRP holds good, find out the effective cost of borrowing on a covered basis in each case.

Ans. i` = 10 % i$ = 6 % i¥ = 20 % (1) Effective cost of ` Borrowing = 10 % p.a. (2) $ Borrowing $ Cost = 6 %

Premium on $ = 1.10 - 1.061.06

× 100 = 3.77 %

i.e. F - S (1 + iA) - (1 + iB) = S (1 + iB)


...................................................................... 40 ..............................................................

Effective cost of $ borrowing for an Indian

= [(1.06) (1.0377) - 1] × 100 = 10 % (3) ¥ Borrowing ¥ Cost = 20 %

Premium on ¥ = 1.10 - 1.201.20

× 100

= - 8.33 % Effective cost of ¥ borrowing for an Indian = [(1.20) (0.9169) - 1] × 100 = 10 % 10. Suppose in the previous sum there is a processing upfront fee of 2% in case of `

borrowing, also Indian Govt. Has announced a withholding tax of 15% in case of borrowing from outside India. Which currency should the firm borrow?

Ans. i` = 10 % i$ = 6 % i¥ = 20 % (i) ` Borrowing ` Interest Cost = 10 % Suppose we borrow ` 100 Processing fee = 2 % Effective inflow = ` 98 Interest on outflow = ` 100 × 10 % = ` 10

Effective cost = (10 + 100) - 98

98

× 100 = 12.24 %

(ii) $ Borrowing

$ cost with withholding tax = 685

× 100 = 7.06 %

Premium on $ = 1.10 - 1.061.06

× 100 = 3.77 %

Effective cost = [(1.0706) (1.0377) - 1] × 100 = 11.096 % (iii) ¥ Borrowing

¥ cost with withholding tax = 2085

× 100 = 23.53 %

Premium on ¥ = 1.10 - 1.201.20

× 100 = - 8.33 %


...................................................................... 41 ..............................................................

Effective cost = [(1.2353) (1-8.33%) - 1] × 100 = 13.24 % Therefore, $ borrowing is the best option. LONG TERM INVESTMENT 11. ABC Limited is considering a project in US, which will involve an initial

investment of US $ 1,10,00, 000. The project will have 5 years of life. Current spot exchange rates are ` 48.00 per US $. The risk free rate of interest in US is 8% and the same in India is 12%. Cash inflow from the project is as follows:

Year Cash Inflow 1 US$20, 00,000 2 US$ 25, 00,000 3 US$ 30, 00,000 4 US$ 40, 00,000 5 US$ 50, 00,000 Calculate the NPV of the project using FOREIGN CURRENCY APPROACH.

Required rate of return on this project is 14%. Ans. → Domestic currency Approach :

(All values in Lakhs) Year Cash

flow ($) E.R. Cash

flow (`)

Pv@14% PV. (`)

0 (110) ` 48.00/$ (5,280) 1 (5,280) 1 20 ` 49.78/$ 995.6 0.877 873.714 2 25 ` 51.62/$ 1,290.5 0.769 992.39 3 30 ` 53.53 /$ 1,605.9 0.675 1,083.98 4 40 ` 55.52 /$ 2,220.8 0.592 1,314.89 5 50 ` 57.57 /$ 2,878.5 0.519 1,493.94 NPV = 478.34

As per IRP,

F1 = 48.00 × 1.121.08

= 49.78

F2 = 49.78 × 1.121.08

= 51.62

F3 = 51.62 × 1.121.08

= 53.53

F4 = 53.53 × 1.121.08

= 55.52

F5 = 55.52 × 1.121.08

= 57.57


...................................................................... 42 ..............................................................

Rp = 1.14 - 11.12

× 100 = 1.79 %

ROR in ($) = [(1.08) (1.0179) - 1] i.e. 14% - 12% = 2%i.e. 8% + 2% = 10%

= 9.93 % → Foreign Currency Approach :

(All values in Lakhs) Year Cash flow PV @ 9.93% PV

$ 110 1.00 ($ 110) 1 $ 20 0.910 $ 18.200 2 $ 25 0.827 $ 20.675 3 $ 30 0.753 $ 22.590 4 $ 40 0.685 $ 27.400 5 $ 50 0.623 $ 31.150 NPV = $ 10.015

(A) PURCHASING POWER PARITY THEORY (PPP)

• Absolute Form of PPP • Relative Form of PPP

→ Relative Form of PPP 12. Spot rate 1 year ago ` 40.0/ $ Spot rate now ` 43.0/ $ Inflation last year (India) 8% Inflation last year (US) 3%

Compute: (a) Nominal appreciation of $ (b) REER (c) Real appreciation of $ (d) Nominal appreciation of Rupee. (e) Real appreciation of Rupee.

Ans. -1 0 +1 ` 40.0/$ ` 41.01/$ ` 43.0/$

Here, inflation rate is iA =iB = $

`


...................................................................... 43 ..............................................................

(1) Nominal appreciation of $ = 43.0/$ - 40.0/$ 40.0/$

` `

` × 10 = 7.5 %

(2) REER (Real Effective Exchange Rate) = ` 43.0/$ × 1 + 0.031 + 0.08

= ` 41.01/$

(3) Real appreciation of $ = 41.01 - 40.040.0

× 100 = 2.53 %

If we want forward rate, we take 1 + iA1 + iB

Similarly if we want backward rate, we should take 1 + iB1 + iA

(4) Nominal appreciation of ` = 40.0 - 43.043.0

× 100 = -6.98 %

(5) Real appreciation of ` = 40.0 - 41.0141.01

× 100 = -2.46 %

If there are 2 countries like India and US and i` = 8% and i$ = 3% then the country having lower inflation rate should trade at forward premium. PPP goes one step ahead to quantify the premium. $ should trade at a premium of (8% - 3%) = 5% approximately

and exactly at a premium of 1.08 - 1.03

1.03

= 4.85 % in order to avoid arbitrage.

If $ appreciates by 4.85 % it is actually trading at par. If it appreciates by more than 4.85 %, there is a real appreciation in $ and if $ appreciates by less than 4.85 % it has actually gone down in real terms.

SHORT TERM CASH MANAGEMENT OF AN MNC 14. Suppose you are a treasurer of XYZ plc. in the UK. XYZ have two overseas

subsidiaries, one based in Amsterdam and one in Switzerland. The Dutch subsidiary has surplus Euros in the amount of 7,25,000 which it does not need for the next three months but which will be needed at the end of that period (91 days). The Swiss subsidiary has a surplus of Swiss Francs in the Amount of 9,98,077 that, again, it will need on day 91. The XYZ plc. in UK has a net balance of £75,000 that is not needed for the foreseeable future. Given the rates below, what is the advantage of swapping Euros and Swiss Francs into Sterling?

Spot Rate (€) £ 0.6858/0.6869 91 day Pts. 0.0037/0.0040 Spot Rate (£) CHF 2.3295/2.3326 91 day Pts. 0.0242/0.0228 Interest rates for the Deposits 91 day Interest Rate % p.a:


...................................................................... 44 ..............................................................

£ € CHF 0 – 100,000 1 ¼ 0 100,001 – 500,000 2 1 ½ 1/4 500,001 – 1,000,000 4 2 1/2 Over 1,000,000 5.375 3 1

Ans. Dutch Subsidiary - Surplus € 7, 25,000 Swiss Subsidiary - Surplus CHF 9, 98,077 U.K. H.O. - Surplus £ 75,000 Spot rates: £ / € = 0.6858 / 0.6869 91 days £ / € = 0.6858 / 0.6869 + 0.0037 / 0.0040

0.6895 / 0.6909 Spot CHF/ £ = 2.3295 / 2.3326 91 days CHF / £ 2.3295 / 2.3326 -0.0242/-0.0228 2.3053/2.3098 IF THE SURPLUS IS INVESTED LOCALLY: (i) Dutch Surplus = € 7,25,000 This amount would be invested @2% p.a. for 91 days

∴ € Inflow = € 7,25,000 + € 7, 25,000 × 2% × 91365

= € 7,28,615.07 £ Equivalent = € 7,28,615.07 × £ 0.6895/€ = £ 5,02,380.09 (ii) Swiss Surplus = CHF 9,98,077 This amount would be invested @ 0.5% p.a. for 91 days

∴ CHF inflow = 9,98,077 + 9,98,077 × 0.5% × 91365

= CHF 9,99,321.18

∴ £ Equivalent = CHF 9,99,321.18CHF 2.3098/£

= £ 4,32,644.03

(iii) UK Surplus = £ 75,000 This amount would be invested @ 1 % p.a. for 91 days


...................................................................... 45 ..............................................................

(iv) ∴ Inflow = £ 75,000 + £ 75,000 × 1% × 91365

= £ 75,186.99

∴ Total inflow = £ 5,02,380.09 + £ 4,32,644.03 + £ 75,186.99 = £ 10,10,211.08 (a) If Euros and Swiss Francs are swapped into Sterling (i) Dutch Swiss = € 7,25,000 This amount would be converted into £ on the spot ∴ £ inflow = € 7,25,000 × £ 0.6858/€ = £ 4, 97,205 (ii) Swiss Surplus = CHF 9,98,077 This amount would be converted into £ on the spot

∴ £ inflow = CHF 998,077CHF 2.3326/£

= £ 427,881.76

(iii) UK Surplus = £ 75,000 ∴ Total £ Surplus = 10, 00,086.76 This would be invested @ 5.375% p.a. for 91 days

∴ Inflow = £10,00,086.76 + £10,00,086.76 × 5.375% × 91365

= £ 10,13,488.61 We recommend the firm to swap € and CHF into £. # FATE OF FORWARD CONTRACTS Whenever any forward contract is entered, normally it meets any of the following three fates (A) Delivery under the contract (B) Cancellation of the contract (C) Extension of the contract Further above of fates of forward contract can further classified into following sub categories (A) DELIVERY UNDER THE CONTRACT

(i) Delivery on Due Date (ii) Early Delivery (iii) Late Delivery

(B) CANCELLATION OF THE CONTRACT

(i) Cancellation on Due Date (ii) Early Cancellation (iii) Late Cancellation


...................................................................... 46 ..............................................................

(C) EXTENSION OF THE CONTRACT (i) Extension on Due Date (ii) Early Extension (iii) Late Extension

15. A bank enters into a forward purchase TT covering an export bill for Swiss Francs

1, 00,000 at ` 32.4000 due 25th April and covered itself for same delivery in the local interbank market at ` 32.4200. However, on 25th March, exporter sought for cancellation of the contract as the tenor of the bill is changed. In Singapore market, Swiss Francs were quoted against dollars as under:

Spot USD/Sw. Fcs. 1.5076/1.5120 One month forward 1.5150/1.5160 Two months forward 1.5250/1.5270 Three months forward 1.5415/1.5445 And in the interbank market US dollars were quoted as under: Spot USD/` 49.4302/0.4455 Spot /April 0.4100/0.4200 Spot/May 0.4300/0.4400 Spot/June 0.4500/0.4600 Calculate the cancellation charges, payable by the customer if exchange margin

required by the bank is 0.10% on buying and selling. Ans. The customer sold forward on Swiss Francs 100,000 @ ` 32.4000 He opted for cancellation on 25th March i.e. a month before. For that he needs to enter

into 1 month forward buy contract. Since `/Swiss Francs is not quotes directly, we need to compute the same.

Spot `/ $ = 49.4302 / 49.4455 1m Forward 49.4302 / 49.4455 + 0.4100 / 0.4200 49.8401 / 49.8655 Margin @ 0.10% - 0.10% / + 0.10% 1m Forward ` /$ 49.7904/ 49.9154 1m Forward Swiss Francs/$ = 1.5150 / 1.5160

1m Forward $/ Swiss Francs = 1 11.5160 1.5150

1m Forward `/Swiss Francs = 1 149.7904 × 49.9154 × 1.5160 1.5150

= 32.8433 / 32.9475 Therefore, Cash flow = (` 32.4000 / Sw. Fcs. - ` 32.9475/ Sw. Fcs.)

× Sw. Fcs. 100,000 = (` 54,750)


...................................................................... 47 ..............................................................

16. On 30th June 2009 when a forward contract matured for execution you are asked by an importer customer to extend the validity of the forward sale contract for US$ 10000 for a further period of three months.

Contracted rate US$ 1 = ` 41.87 The US Dollar quoted on 30.6.2009 Spot ` 40.4800/40.4900 Premium July 0.1100/0.1300 Premium August 0.2300/0.2500 Premium September 0.3500/0.3750 Calculate the cost for your customer in respect of the extension of the forward

contract. Rupee values to be rounded off to the nearest rupee. Margin 0.80% for buying rate Margin 0.25% for selling rate Ans. (1) As given, the imported customer entered into forward buy contract @ ` 41.87/$ However, on the day of maturity, he opted for extension. Extension would involve

cancellation of existing contract at the rate computed below:

Spot Rate for cancellation = ` 40.4800/$ ( Customer will sell $ on cancellation)

- TT margin @ 0.80 % = (0.3238) 40.1562/$`

`

Cash flow on cancellation = (` 40.1562 - ` 41.87) × $ 10,000 = ` (17,138) (2) He also buys a new contract 3 month forward at the rate computed below:

Basic Rate ` 40.4900/ $ (Ask Rate ∵ $ is bought customer) + 0.3750 ` 40.8650 / $ + TT margin @ 0.25 % ` 0.1022 ` 40.9672 / $

(3) Final outflow on maturity

Purchase cost ($ 10,000 × 40.9672/$ 4,09,672

+ Extension charges 17,138 4,26,810

` `

`

`

17. An importer booked a forward contract with his bank on 10th April for USD

2,00,000 due on 10th June @ ` 64.4000. The bank covered its position in the market at ` 64.2800.

The exchange rates for dollar in the interbank market on 10th June and 20th June were:


...................................................................... 48 ..............................................................

10th June 20th June Spot USD 1 = ` 63.8000/8200 ` 63.6800/7200

Spot/June ` 63.9200/9500 ` 63.8000/8500 July ` 64.0500/0900 ` 63.9300/9900

August ` 64.3000/3500 ` 64.1800/2500 September ` 64.6000/6600 ` 64.4800/5600

Exchange Margin 0.10% and interest on outlay of funds @ 12%. The importer requested on 20th June for extension of contract with due date on 10th August.

Rates rounded to 4 decimals in multiples of 0.0025. On 10th June, Bank Swaps by selling spot and buying one month forward. Calculate:

(i) Cancellation rate (ii) Amount payable on $ 2,00,000 (iii) Swap loss (iv) Interest on outlay of funds, if any (v) New contract rate (vi) Total Cost

Ans. (i) The forward can be cancelled by reversing on the spot @ ` 63.68 Rate applicable to the customer = ` 63.68 - 0.10% = ` 63.6163/$ ≈ ` 63.6175/$

(ii) Amount payable on $ 200,000 = (` 63.6163 - ` 64.4000/$) × $ 200,000 = ` 156,740 (iii) Swap Loss = (` 63.80/$ - ` 63.95/$) × $200,000 = ` 30,000(loss) (iv) The bank buys $ 200,000 from inter -bank market @ ` 64.2800/$ as contracted but sells

the same on the spot @ ` 63.8000/$ due to non-performance of the customer. The bank would charge/ pay interest on loss/gain Cashflow = (` 63.80/$ - ` 64.28/$) × $ 200,000 = (` 96000) Interest on outlay of funds = ` 96000 × 12% × 10/365 = ` 315.62 (v) New contracted rate = ` 64.25000 + 0.10% = ` 64.314/$ ~ ` 64.3150/$ (vi) Total cost to the customer Cancellation charges = ` 156,740.00 + Swap Loss = ` 30,000.00 + Interest = ` 315.62

` 1,87,055.62


...................................................................... 49 ..............................................................

18. On 1 October 2015 Mr. X an exporter enters into a forward contract with a BNP Bank to sell US$ 1,00,000 on 31 December 2015 at ` 65.40/$. However, due to the request of the importer, Mr. X received amount on 28 November 2015. Mr. X requested the bank the take delivery of the remittance on 30 November 2015 i.e. before due date. The inter-banking rates on 28 November 2015 was as follows:

Spot ` 65.22/65.27 One Month Premium 10/15 If bank agrees to take early delivery then what will be net inflow to Mr. X

assuming that the prevailing prime lending rate is 18%. Ans. Bank will buy from customer at the agreed rate of ` 65.40/$. In addition to the same if

bank will charge/pay swap difference and interest on outlay funds. (a) Swap Difference ` Bank Sells at Spot Rate on 28 November 2015 65.22 Bank Buys at Forward Rate of 31 December 2015 (65.27 + 0.15) 65.42 Swap Loss per US$ 00.20 Swap loss for US$ 1, 00,000 = 20,000.00 (b) Interest on Outlay Funds On 28th November Bank sells at 65.22 It buys from customer at 65.40 Outlay of Funds per US$ 00.18 Interest on Outlay fund for US$ 1,00,000 for 31 days 275.00

31US$ 1,00,000 × 0.18 × × 18%365

(c) Charges for early delivery Swap loss 20,000.00 Interest on Outlay fund for US$ 1,00,000 for 31 days 275.00 20,275.00 (d) Net Inflow to Mr. X Amount received on sale (` 65.40 × $ 1,00,000) 65,40,000.00 Less: Charges for early delivery payable to bank (20,275.00) 65,19,725.00

PREPARATION OF A NOSTRO A/C AND EXCHANGE POSITION 19. An Indian bank has its Nostro Account with bank of America. From the following

details of the transactions of a particular day. Prepare the Nostro Account. Opening balance $20,000 (overdrawn) Purchased TT $ 50,000 Issued DD on New York $ 20,000 TT remittance outward $ 25,000


...................................................................... 50 ..............................................................

Purchased bill of exchange, maturity 1 month $75,000 Forward sales $ 75,000 Export bills, purchased earlier, realized $ 45,000 What steps the Indian bank will take if it wants to maintain a credit balance of

$20,000 in its Nostro Account? Ans. Nostro A/C of Indian Bank in the books of Bank of America

Particulars Amount $

Particulars Amount $

Balance brought forward 20,000 TT purchase 50,000 TT remittance 25,000 Export bills realized 45,000 *TT sale (adjustment

entry)

30,000

Balance carried forward 20,000 95,000 95,000

We are required to maintain credit balance of $ 20,000, so the entry “TT sale” is passed to adjust the credit balance.

#Continue the same sum and prepare exchange position with a credit balance of $ 10,000 Exchange position of Indian Bank in the books of BOA.

Particulars (Credit) $

(Debit) $

Balance B/F TT purchase Issued DD on New York TT remittance Purchase of bill of Exchange Forward sales TT sale* Balance C/F

Total

Purchase 10,000 50,000

- -

75,000 - -

15,000 1,50,000

Sales - -

20,000 25,000

- 75,000 30,000

- 1,50,000

6. TYPES OF EXPOSURE (A) Transaction Exposure

• Internal Hedging techniques


...................................................................... 51 ..............................................................

LEADING AND LAGGING 20. NP & Co. has imported goods for US $ 700,000. The amount is payable after 3

months. The company has also exported goods for US $4,50,000 and this amount is receivable in two months. For receivable amount a forward contract is already taken ` 48.90. The market rates for ` and Dollar are as under:

Spot ` 88.50/70 Two months 25/ 30 points Three months 40/ 45 points The company wants to cover the risk and it has two options as under: To cover the

payables in the forward market and To lag the receivables by one months and cover the risk only for the net amount. No interest for delaying the receivables is earned. Evaluate both the alternatives if the cost of the Rupee funds is 12%. Which option is preferable?

Ans. (i) Cover the payables in forward market The firm can book a forward cover @ ` 48.70 + 0.45 ` 49.15/$ for 3 month maturity. Also the firm receives the receivables @ ` 48.90 /$ at the end of second month. ` Inflow @ the end of 2nd month= $ 450,000 × ` 48.90/$ = ` 2,20,05,000 → This amount is invested @ 12% p.a for 1month

= ` 2,20,05,000 + 1 2,20,05,000 × 12% × 12

`

= ` 2,22,25,050 → ` Outflow on account of payable = $ 7,00,000 × ` 49.15/$ = ` 3,44,05,000 ∴ Net outflow = ` (3,44,05,000 – 2,22,25,050) = ` 1,21,79,950 (ii) Buy Forward cover on the net amount of $ 250,000 In this case, the firm can lag it’s receivables by one month and buy a forward cover on

the net amount of $ 250000 only @ ` 49.15/ $ Also for doing that it needs to cancel, the existing forward on receivables. → Cancellation : Cancellation would involve entering into reverse contract @ ` 48.70/$ + 0.30 ` 49.00/$ Cash flow on cancellation = (` 48.90 /$ - ` 49.00 |$) × $ 4,50,000 = (` 45,000) This amount becomes due to be paid at the end of 2nd month


...................................................................... 52 ..............................................................

` outflow on net payables = $ 2,50,000 × ` 49.15/$ = `1,22,87,500

+ Cancellation charges = ` 145,000 + 45,000 × 12% × 12

= 45,450

∴ Total outflow = (1,22,87,500 + 45,450) = ` 1,23,32,950 CONCLUSION : We suggest forward cover on the whole amount of $700,000 NETTING : 21. An Indian company has $ 1,00,000 payable and $ 30,000 receivable from a UK

company. The following rates are quoted `/£ = 74.60/10 $/£ = 1.40/1.45 Calculate the benefit of netting for the Indian and UK Company. Ans. `/£ = 74.60 | 75.10 $/£ = 1.40 | 1.45

∴ Synthetic £ | $ = 1 1

1.45 1.40

∴ `/$ = 74.60 × 1 175.10 ×

1.45 1.40

= 51.45 /53.64 → From Indian Co. point of view Without netting Payable = $ 1,00,000 × ` 53.64/$ = ` 53,64,000 Receivable = $ 30,000 × ` 51.45/ $ = ` 15,43,500 ∴ Net payable = ` 53,64,000 - ` 15,43,500 = ` 38,20,500 With Netting Net payable = $ 70,000 × ` 53.64 / $ = ` 37,54,800 Benefit of netting = ` 38,20,500 - ` 37,54,800 = ` 65,700


...................................................................... 53 ..............................................................

→ From UK Co. point of view: Without Netting:

Receivable $ 1,00,000= $ 1.45/£

= £ 68,965.52

Payable $ 30,000= $ 1.40/£

= £ 21,428.57 ∴ Net receivable = £ 68,965.52 - £ 21,428.57 = £ 47,536.95 With Netting

Net receivable $ 70,000= $ 1.45/£

= £ 48,275.86 Benefit of netting = £ 48,275.86 - £ 47,536.95 = £ 738.91 • EXTERNAL HEDGING TECHNIQUE

o Forward Cover o Money Market Cover o Futures Cover o Options Cover

A. Accounting Exposure / Translation Exposure B. Economic Exposure / Operating Exposure


...................................................................... 54 ..............................................................

INTERNATIONAL FINANCIAL MANAGEMENT

INTERNATIONAL CAPITAL BUDGETING: Multinational capital budgeting stands for long term investment like a project, but outside the country. There are various factors and complexities involved in a foreign project in comparison to domestic project. There would be various factors affecting the cashflows of a foreign project. Some of them are: 1. The cashflows of a foreign project would be affected tremendously due to exchange

fluctuation. 2. There is a huge amount of political risk involved with respect to foreign cashflows. 3. There could be restrictions involved with respect to repatriation of cashflows. 4. The macro and micro economic factors of foreign environment is completely different

in comparison to domestic atmosphere. 5. The discounting factor used to discount the cashflows of foreign project needs to be

calibrated accordingly, reflecting the risk involved and expectation of both locals and foreign investors.

In order to appraise a foreign project, we can use ‘Net present Value Method’ i.e. NPV Where, NPV = PV of cash inflows - PV of cash outflows • The discounting of cashflows would take place at an appropriate rate of return as

required and provided in the question. One of the very important adjustment, that the question would provide real cash flows (without inflation) and nominal discounting factor (with inflation).

Ideally, a real cashflow must be discounted with a real rate and nominal cash flow must be discounted at a nominal rate.

• Also, if the exchange rate for the future is not provided, the question must provide information on either interest rates or inflation rates. Accordingly, PPP or IRP can be used to compute future spot value.

1. Opus Technologies Ltd., an Indian IT company is planning to make an investment

through a wholly owned subsidiary in a software project in China with a shelf life of two years. The inflation in China is estimated as 8 percent. Operating cash flows are received at the year-end. For the project an initial investment of Chinese Yuan (CN¥) 30,00,000 will be in land. The land will be sold after the completion of project at estimated value of CN¥ 35,00,000. The project also requires an office complex at cost of CN¥ 15,00,000 payable at the beginning of project. The complex will be depreciated on straight-line basis over two years to a zero salvage value. This complex is expected to fetch CN¥ 5,00,000 at the end of project. The company

KHETAN EDUCATION INTERNATIONAL FINANCIAL MANAGEMENT

...................................................................... 55 ..............................................................

is planning to raise the required funds through GDR issue in Mauritius. Each GDR will have 5 common equity shares of the company as underlying security, which are currently trading at ` 200 per share (Face Value = ` 10) in the domestic market. The company has currently paid the dividend of 25%, which is expected to grow at 10% p.a. The total issue cost is estimated to be 1 percent of issue size. The annual sales is expected to be 10,000 units at the rate of CN¥ 500 per unit. The price of unit is expected to rise at the rate of inflation. Variable operating costs are 40 percent of sales. Fixed operating costs will be CN¥ 22, 00,000 per year and expected to rise at the rate of inflation. The tax rate applicable in China for income and capital gain is 25 percent and as per GOI Policy no further tax shall be payable in India. The current spot rate of CN¥ 1 is ` 9.50. The nominal interest rate in India and China is 12% and 10% respectively and the international parity conditions hold.

You are required to: (a) Identify expected future cash flows in China and determine NPV of the

project in CN¥. (b) Determine whether Opus Technologies should go for the project or not

assuming that there neither there is restriction on the transfer of funds from China to India nor any charges/taxes payable on the transfer of funds.

Ans. WN: Computation of Post tax salvage value of fixed assets: a. Land Cost @ t= 0 = CN ¥ 30,00,000 Salvage @ t= 2 = CN ¥ 35,00,000 Capital gain = CN ¥ 5,00,000 Tax @25% = CN ¥ 5,00,000 × 25% = CN ¥ 1,25,000 ∴ Post tax salvage value = CN ¥ 35,00,000 – CN ¥ 1,25,000 = CN ¥ 33,75,000 b. Office Cost = CN ¥ 15,00,000 Book Value on maturity = (Since 100% depreciation) Salvage Value on maturity = CN ¥ 5,00,000 ∴ Capital Gain = CN ¥ 5,00,000 Tax = CN ¥ 5,00,000 × 25% = CN ¥ 1,25,000 ∴ Post tax salvage value = CN ¥ 3,75,000 In order to discount the cashflows, we require the rate of return WN: Computation of ROR/Ke

Ke = 1

0

D 2.5 (1.10) + g = P - f 200 - 1%

`

` + 0.10 = 11.39%


...................................................................... 56 ..............................................................

A. Preparations of Cashflows: Life = 2years Particulars 1 2

No. of units 10,000 10,000 Price/unit (CN ¥) i.e. add inflation 540 (500 + 8%) 583.20 (540 + 8%) Annual sales (CN ¥) CN ¥ 54,00,000 CN ¥ 5,832,000 - Variable op. cost(40%) (CN ¥) (21,60,000) (23,32,800) - Fixed op. cost (CN ¥) (23,76,000)

(22L + 8%) (25,66,080)

(23.76L + 8%) EBDIT (CN ¥) 8,64,000 9,33,120 - Depreciation (CN ¥) 7,50,000 7,50,000 EBIT (CN ¥) 1,14,000 1,83,120 Tax @ 25% (28,500) (45,780) NOPAT (CN ¥) 85,500 1,37,340 + Depreciation (CN ¥) 7,50,000 7,50,000 Operating Cashflow (CN ¥) 8,35,500 8,87,340

⇒ Check for working capital if given in question. W.C. shall be recovered entirely at the

end of the life of the project. - Initial investment - Operating cashflows - Terminal cashflow

0 1 2 Initial cash outflow (CN ¥) 45,00,000(35L+10L) Operating cashflow (CN ¥) 8,35,500 8,87,340 Terminal cashflow: a. Land 33,75,000 b. Office 3,75,000 Net cashflow(CN ¥) 45,00,000 8,35,500 46,37,340

Computation of NPV in CN ¥

Year Cashflow(CN ¥) PV @ 11.39% PV (CN ¥) 0 (45,00,000) 1.000 (45,00,000) 1 8,35,500 0.898 7,50,279.00 2 46,37,340 0.806 37,37,696.04

Total -12,024.96

KHETAN EDUCATION INTERNATIONAL FINANCIAL MANAGEMENT

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B. Computation of NPV from Opus point of view: Particulars 0 1 2

Cashflow CN ¥ (45,00,000) 8,35,500 46,37,340 Exchange rate (`/CN ¥)

9.50 (Spot rate) 9.5 × 1.121.10

= 9.67 2

29.5 × (1.12)

(1.10) = 9.85

Cashflow ` 45,00,000 × 9.5 = 4,27,50,000

8,35,500 × 9.67 = 80,79,285

46,37,340 × 9.85 = 4,56,77,799

PV @12% 1.000 0.893 0.797 Present value(CN ¥) (4,27,50,000) 72,14,801.51 3,64,05,205.80

∴ NPV = ` 8,70,007.313 Thus, we can see that the project is not viable from Chinese shareholders point of view

but it is viable in Indian Rupees.


...................................................................... 58 ..............................................................

DERIVATIVES – FUTURES & OPTIONS

I. DIFFERENCE BETWEEN FUTURES AND FORWARDS · FORWARDS: A forward is a promise to buy or sell any asset on a particular date or maturity at a pre

specified rate. A forward is an OTC product and banks play a major market maker for the same. The

most commonly asset traded in forward market are currencies. It provides good opportunity to exporters and importers for hedging their exposures like a payable or receivable of foreign currency.

For E.g. An importer imported goods worth $ 5,00,000 on 1st Jan, maturity 31st March. He is afraid of $ going up and hence he buys Forward @ ` 70.00/$.

On maturity he pays (` 70.00/$ × $ 5,00,000) and receives $ 5,00,000. The spot on maturity is ` 72.00/$ but the hedger could get at ` 70.00 only due to Forward Agreement.

· FUTURES: Futures are a sophisticated form of Forwards traded on Exchange. The contracts are

standard in terms of quality, quantity and maturity. They are marked to market on daily basis.

II. MARK TO MARKET AND TYPE OF MARGINS :

In order to avoid counter party default, the Exchanges stipulate margins which is nothing but a form of guarantee deposit. There are 3 types of margins: • Initial Margin • Maintenance Margin • Variation Margin

1. A trader has gone long on 5 Brent crude futures for December settlement at $26.32

per barrel. The minimum contract size for Brent futures contract is 1,00,000 per barrel. The initial margin is $50,000 and the maintenance margin is $ 30,000. The futures close at the following prices on the next ten trading days.

Day 1 $26.19 Day 6 $ 26.21 Day 2 $ 26.30 Day 7 $ 25.98 Day 3 $ 26.45 Day 8 $ 25.87 Day 4 $ 26.48 Day 9 $ 25.90 Day 5 $ 26.34 Day 10 $ 25.95

KHETAN EDUCATION DERIVATIVES – FUTURES & OPTIONS

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The trader will take out the profit out of the margin whenever he gets the opportunity to do so. You are required to prepare the margin account showing all the cash flows. Find the profit/ loss for the trader after 10 trading days.

Ans. Position: Long

Profit = ($ 2,35,000 + $ 65,000 + $ 15,000) - ($ 2,50,000 + $ 1,35,000 + $ 1,15,000) = ($1,85,000) Loss III. FAIR PRICING OF FUTURES USING COST OF CARRY MODEL TF = Theoretical Futures Price TF Applicable = Spot + Interest Saved + Storage cost saved – Convenience yield foregone TF Applicable to stocks = Spot + Interest saved – Dividend yield foregone → TF = S + I – DY [When the rates are compounded once in a

year i.e. p.a. or Annualized]

→ TF = n

nS(1 + i)(1 + dy)

[When the rates are compounded more than

once in a year] → TF = S × e(i – dy) × n [When the rates are compounded continuously

or daily] IV. STOCK FUTURE ARBITRAGE 2. The stock of Reliance Energy trades 1200 while 3-month Future on the stock trade

at ` 1290. The risk free rate of interest is 10% p.a. the stock is expected to provide a dividend yield of 1%. The lot size is 250 shares.

Day Price +/- Margin Closing bal Profit withdrawal

Margin call

0 $ 26.32 - $ 2,50,000 - - 1 $ 26.19 $ (65,000) $ 1,85,000 - - 2 $ 26.30 $ 55,000 $ 2,40,000 - 3 $ 26.45 $ 75,000 $ 3,15,000 $ 65,000 - 4 $ 26.48 $ 15,000 $ 2,65,000* $ 15,000 5 $ 26.34 ($ 70,000) $ 1,80,000 -

6 $ 26.21 ($ 65,000) $ 1,15,000 - $ 1,35,000 7 $ 25.98 ($ 1,15,000) $ 1,35,000# - $ 1,15,000 8 $ 25.87 ($ 55,000) $ 1,95,000 - - 9 $ 25.90 $ 15,000 $ 2,10,000 - - 10 $ 25.95 $ 25,000 $ 2,35,000 - -


...................................................................... 60 ..............................................................

i. Find out the Theoretical Futures price ii. Check for arbitrage and process of arbitrage if the price on maturity turns

out to be • Case I – 1000 • Case II – 1500 • What are the limitations of stock future arbitrage?

Ans. Spot = 1200, AF = 1290, Rf = 10% p.a, DY = 1% Lot Size = 250 Shares, n = 3months

A) TF = 1200 + 1200 x 10% × 312

– 1200 x 1%

= 1200 + 30 – 12 TF = 1218 B) AF = 1290, TF = 1218

Since, AF > TF, Futures are relatively overvalued & spot is undervalued. We sell futures at AF = 1290, & Buy stock @ Spot = 1200.

On Maturity :

Particulars S=F = 1000 S=F = 1500 1) Profit on Futures

= (1290 – 1000) × 250 = 72,500

= (1290 - 1500) × 250 = (52,500)

2) Profit on Stock

= (1000 – 1200) × 250 = (50,000)

= (1500 – 1200) × 250 = 75,000

3) Interest Expense = 1200 × 250 × 10% ×

312

= (7,500)

= 1200 × 250 × 10% × 3

12

= (7,500) 4) Dividend Gain = 1200 × 250 × 1%

= 3,000 = 1200 × 250 × 1% = 3,000

Net Profit on maturity ` 18,000 ` 18,000

= (AF - TF) × lot = (1290 – 1218) × 250 = ` 18,000 NOTE : A) Cost of Carry Model assume no transaction costs like margins, brokerage, commission

or taxes. B) When we open a ‘sell position’, we mean ‘Short Sell’ i.e. Sell first & Buy later. → For futures there is no inflow in case of short sell but, there would be cash inflow

in case of short sell in cash market & position on be carried forward for any maturity.

→ Practically, a short position in Cash Market must be closed intraday.


...................................................................... 61 ..............................................................

V. HEDGING OF FOREIGN CURRENCIES USING FUTURES There are various tools of hedging: a. No cover b. Forward cover c. Money market cover d. Futures cover e. Options cover The hedger has an exposure of payable or receivable and hence he is afraid of currency price going up or down. In order to hedge himself he can use futures where by the cash profits of futures market would reduce or increase the overall cost / in flows in the spot market. 3. On 10/ 07, an Indian firm knows that it has $ 590,000 payables on the 10/ 09. The

spot rate is ` 47.64/ $ and the 2-month forward rate is ` 47.85/ $. Dollar futures of maturity on the same date are trading at ` 47.89/$ (contract size is $ 1,00,000). On the 10/ 09, the spot rate happens to be ` 47.95/ $ and the futures quote at ` 48.07/ $. Compare no cover, forward cover and futures cover with respect to Rupee outflow on the 10/ 09?

Ans. Payable = $ 5,90,000 2 months forward ₹/$ = 47.85 $ Futures @ t = 0 : ₹ 47.89/$ $ Future @ t = maturity : ₹ 48.07/$ E (S) i.e. Expected spot = ₹ 47.95/$ Lot size = $ 1,00,000 1. No cover Outflow or maturity = $ 5,90,000 × ₹ 47.95/$ = ₹ 2,82,90,500 2. Forward cover Outflow on maturity = ₹ 5,90,000 × ₹ 47.85 /$ = ₹ 2,82,31,500 3. Futures cover

The Indian firm has $ payable and hence, it is afraid of $ going up. Ideally it should buy $ futures and since $ futures are available, it buys them at the rate of ₹ 47.89/$ at t = 0 and squares them off at a price ₹ 48.07/$ on the day of maturity.

• Since futures are traded in lots, we need to convert the exposure into lots.

No. of lots = $ 5,90,000$ 1,00,000

= 5.90 lots


...................................................................... 62 ..............................................................

Case 1: Round –Off the lots to 6 lots a. Profit on squaring off in futures market = (₹ 48.07/$ - ₹ 47.89/$) × 6 lots × $ 1,00,000 = ₹ 0.18/$ × $ 6,00,000 = ₹ 1,08,000 b. Cost of purchase in the Spot market on maturity = $ 5,90,000 × ₹ 47.95/$ = ₹ 2,82,90,500 c. Net outflow on maturity = ₹ 2,82,90, 500 - ₹ 1,08,000 = ₹ 2,81,82,500 We recommend futures cover as outflow/cost is the least. Case 2 : → Hedge for 5 lots in futures market and hedge for 0.90 lots in is Forward market. a. Profit on squaring off in futures market = (₹ 48.07/$ - ₹ 47.89/$) × 5 lots × $ 1,00,000 = ₹ 90,000 b. Cost of purchase in Forward market = $ 90,000 × ₹ 47.85/$ = ₹ 43,06,500 c. Cost of purchase in E(S) Market = ₹ 47.95/$ × $ 5,00,000 = ₹ 2,39,75,000 d. Net outflow = ₹ 43,06,500 + ₹ 2,39,75,000 - ₹ 90,000 = ₹ 2, 81, 91,500 We recommend futures cover to the Indian firm.

VI. HEDGING OF A STOCK PORTFOLIO USING FUTURES 4. Consider a fund manager managing a corpus of 250 crore comprised as follows:

Equity=150 crore with a beta of 3 Debt = 80 crore with a beta of 0.8 Cash and cash equivalents = 20 crore and beta = 0. Nifty futures trade at a multiple of 50. a. How many Nifty Future Contracts should be bought or sold for complete

hedging? Prove the same. b. How many Nifty future contracts should be bought/sold to achieve a target

beta of 0.5? Prove the same.

Ans. No. of Lots = Vp( T - p)F × lot × future price

β ββ

Vp = ` 250 Cr

βp = 150 × 3 + 80 × 0.8 + 20 × 0150 + 80 + 20

= 2.056 (∴ 𝛽𝛽𝛽𝛽 = 1)


...................................................................... 63 ..............................................................

Since we are using Market Futures hence, the Beta = 1, as beta of market is always = 1, lot = 50.

A) Future price = ` 5000

∴ No of lots = 250 Cr [0 - 2.056]1 × 50 × 5000

∴ No of lots = 250 Cr [0 - 2.056]2,50,000

= - 20,560 lots. Suppose Nifty ↓ 10%

Cash Futures Loss ⇒ = 250cr × 2.056 × 10% = ` 51.40cr

Opening price (Short) = 5000 Closing price = 5000 – 10% = 4500 Profit on futures = (5000 - 4500) × 20560 × 50 = ` 51.40cr

Hence, no profit & no loss.

B) No. of lots = 250 Cr [0.5 - 2.056]1 × 50 × 5000

= - 15,560 lots Suppose market goes ↑ 3%

Cash Futures Gain = 250cr × 2.056 × 3% = `15.42cr

Opening price (Short) = 5000 Closing price = 5,000 + 3% = 5150 Loss = (5000 - 5,150) × 15,560 × 50 = - ` 11.67 Cr (Loss)

Net gain = ` 15.42Cr – ` 11.67Cr = 3.75cr

% Gain on portfolio = 3.75250

× 100 = 1.5%

Beta = % in portfolio 1.5 = % in market 3∆∆

= 0.50

VII. HEDGE RATIO 5. A company is long on 10 MT of copper @ ` 474/ kg (spot) and intends to remain so

for the ensuing quarter. The standard deviation of the changes of its spot and futures price is 4% and 6% respectively, having coefficient of correlation of 0.75. What is its hedge ratio? What is the amount of copper futures it should short to achieve a perfect hedge?


...................................................................... 64 ..............................................................

Ans. 1 MT = 1,000 kgs

Hedge ratio = SFS × F

σγ

σ = 0.75 × 4%

6% = 0.5

Long position in Cash market = ₹ 474/kg × 10 MT × 1,000 kgs = ₹ 47,40,000 Short position on Copper futures = ₹ 47,40,000 × 0.5 → Hedge ratio = ₹ 23,70,000

OPTIONS 1. BASIC STRATEGIES OF OPTIONS

Buy Call → C+ Call Holder Payoff of a Call Holder = Max (S-E,0) Payoff of call holder will always be “Zero” or Positive.

Sell Call→ C− Call writer - Payoff of call Writer will always be “Zero” or negative.

Buy Put → P+ Put Holder Payoff of a Put Holder = Max (E-S,0) Payoff of Put holder will always be “Zero” or Positive.

Sell Put→ 𝑃𝑃− Put writer - Payoff of Put Writer will always be “Zero” or negative.

NOTES: A. Call will be always exercised above strike price Put will be always exercised below strike price B. There are 2 types of options traded in the market: a. European Option The options that can be exercised only on the day of maturity are called

European option. b. American option Options which can be exercised any day before the maturity are called

American option. C. In case of call, In case of put If S > E → in the money If S > E →out the money If S = E → at the money If S = E →at the money If S < E → out the money If S < E → in the money


...................................................................... 65 ..............................................................

6. Consider a 2-month call option on the stock of Tata Motors at a strike price of 800 trading at a premium of ` 25. Show profit profile for the call holder and call writer.

Ans. For call holder C+ @ 800; premium = (25) Spot E/L Pay off [Max = (S-E,0)] Initial prem. Net profit 750 L 0 (25) (25) 775 L 0 (25) (25) 800 L 0 (25) (25) 825 E (825 – 800) = 25 (25) 0 850 E (850 – 800) = 50 (25) 25 875 E (875 – 800) = 75 (25) 50 900 E (900 – 800) = 100 (25) 75

For call writer C− @ 800; premium = 25 Spot E/L payoff initial Net profit 750 L 0 25 25 775 L 0 25 25 800 L 0 25 25 825 E (25) 25 (0) 850 E (50) 25 (25) 875 E (75) 25 (50) 900 E (100) 25 (75)

7. Consider a 3 month put option on the stock of HUL at a strike price of 200 trading

at a premium of ` 10. Show the profit profile for the put holder and put writer. Ans. For put holder → Put will always be exercised below strike price

P+ @ 200; premium = (10) Spot E/L Payoff = Max (E-S,O) Initial

premium Net profit

150 E 200 – 150 = 50 (10) 40 160 E 200-160 = 40 (10) 30 170 E 200 – 170 = 30 (10) 20 180 E 200 – 180 = 20 (10) 10 190 E 200 – 190 = 10 (10) 0 200 L 0 (10) (10) 210 L 0 (10) (10) 220 L 0 (10) (10) 230 L 0 (10) (10)


...................................................................... 66 ..............................................................

For put writer → the put writer has to buy option at 150 P−@200; premium = 10 Spot E/L Payoff initial Net profit 150 E (50) 10 (40) 160 E (40) 10 (30) 170 E (30) 10 (20) 180 E (20) 10 (10) 190 E (10) 10 0 200 L 0 10 10 210 L 0 10 10 220 L 0 10 10 230 L 0 10 10

VIII. HEDGING OF FOREIGN CURRENCIES USING OPTIONS

8. An Indian firm has $ 2 lakhs payable 3 months from now. The spot rate is

presently ` 43.05/ $. The three-month forward rate is ` 43.60/ $. The following three month European options are traded. Options Strike price/ exercise price Premium Put 42.50 50 paisa Call 43.50 40 paisa The treasury department has the following forecast to share with you. Spot rate after 3- month Probability 41.50 0.2 43.00 0.4 44.50 0.1 46.00 0.3 Evaluate No cover, Forward cover, Call cover, Put cover, and Range forward.

Ans. 1. No cover E(s) = [(41.50) × 0.2] + (43.0 × 0.4) + (44.5 × 0.1) + (46.0 × 0.3) = ₹ 43.75/$ Outflow on maturity = $ 2 lakhs × ₹ 43.75/$ = ₹ 87, 50,000 2. Forward cover Outflow on maturity = $ 2 lakhs × ₹ 43.60/$ = ₹ 87, 20,000 3. Call cover (Since the quotes given in the question are direct, we will buy Call) (i.e. C+) C+ @ E = ₹ 43.50/$ Premium = ₹ 0.40/$ Net outflow = $ 2 lakhs × ₹ 0.40/$ = ₹ 80,000


...................................................................... 67 ..............................................................

Spot ₹/$

(𝐂𝐂+)𝐄𝐄/𝐋𝐋 (S-E,0)

Payoff ₹/$

Rate of buy ₹/$

Net rates ₹/$

Purchase cost ₹

Premium ₹

Total ₹

41.50 L 0 (41.5) (41.5) (83 Lakhs) (0.8 lakhs) (83.8L) 43.00 L 0 (43.0) (43.0) (86 Lakhs) (0.8 lakhs) (86.8L) 44.50 E 1.00 (44.5) (43.5) (87 Lakhs) (0.8 lakhs) (87.8L) 46.00 E 2.50 (46.0) (43.5) (87 Lakhs) (0.8 lakhs) (87.8L)

Total (₹) Probability (P) Px ₹ (83.80 L) 0.20 (16.76 L) (86.80 L) 0.40 (34.72 L) (87.00 L) 0.10 (8.78 L) (87.80 L) 0.30 (26.34 L)

Total (86.60 L) Expected value of outflow = ₹ 86.60 L Put cover P− @ E = ₹ 42.50/$ Premium = ₹ 0.50/$ Net inflow = $ 2 lakhs x ₹ 0.50/$ = ₹ 1,00,000

Spot ₹/$

𝐄𝐄/𝐋𝐋 (E-S,0) Payoff ₹/$

Rate of buy ₹/$

Net rates ₹/$

Purchase cost ₹

Premium ₹

Net ₹

P Px ₹

41.50 E (1.0) (41.50) (42.50) (85 Lakhs) 1.0 L (84L) 0.2 (16.8L) 43.00 L 0 (43.00) (43.00) (86 Lakhs) 1.0 L (85L) 0.4 (34 L) 44.50 L 0 (44.50) (44.50) (89 Lakhs) 1.0 L (88L) 0.1 (8.8L) 46.00 L 0 (46.00) (46.00) (92 Lakhs) 1.0 L (91L) 0.3 (27.3L)

(86.9L)

Expected value of outflow = ₹ 86.90 L 4. Range forward: Call cover C+ @ E = ₹ 43.50/$ ; Premium = ₹ 0.40/$ , Outflow = ₹ 80,000 Put cover P− @ E = ₹ 42.50/$; Premium = ₹ 0.50/$ , inflow = ₹ 1,00,000

(In range forward, the importer buys one call (𝐶𝐶+) and sells one put (𝑃𝑃−) in order (to reduce the premium outflow.) Net premium = ₹ 20,000 (inflow) If he goes for range forward, in this example, his cost will not go beyond ₹ 43.50/$ but it cannot come below ₹ 42.50/$


...................................................................... 68 ..............................................................

Spot

₹/$

(S-E,0) Payoff (𝐂𝐂+)

₹/$

(𝐄𝐄 − 𝐒𝐒,𝐎𝐎)𝐏𝐏𝐏𝐏𝐏𝐏𝐏𝐏𝐏𝐏𝐏𝐏 (𝐏𝐏−

₹/$

Rate of buy

₹/$

Net

₹/$

Purchase cost ₹

In Lakhs

Premium ₹

Net ₹

P Px ₹

41.50 0 (1.0) (41.50) (42.50) (85) 0.2 L (84.8L) 0.2 (16.96L) 43.00 0 0 (43.00) (43.00) (86) 0.2 L (85.8L) 0.4 (34.32L) 44.50 1.0 0 (44.50) (43.05) (87) 0.2 L (86.8L) 0.1 (8.68L) 46.00 2.5 0 (46.00) (43.05) (87) 0.2 L (86.8L) 0.3 (26.04L)

86.0 L

Expected value of outflow = ₹ 86 L 9. A Ltd. of UK has imported some chemicals worth of USD 3,64,897 from one of the

US supplier. The amount is payable in six- months time. The relevant spot and forward rates are: Spot Rate USD 1.5617 - 1.56736 months’ Forward rate USD 1.545 - 1.5609 The Borrowing rate in UK & US are 7% and 6% respectively and the deposit rates are 5.5% and 4.5% respectively. Currency options are available under which one option contract is for GBP 12,500. The options premium for GBP at a strike price of USD 1.70/ GBP is USD 0.037 (call option) and USD 0.096 (Put option For 6 months period)

The company has three choices: 1. Forward cover 2. Money Market Cover 3. Currency Options

Ans. Spot $/£ = 1.5617/ 1.5673 6 m Forward $/£ = 1.545/ 1.5609 1 $ = 4.5%/ 6 % 1 £ = 5.5%/ 7 % Call @ E = $ 1.70/£ ; premium = $ 0.037/£ Put @ E = $ 1.70/£ ; premium = $ 0.096/£

(i) Forward cover

Outflow on maturity = $ 3,64,897$ 1.545 / £

= £ 2,36,179.29

Sell £ @ $ 1.545/£ i.e. Bid rate (ii) Option cover NOTE : (1) The UK firm has $ payable and hence it is afraid of $ going up. It should ideally

buy $ options (C+), but since $ options are not available rather £ options (P+) are available and hence instead of C+ (Right to Buy $) we can go for P+ (i.e. Right to sell £).

(2) In order use £ options, we need to convert $ exposure into £, (Using Options rate).


...................................................................... 69 ..............................................................

1. £ Equivalent = $ 3,64,897$ 1.70 / £

= £ 2,14,645.29

2. No of lots = £ 2,14,645.29£ 12,500 per lot

= 17.17 lots

3. Amount of $ exposure to be hedged through option = [17 lots × £ 12,500 per lot] × $ 1.70/£ = $ 3,61,250 Amount of $ to be hedged through forward = $ 3,64,897 - $ 3,61,250 = $ 3,647 5. Computation of total outflow

Outflow of £ under option cover i.e. $ 3,61,250$ 1.70 / £

= £ 2,12,500

Outflow of £ under forward cover = $ 3,647$ 1.545 / £

= £ 2,360.52

6mth Forward rate → Premium cost under options = $ 0.096/£ × £ 2,12,500 = $ 20,400

Outflow of £ for premium = $ 20,400$ 1.5617 / £

= £ 13,062.69

∴ Total outflow = £ 2,12,500 + £ 2,360.52 + £ 13,062.69 = £ 2,27,923.21

(iii) Money market cover Invest – Buy – Borrow 1. Invest the present values of $ 3,64,897 @ 4.5 % for 6 months

= $ 3,64,897 × 161 + 0.045 ×

12

= $ 3,56,867.48

2. Buy $ 3,56,867.48 on the spot @ $ 1.5617/£

= $ 3,56,867.48$ 1.5617 / £

= £ 2,28,512.19

3. Borrow £ 2,28,512.19 @ 7% for 6 months

= £ 2,28,512.19 + (£ 2,28,512.19 × 7 % × 612

) = £ 2,36,510.12

# We recommend Options Cover as the outflow is least.


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IX. VALUATION OF OPTIONS Valuation of option stands for computing the Should be value of a Call premium and Put premium. A. Binomial model 1. Risk Neutral Method 2. Portfolio Replicating Approach B. Put Call Parity Model C. Black Scholes Model Binomial Model Risk Neutral Approach /Risk Neutralization Approach 10. Consider a one-year Call option on a stock at Strike price of 480. The stock

presently trades at 500. At the end of the year the stock price can go up by 20% or come down by 10%. Risk free interest rate is 6% p.a. Find out the price of the call using Risk Neutralization method.

Ans. US = 500 + 20 % =600 DS = 500 – 10 % = 450 Cu = [600 – 480, 0]= 120 Cd = [450 – 480, 0]= 0

P = R - du - d

Where, P = probability of market going ↑

u = upgoing factor d = down going factor us = stock price if market goes ↑ ds = stock price if market goes ↓ Cu = call payoff is market – goes ↑ Cd = call payoff if market goes ↓ C0 = call value @ t =0

R = 1 + rt/(1 + r)t or ert

u = 1 + Upgoing % or uss

d = 1 – Down going % or dss

u = 1 + 20% = 1.20 d = 1 – 10 % = 0.90


...................................................................... 71 ..............................................................

R = 1 + 126% × 12

= 1.06

→ P = R - d 1.06 - 0.9 = µ - d 1.20 - 0.9

= 0.53

1 – P = 0.47

C0 = P × Cu + (1 - p) × CdR

C0 = (0.53 × 120) + (0.47) (0)1.06

= 60.0

*The price of an asset (i.e. options) is the PV(present value) of expected future cashflows.

11. Mr. Dayal is interested in purchasing equity shares of ABC Ltd. Which are

currently selling at ` 600 each. He expects that price of share may go up to `780 or may go down to ` 480 in three months. The chances of occurring such variations are 60% and 40 % respectively. A call option on the shares of ABC Ltd can be exercised at the end of three months with a strike price of ` 630. a) What combination of share and option should Mr. Dayal select if he wants a

perfect hedge? b) What should be the value of option today (the risk free rate is 10% p.a.)? c) What is the Expected rate of return on the option?

Ans. a. Cu - Cd 150 - 0 = Delta = = US - DS 780 - 480

∆ = 0.5

A delta of 0.5 means a combination of 0.5 share for every 1 call would provide a perfect hedge.

b. On maturity (Substitute value of ∆ in following equation)

If market goes up, payoff = ∆ US – Cu = 0.5 × 780 – 150 = 240 If market goes down, payoff = ∆ DS – Cd = 0.5 × 480 – 0 = 240

At t = 0, ∆S – C = PV of 240

0.5 × 600 – C = 240 × 131 + 0.10 ×

12

C = 65.85 If we buy a Call, this premium is paid. c. Expected value on maturity = (0.6 × 150) + (0.4 × 0) = 90

Expected return = 90 - 65.8565.85

× 100 = 36.67 %


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X. PUT CALL PARITY MODEL As per put-call parity, if we have 2 assets and if the pay-off of both the assets on maturity is same, the price of both the asset should be the same at t = 0. Otherwise, there will be an arbitrage opportunity. If we have 2 portfolios,

a. Protective put = S+ + P+ b. Fiduciary call = C+ + PV of E

At Equilibrium Protective put = Fiduciary call S+ + P+ = C+ + PV of E

Assumptions of Put – Call Parity model a. The put and call has a same underlying stock (“S”). b. The exercise price of both, call and put, should be the same. c. The options under contemplation are European in nature. d. There are no transaction costs like brokerage, commission, taxes. e. Unlimited amount of borrowing and lending is possible at Rf. f. The securities can be bought and sold in fractions. 12. Consider the following options on a stock.

Option Strike Price Maturity Premium Call 500 6 months 60 Put 500 6 months 65

The share is presently trading at 495 and Risk free interest rate is 6% p.a. Spot mispricing and advice arbitrage.

Ans. As per Put – Call Parity, Protective put (PP) = Fiduciary Call (FC) a. Protective Put = S+ + P+ = 495 + 65 = 560 b. Fiduciary Call = C+ + PV of E

= 60 + 50061 + 0.06 ×

12

= 545

Since PP is greater than FC, PP is relatively overvalued and FC is relatively undervalued and, hence there is an arbitrage opportunity.

Arbitrage profit = 560 – 545 =15 (rounded off)

=15 + (15 × 6%) × 612

= 15.45

DERIVATIVES – KHETAN EDUCATION INTEREST RATE RISK MANAGEMENT

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DERIVATIVES – INTEREST RATE RISK MANAGEMENT

I. SWAPS A swap is an agreement between two companies to exchange cash flows in the future. The agreement defines the dates when the cash flows are to be paid and the way in which they are to be calculated. # SWAPS BASED ON THE CONCEPT OF ABSOLUTE ADVANTAGE AND

COMPARATIVE ADVANTAGE 13. Companies A and B face the following interest rates:

A B U.S. Dollars (floating rate) Libor + 0.5% Libor + 1.0% Canadian (fixed rate) 5.0% 6.5% Assume that A wants to borrow U.S. dollars at a floating rate of interest and B wants to borrow Canadian Dollars at a fixed rate of interest. A financial institution is planning to arrange a swap and requires a 50 basis point spread. If the swap is equally attractive to A and B what rates of interest will A and B end up paying.

Ans. Particulars Canadian

(Fixed rate) US dollars

(Floating rate) Preference

A 5.0% L + 0.5% Floating B 6.5% L + 1.0% Fixed

Difference 1.5% 0.5% a. Total cost of borrowing without swap = (L + 0.5%) + 6.5% = L + 7.0% b. Total cost of borrowing with swap = 5% + (L + 1.0%) = L + 6.0% c. Quality Differential = (L + 7.0%) – (L + 6.0%) = 1.0%


...................................................................... 74 ..............................................................

d. Share of A = 1.0% × ¼ = 0.25 % Share of B = 1.0% × ¼ = 0.25 % Intermediary = 1.0% × ½ = 0.50 % e. Effective cost of A = (L + 0.50%) – 0.25 % = L + 0.25 % Effective cost of B = 6.50 % - 0.25 % = 6.25 % # SWAPS ENTERED INTO FOR PREFERRED FORM OF ASSET/LIABILITY

POSITION 14. X Ltd wants to borrow floating rate funds for 5 year. It can do so at a spread of

250 basis points over LIBOR. It considers the interest rate to be too high. Instead it may borrow fixed rate funds at 11%. However, it does not want to borrow fixed. When it approached its bank for advice, the bank quoted fixed v/s libor swap at 30/ 130 basis points over 5 year treasuries v/s libor. Five year treasuries are presently yielding 9%.

a. Explain how X Ltd. can use a swap to achieve floating rate funding at a cheaper cost?

b. If Libor at the beginning of each year in the 5-year period to be 8%, 10%, 7%, 9% and 8%. Find out the average annual cost of funds.

Ans. (a) Swap quotation → 9.30%/10.30% VS. Libor Net liability = 11.0% + L – 9.30% = L + 1.70%

(b) Avg. Libor = 8 + 10 + 7 + 9 + 8

5 = 8.40 %

Avg. cost = L + 1.70% = 8.40% + 1.70% = 10.10% # OVERNIGHT INDEXED SWAPS 15. Derivative Bank entered into a plain vanilla swap through on OIS (Overnight

Index Swap) on a principal of ` 10 crores and agreed to receive MIBOR overnight floating rate for a fixed payment on the principal. The swap was entered into on Monday, 2nd August, 2010 and was to commence on 3rd August, 2010 and run for a period of 7 days. Respective MIBOR rates for Tuesday to Monday were: 7.75%, 8.15%, 8.12%, 7.95%, 7.98%, 8.15%. If Derivative Bank received Rs317 net on settlement, calculate fixed rate and interest under both legs. NOTES: (i) Sunday is holiday. (ii) Work in rounded rupees and avoid decimal working.


...................................................................... 75 ..............................................................

Ans. Day Principal (`) MIBOR(%) Interest (`)

Tuesday Wednesday Thursday Friday Saturday & Sunday (*) Monday Total interest @ floating Less : Net Received Expected interest @ fixed Thus fixed Rate of interest Approx

10,00,00,000 10,00,21,233 10,00,43,567 10,00,65,823 10,00,87,618 10,01,31,382

7.75 8.15 8.12 7.95 7.98 8.15

21,233 22,334 22,256 21,795 43,764 22,358 1,53,740 -317 1,53,423 0.07999914

8% (*) i.e. Interest for two days. NOTE : Alternative, answer can also be calculated on the basis of 360 days in a year. # CURRENCY SWAPS 16. Drilldip Inc. a US based company has won a contract in India for drilling oil field.

The project will require an initial investment of 500 Crores. The Oil field along with equipment will be sold to Indian Government for ` 740 crores in one-year time. Since the Indian Government will pay for the amount in Indian Rupee, the company is worried about exposure due to exchange rate volatility. You are required to: (a) Construct a swap that will help the Drilldip to reduce the exchange rate risk. (b) Assuming that Indian Government offers a swap at spot rate which is 1 US$

= ` 50 in one year, then should the company opt for this option or should it just do nothing. The spot rate after one year is expected to be 1US $ = ` 54. Further you may also assume that the Drilldip can also take a US $ loan at 8% p.a.

Ans. a) The following swap arrangement can be entered by Drilldip: i) Swap a US $ loan today at an agreed rate with any party to obtain Indian

Rupees to make initial investment. ii) After one-year swap back the Indian Rupees with US $ at the agreed rate. In

such case the company is exposed only on the profit earned from the project b) With the swap

Year 0 (Million US $)


Buy ` 500 crores at spot rate of 1 US $ = ` 50 (100.00) - Swap ` 500 crores back at agreed rate of ` 50 - 100.00


...................................................................... 76 ..............................................................

Sell ` 240 crores at 1 US $ = ` 54 - 44.44 Interest on US $ loan @ 8% for one year - (8.00) (100.00) 136.44

Net Result is a net receipt of US $ 36.44 million. Without Swap:



Buy ` 500 crores at spot rate of 1 US $ = ` 50 (100.00) - Sell ` 740 crores at ` 54 - 137.04 Interest on US $ loan @ 8% for one year - (8.00) (100.00) 129.04

Net Result is a net receipt of US $ 29.04. DECISION: Since the net receipt is higher in swap option the company should opt for the same.

II. FORWARD RATE AGREEMENT FRAs are forwards on interest rates for short-term borrowing or lending a prospective borrower or investor can book an FRA and block his rate to avoid future dis-comfort. 1. Electra space is consumer electronics wholesaler. The business of the firm is highly

seasonal in nature. In 6 months of a year, firm has a huge cash deposits and especially near Christmas time and other 6 months’ firm cash crunch, leading to borrowing of money to cover up its exposures for running the business. It is expected that firm shall borrow a sum of €50 million for the entire period of slack season in about 3 months. A Bank has given the following quotations: Spot 5.50% - 5.75% 3 × 6 FRA 5.59% - 5.82% 3 × 9 FRA 5.64% - 5.94% How a FRA, shall be useful if the actual interest rate after 6 months’ turnout to be:

• 4.5% • 6.5% Ans. Case 1 : Spot Libor = 4.5 % Hedger → The firm borrows $ 500,00,000 @ 4.5 % in the spot market, out flow on maturity


...................................................................... 77 ..............................................................

= $ 5,00, 00,000 + 6$5,00,00,000 × 4.5% × 12

= $ 5,11,25,000

Pay off from FRA = (4.5 % - 5.94 %) × $ 5,00,00,000 × 6

12 = $ 3,60,000 → Outflow

∴ Net outflow = $ 5,11,25,000 + $ 3,60,000 = $ 5,14,85,000

∴ Effective cost = $ 5,14,85,000 - $ 5,00,00,000 12 × 100 × $ 5,00,00,000 6

= 5.94 %

For Speculator

Payoff = 1 01

Notional Principal [r - r ] × t1 + r × t

r1 − r0 → for Borrowerr0 − r1 → for Investor

Payoff =

6$ 5,00,00,000 (4.5% - 5.94%) × 12

61 + 4.5% × 12

= ($ 3,52,078.24) Outflow Case 2 : Spot Libor = 6.5 % Hedger → The firm borrows $ 50, 00,000 @ 6.5 % in the spot market,

Out flow on maturity = $ 500,00,000 + 6$5,00,00,000 × 6.5% × 12

= $ 5,16,25,000

Pay off from FRA = (6.5 % - 5.94%) × $ 5,00,00,000 × 6

12

= $ 1,40,000 → Inflow ∴ Net outflow = $ 5,16,25,000 - $ 1,40,000 = $ 5,14,85,000

∴ Effective cost = $ 5,14,85,000 - $ 5,00,00,000 12 × 100 × $ 5,00,00,000 6

= 5.94 %

For Speculator

Payoff = 1 01

Notional Principal [r - r ] × t1 + r × t

r1 − r0 → for Borrowerr0 − r1 → for Investor

Payoff =

6$ 5,00,00,000 (6.5% - 5.94%) × 12

61 + 6.5% × 12

= $1,35,593.22 Inflow


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III. INTEREST RATE OPTIONS i. Caps ii. Floors iii. Collars 𝐂𝐂+ 𝐂𝐂− Right to Buy @ E Obligation to Sell @ E Buy Call Sell Call Right to Borrow @ E Obligation to Invest @ E Buy Cap Sell Cap → pay premium → receive premium 𝐏𝐏+ 𝐏𝐏− Right to Sell @ E Obligation to Buy @ E Buy Put Sell Put Right to Invest @ E Obligation to Borrow @ E Buy Floor Sell Floor → Pay Premium → Receive Premium 2. XYZ Inc. issues a £ 10 million floating rate loan on July 1, 2013 with resetting of

coupon rate every 6 months equal to LIBOR + 50 bps. XYZ is interested in a collar strategy by selling a Floor and buying a Cap. XYZ buys the 3 years Cap and sell 3 years Floor as per the following details on July 1, 2013: Notional Principal Amount $ 10 million Reference Rate 6 months LIBOR Strike Rate 4% for Floor and 7% for Cap Premium 0* *Since Premium paid for Cap = Premium received for Floor. Using the following data, you are required to determine: (i) Effective interest paid out at each reset date, (ii) The average overall effective rate of interest p.a.

Reset Date LIBOR (%) Reset Date LIBOR (%) 31-12-2013 6.00 30-06-2014 7.00 31-12-2014 5.00 30-06-2015 3.75 31-12-2015 3.25 30-06-2016 4.25

Ans. The borrower buys a cap (C+) and sells a floor (P−) on a principal of £ 10 m C+@ E = 7 % P−@ E = 4 % (Here, assume that the strike rate of 7% and 4% includes spread of 0.5 % hence, the Libor of reset period will should also include spread of 0.5 % → so we add 0.5 % to it)


...................................................................... 79 ..............................................................

Date Days Count

Spot Rate Payoff (S-E,O)

Payoff (E-S,O) Int. Cost Net Outflow

31-12-2013 184 6+0.5= 6.50% 0 0 (£ 327,671.23) (£ 327,671.23)

30-06-2014 181 7+0.5=7.50 % *£ 24794.52 0 (£3,71,917.81)) (£3,47,123.29)

31-12-2014 184 5 +0.5= 5.50% 0 0 (£2,77,260.27) (£2,77,260.27)

30-06-2015 181 3.75+0.5=4.25 % 0 0 (£2,10,753.43) (£2,10,753.43)

31-12-2015 184 3.25+0.5=3.75% 0 **(£ 12,602.74) (£1,89,041.10) (£2,01,643.84)

30-06-2016 182 4.25+0.5=4.75% 0 0 (£2,36,202.19) (£2,36,202.19)

Total 1096 (£16,00,654.25)

* (7.5% - 7%) × £ 10 m × 181365

= £ 24,794.52 (Payoff from Cap)

**(4% - 3.75%) × £ 10 m × 184365

= £ 12,602.74 (Payoff from Floor)

Int. Cost per day = £ 16,00,654.231,096 days

= £ 1460.45 Per Day

(int. Cost p.a. = £ 1460.45 × 365 Days = £ 533064.59)

Annual % = £ 5,33,064.59

£ 10 m × 100 = 5.33 %


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PORTFOLIO MANAGEMENT SFT

I. WHAT IS A PORTFOLIO Collection of assets is called a portfolio. There are various asset categories with can be

included in a portfolio. -Equity/stocks -Fixed income securities. Eg; Bond/Debentures -Commodities -Bullion -Foreign Currencies -Real Estate -Derivatives

II. PORTFOLIO THEORIES: Modern Portfolio Theory By Harry Markowitz (MPT): As per Markowitz, it is the duty of every investor to create an optimum portfolio. A

portfolio can be called optimum if it has highest utility. Utility can be measured or quantified with “Risk and Return”. Returns can be measured by “Mean”, & Risk can be measured by “Standard Deviation”.

i. Computation of Risk and Return of Securities • Ex-Post Data / Historical Data

Average return/ mean = x̅ =x

n∑

Holding period return (HPR) = D + P - P1 1 0

P0× 100

Risk/ Variance = 2(x - x)

n∑ = 2xσ

Risk/ Standard Deviation = 2(x - x)

n∑ = xσ

Where, x = Return of an individual security N = No. of data points

2xσ = Variance σ x = Standard Deviation D1 = Dividend per share P1 = Expected price at the end of the year P0 = Current price

KHETAN EDUCATION PORTFOLIO MANAGEMENT SFT

...................................................................... 81 ..............................................................

• Ex- Ante Data / Future Data Expected Return = Px∑

Risk = Variance = 2P(x - x)∑ Where, P = Probability

Risk = Standard deviation = 2P(x - x)∑

ii. Computation of Covariance and Coefficient of Co-relation Covariance is the product of absolute deviations of two variables ‘X’ and ‘Y’. Usually, Co-variance is a large squared number which is difficult to interpret. It only indicates whether the variables have a relationship which is positive, negative or neutral. Coefficient of correlation not only indicates the positive or negative relation, it also indicates the strength of relationship. It varies between + 1 and -1

COVxy =(x - x) (y - y)

n∑ [Used for ex-post data]

COVxy = ∑P (x - x̅) (y - y) [Used for ex-ante data]

rxy = COVxyx yσ × σ

Where, COVxy = Covariance between x and y. rxy = Coefficient of correlation between x and y. 1. The historical data of return of two securities over the past ten years are given.

Calculate the covariance and the correlation coefficient of the two securities: Years 1 2 3 4 5 6 7 8 9 10 Security 1(%) 12 8 7 14 16 15 18 20 16 22 Security 2(%) 20 22 24 18 15 20 24 25 22 20

Ans. Its Ex-post data x y (x - x ) 2(x - x) (y - y) 2(y - y) (x - x) (y - y)

12 20 -2.80 7.84 -1 1 2.80 8 22 -6.80 46.24 +1 1 -6.80 7 24 -7.80 60.84 +3 9 -23.40 14 18 -0.80 0.64 -3 9 2.40 16 15 1.20 1.44 -6 36 -7.20 15 20 0.20 0.04 -1 1 -0.20 18 24 3.20 10.24 3 9 9.60 20 25 5.20 27.04 4 16 20.80 16 22 1.20 1.44 1 1 1.20 22 20 7.2 51.84 -1 1 -7.2 148 210 207.6%2 84%2 -8%2


...................................................................... 82 ..............................................................

x̅ = x

n∑ = 148

10 =14.8%

y = y

n∑ = 210

10 = 21%

σ× = 2(x - x)

n =

2207.6%10

= 4.56%

σy = 2(y - y)

n =

284%10

= 2.89%

COVxy = (x - x)(y - y)

n∑ =

2-8%10

= 2-0.8%

rxy = xyCOVx yσ σ

= 2-0.8%

4.56% × 2.89% = 0.061

2. The following table provides a probability distribution on the returns of 2 stocks X and Y. Probability Return from X Return from Y

0.4 40 16 0.3 25 20 0.3 10 28

a. Find out the expected return, risk and coefficient of variation for each stock. b. Find out the covariance and correlation coefficient between the two stocks. Ans.

p x y px py (x - x) p 2(x - x)

0.4 40 16 16 6.4 13.5 72.9 O.3 25 20 7.5 6 -1.5 0.675 0.3 10 28 3 8.4 -16.5 81.675

26.5% 20.8% 155.25%2

(y - y) P 2(y - y) p(x - x ) (y - y)

-4.8 9.216 -25.92 -0.8 0.192 0.36 7.2 15.552 -35.64

24.96%2 -61.2%2

x̅ =∑P× = 26.5%

y = ∑Py = 20.8%

σ× = 2P(x - x)∑ = 2155.25% = 12.46%

σy = 2P(y - y)∑ = 224.96% = 5% ≈ 4.99%


...................................................................... 83 ..............................................................

Cov(xy) = ∑P(x - x̅) (y - y) = -61.2%2

rxy = Cov(xy)σ × σy

= 2-61.2%

12.46% × 5% = -0.98

Coefficient of variation = SDMean

For X = xxσ = 12.46

26.5 = 0.47 For Y = y

yσ = 5

20.8 = 0.24

i. Computation of Risk and Return of a Portfolio • Return of a portfolio Return of a portfolio would always be a weighted average, where the weights are

proportionate to the amount invested in a particular category.

RP = WA RA + WB RB

Where, RP = Average return of portfolio RA = Average return of Stock A

RB = Average return of Stock B WA = Amount invested in Stock A WB = Amount invested in Stock B

Risk of the Portfolio

σP = 2 2 2 2AB A BW Aσ A + W Bσ B + 2 × WA × WB × r × σ × σ

OR

σP = 2 2 2 2ABW Aσ A + W Bσ B + 2 × WA × WB × COV

3. Mr. Shyam Bachhan has constructed two portfolios, the details of which are given below:

Portfolio - 1 Securities Weights Return S.D. Correlation Matrix ICICI Infosys ICICI 0.3 18% 10% 1.00 0.75 Infosys 0.7 23% 16% 0.75 1.00

Portfolio - 2 Securities Weights Return S.D. Correlation Matrix

ICICI Infosys HLL ICICI 0.3 18% 10% 1.0 0.75 0.86 Infosys 0.4 23% 16% 0.75 1.00 0.68 HLL 0.3 16% 12% 0.86 0.68 1.00

You are required to: a. Calculate the risk and return on portfolio 1 & 2. b. Construct a portfolio out of the portfolios 1 & 2 in order to generate a return of

20.50%. Find out the SD of such a portfolio.


...................................................................... 84 ..............................................................

Ans.

a. 1RP = WA RA + WB RB

= 0.3 × 18 + 0.7 × 23 = 21.5%

1Pσ = 2 2 2 2ABW Aσ A + W Bσ + 2 × WA × WB × r × σA × σB

= 2 2 2 2(0.3) (10) + (0.7) (16) + 2 × 0.3 × 0.7 × 0.75 10 × 16 ×

= 13.60%

2RP = WA RA + WB RB + WC RC

2RP = 0.3 × 18 + 0.4 × 23 + 0.3 × 16 = 19.45

2Pσ = 2 2 2 2 2 2

AB A B

AC A c BC C

W Aσ A + W Bσ B + W Cσ C + 2 × WA × WB × r × σ × σ+ 2 × WA × WC × r × σ × σ + 2 × WB × WC × r × σB × σ

= 2 2 2 2 2 2(0.3) (10) + (0.4) (16) + (0.3) (12) + 2 × 0.3 × 0.4 × 0.75 × 10 × 16

+ 2 × 0.3 × 0.3 × 0.86 × 10 × 12 + 2 × 0.4 × 0.3 × 0.68 × 16 × 12

= 11.90%

b. 1RP = 21.5%, 2RP = 19.45%

We want a return of 20.50%.

3RP = 1 1 2 2WP RP + WP RP

20.50 = 1 1WP × 21.5 + (1 - WP ) ×19.4

20.50 = 21.5 1 1WP × 19.4 (1 - WP )

20.50 = 1 121.5 WP + 19.4 - 19.4 WP

20.50 = 2.1 1WP 19.4+

WP1 = 0.52 WP2 = 0.48 P1 P2 52% 48% A B A B C 30% 70% 30% 40% 30% In portfolio 3, Computation of weights of securities A,B, C in 𝑃𝑃3

AW = 52% × 30% + 48% × 30% = 30%

BW = 52% × 70% + 48% × 40% = 55.6%


...................................................................... 85 ..............................................................

CW = 52% × 0% + 48% × 30% = 14.4%

3Pσ = 2 2 2 2 2 2(0.3) (10) (0.556) (16) (0.144) (12)+ +

+ 2 × 0.3 × 0.556 × 0.75 × 10 × 16 + 2 × 0.3 × 0.144 × 0.86 × 10 × 12 + 2 × 0.556 × 0.144 × 0.68 × 16 × 12 = 12.69% In the given sum, we converted P3 in terms of A, B, C because in order to computer 𝝈𝝈𝝈𝝈𝟑𝟑 we need: - i. Weights of 1 2P & P –available

ii. Risks of 1 2P & P –available

iii. Relationship or P1P2 P1P2COV / r - NOT AVAILABLE

The sum does not provide data like distribution of result of P1, P2 and hence we cannot compute the same. Perfectly Co-related Stocks If two stocks are perfectly positively corelated with each other or if A and B are two stocks and coefficient of correlation( rAB) = +1, then risk of the portfolio would be a weighted average. Pσ = WAσA + WBσB

NOTE : Return of a portfolio is anyways a weighted average, and weights are proportionate to amount invested in particular category of stocks. 4. Consider the following information relating to two stocks:

Stock Expected return (%) Standard Deviation of return (%) P 15 30 Q 10 20

The returns of the two stocks exhibit perfect correlation. You are required to determine the return and risk of the following combinations of the two stocks:

A. 70% of P and 30% of Q B. 50% of P and 50% of Q C. 30% of P and 70% of Q D. 10% of P and 90% of Q Ans. Perfect co-relation implies r = +1, then

RP = WP RP + WQ RQ

σP = WPσP + WQσQ a. 70% of P and 30% of Q

RP = 0.7 × 15 + 0.3 × 10 = 13.50% σP = 0.7 × 30 + 0.3 × 20 = 27%


...................................................................... 86 ..............................................................

b. 50% of P and 50% of Q

RP = 0.5 × 15 + 0.5 × 10 = 12.50% σP = 0.5 × 30 + 0.5 × 20 = 25% c. 30% of P and 70% of Q

RP = 0.3 × 15 + 0.7 × 10 = 11.50% σP = 0.3 x 30 + 0.7 x 20 = 23% d. 10% of P and 90% of Q

RP = 0.1 × 15 + 0.9 × 10 = 10.50% σP = 0.1 × 30 + 0.9 × 20 = 21% Minimum Variance portfolio

WA = 2

AB2 2

AB

σ B - COVσ A + σ B - 2 × COV

= 2

AB A B2 2

AB A B

σ B - r · σ . σσ A + σ B - 2 × r × σ . σ

WB = 1- WA Benefit of Diversification 1. pσ = WAσA+WBσB

2. bσ = 2 2 2 2ABW A A W B B 2.WA.WB.COVσ + σ +

Benefit of Diversification = 1 - 2 5. Consider the following data.

Stock Expected return (%)

Variance - (%)2 Covariance matrix

A B A 20% 196 -60 B 14% -60 144

a. Find out the minimum risk portfolio. b. Find out the benefit of diversification. c. Find out the coefficient of variation of the minimum risk portfolio.


...................................................................... 87 ..............................................................

Ans. a. A minimum risk portfolio is given by,

WA = 2

AB2 2

AB

σ B - COVσ A + σ B - × 2COV

= 144 - (-60)196 + 144 - 2 × (-60)

= 204460

= 0.44 ∴WA = 0.44 WB = 1 - 0.44 = 0.56 b. σP = WA · A + WB Bσ σ

= 0.44 × 196 + 0.56 × 144 = 12.88%

pσ = σ 2 2 2ABW A · σ A + W B · σ B + 2 · WA · WB · COV

= 2 2(0.44) × 196 + (0.56) × 144 + 2 × 0.44 × 0.56 × (-60) = 7.32% ∴ Benefit of diversification = 12.88% - 7.32% = 5.56%

c. Coefficient of variation = S.DMEAN

= σPRP

Pσ = 7.32%

RP = 0.44 × 20 + 0.56 × 14 = 16.64

∴ Coefficient of variation = 7.3216.64

= 0.44

⇒ Benefit of Diversification: This computation means the maximum risk possible is 12.88% and minimum risks

possible is 7.32% (since the weights are as per minimum risk) with given data, it is possible to bring 𝜎𝜎𝑃𝑃 down by max of 5.56%.

i. Discussion on Efficient Frontier and selection of Optimal Portfolio Capital allocation Line (CAL) Capital Market Line (CML) Security Market Line (SML) Characteristic Line (CL)


...................................................................... 88 ..............................................................

6. The following table provides the historical returns on the Sensex and the stock of Infosys for the last 5 years –

Period Return on Sensex Return on Infosys 1 12% 16% 2 8% 6% 3 15% 20% 4 25% 35% 5 30% 50%

Find out the characteristic line for the stock and interpret its coefficient. Ans. Sensex and stock → ∴ Sharpe’s theory

Year Sensex (X) Return(Y) 1 12 16 2 8 6 3 15 20 4 25 35 5 30 50 90 127

CL given by, Re = α + βX

β = XY2

COVσ X

α = y - xβ = 25.4 – 1.86 × 18 = -8.08%

XYCOV 2

2(x - x) (y - y) 125.8%= =

n 67.6%∑ = 1.86

2σ x =

2(x - x)n

∑ = 67.6%2

x = x

n∑ = 90

5 = 18%

y = y

n∑ = 127

5 = 25.4%

Year X Y (x - x) (x - x)2 (y - y) (x - x) (y - y) 1 12 16 -6 36 -9.4 56.4 2 8 6 -10 100 -19.4 194 3 15 20 -3 9 -5.4 16.2 4 25 35 +7 49 9.6 67.2 5 30 50 +12 144 24.6 295.2 6 338%2 629.3%2


...................................................................... 89 ..............................................................

• Computation Of Portfolio Beta Beta of portfolio will always be a weighted average, where weights are proportionate to

amount invested in a particular category of stocks.

βp = Wi iWiβ∑

∑

7. Mr. Bharat has the following scrips in his portfolio

Particulars Beta Proportion of investment (%)

Ballarpur Industries 0.95 15 GE Shipping 1.1 20 SBI 1.25 30 Ahmadabad Electric Co. 0.8 5 BSES 1.05 20 Bombay Dyeing 0.70 10

Calculate the expected return on his portfolio if the risk free return is 4% and return on market is 14%?

Ans. βp = 0.95 × 0.15 + 1.10 × 0.20 + 1.25 × 0.30 + 0.8 × 0.05 + 1.05 × 0.20 + 0.70 × 0.10 = 1.0575

As per SML, Rp = RF + (Rm - Rf) βp = 4 + (14 - 4) × 1.0575 = 14.575% • Overvalued and Undervalued Stocks

If Expected Return/Actual Return > CAPM Return = Stock is Undervalued If Expected Return/Actual Return > CAPM Return = Stock is Overvalued

8. Given the risk free rate is 10% and the expected return on the market portfolio is

15%. The following are the expected returns for five stocks with their betas: Stock Expected return (%) Expected beta

A 19 1.5 B 15 0.9 C 17 1.25 D 24.5 0.75 E 25 1.40

Based on this expectation, find out the stocks that are overvalued and undervalued?

Ans. Rf = 10%, Rm = 15%


...................................................................... 90 ..............................................................

Stock E(r) Rf + (Rm - Rf)β A 19 10 + 5(1.5) = 17.5 B 15 10 + 5(0.9) = 14.5 C 17 10 + 5(1.25) = 16.25 D 24.5 10 + 5(0.75) = 13.75 E 25 10 + 5(1.40) = 17

Hence, all the stocks are undervalued because Expected Return > CAPM Return.

• Systematic Risk and Unsystematic Risk- Computation i. Systematic risk / Non-diversifiable risk / Market risk.

The risk to an asset due to broad macro and micro economic factors like inflation rate, interest rates, GDP growth rate and so on. The risk is general to the economy and cannot be diversified.

ii. Unsystematic risk / Diversifiable risk / Firm specific SD. This risk is unique to afirm and it can be diversified away completely. Eg: poor internal controls, manipulation of financials, non- reliable management, disturbed

human resource. Total Risk = Systematic risk + Unsystematic Risk

2σ P = 2 2 2 β Pσ X + σ eP (For Portfolio)

2σ A = 2 2 2β Aσ X + σ eA (For Stock A)

NOTE : rXY · Y = Xσ

βσ

Where rXY = coefficient of correlation between stock & market. σY = SD. of stock σX = SD. of market 9. Consider three stocks A, B & C whose data is shown below :

Particulars S.D. of stock Coefficient of correlation with market

(r) A 22% 0.9 B 30% 0.7 C 25% 1.0

Find Beta of each stock as well as unsystematic risk (in terms of S.D. of the error term) Given S.D. of the market is 10%

Ans. Total Risk = Systematic Risk + Unsystematic Risk

a. 2σ A = 2 2 2Aβ σ X + σ eA

βA = rAX × σAσX

= 0.9 × 2210

= 1.98

(22)2 = (1.98)2 (10)2 + σ2eA


...................................................................... 91 ..............................................................

484 = 392.04 + σ2eA ∴ σ2eA = 91.96%2

σeA = 291.96% = 9.59%

b. βB = rBX × σBσX

= 0.7 × 3010

= 2.1

∴ σ2eB = σ2B – β2

Bσ2X

σ2eB = (30)2 – (2.1)2(10)2 = 459%2

σeB = 2459% = 21.42%

c. βC = rCX × σCσX

= 1 × 2510

= 2.5

∴ σ2eC = σ2C - β2

Cσ2X

σ2eC = (25)2 - (2.5)2(10)2 = 0 σeC = 0 • Computation of Covariance between two stocks with the help of Beta of two stocks.

If we know the Beta of two stocks, we can compute the covariance between two stocks

COVAB = 2β β σ XA B 10. A study by a Mutual fund has revealed the following data in respect of three

securities: Security δ (%) Correlation with Index, Pm

A 20 0.60 B 18 0.95 C 12 0.75

The standard deviation of market portfolio (SSE Sensex) is observed to be 15%. i. What is the sensitivity of returns of each stock with respect to the market? ii. What are the co variances among the various stocks? iii. What would be the risk of portfolio consisting of all the three stocks equally? iv. What is the beta of the portfolio consisting of equal investment in each stock? v. What is the total systematic and unsystematic risk of the portfolio in (iv)? Ans.

a. βA = rAX × σAσX

= 0.60 × 2015

= 0.80

βB = rBX × σBσX

= 0.95 × 1815

= 1.14

βC = rCX × σCσX

= 0.75 × 1215

= 0.60


...................................................................... 92 ..............................................................

b. COVAB = βA × βB × σ2X = 0.80 × 1.14 × (15)2 = 205.2%2

COVAC = βA × βc × σ2X = 0.80 × 0.60 × (15)2 = 108%2

COVBC = βB × βc × σ2X = 1.14 × 0.6 × (15)2 = 153.9%2

c. σP = 2

2 2 21 1 1[(20) + (18) + (12) ] + 2 × × [205.2 + 108 + 153.9]3 3 3

σP = 14.15 %

d. βP = 0.8 + 1.14 + 0.63

= 0.85

e. 2σ P = 2 2 2ePσ X + σ Pβ

2 2β Pσ X = (0.85)2(15)2 = 162.56%2 (Systematic Risk of Portfolio)

2σ P = (14.15)2 = 200.22%2

2eσ P = Unsystematic Risk = 200.22 – 162.56 = 37.66%2

• Reducing the risk of existing portfolio

If a fund manager wants to reduce the existing risk of his portfolio, he can sell a high beta stock and use the proceeds to buy a low beta stock, as a result of which the weighted average risk would go down

11. India Investment Fund holds the following portfolio:

Stock A B C Investment(Rs. Crore) 200 200 100 Beta 0.5 2 4

The required rate of return on the market is 14% and that of the above portfolio according to CAPM is 20.40%. The fund manager has proposed to sell C for Rs. 100 crore and use the proceeds to purchase stock ‘D’ which has a beta of 3. The required rate of return of the portfolio according to CAPM is?

Ans. As per CAPM, Rp = Rf + (Rm - Rf) βp 20.4 = Rf + (14-Rf) βp → βP = [200 ×0.5+200×2+100×4] / 500 = 1.8 ∴ 20.4 = Rf + (14-Rf) 1.8 20.4 = Rf +25.2 –1.8Rf 0.8 × Rf = 4.8 Rf = 6


...................................................................... 93 ..............................................................

→ New βp = 200 × 0.5 + 200 × 2 + 100 × 3500

= 1.6 New Rp = 6 + (14 - 6)1.6 = 18.8% 12. Details about portfolio of shares of an investor is as below:

Shares No. of shares (Lakh) Price per share Beta A Ltd. 3.00 500 1.40 B Ltd. 4.00 750 1.20 C Ltd. 2.00 250 1.60

The investor thinks that the risk of portfolio is very high and wants to reduce the portfolio beta to 0.91. He is considering two below mentioned alternative strategies: i. Dispose off a part of his existing portfolio to acquire risk free securities, or ii. Take appropriate position on Nifty Futures which are currently traded at `

8,125 and each Nifty points is worth ` 200. You are required to determine:

(1) Portfolio beta (2) The value of risk free securities to be acquired (3) The number of shares of each company to be disposed off (4) The number of Nifty contracts to be bought/sold; and (5) The value of portfolio beta for 2% rise in Nifty.

Ans. 1.

Stocks No of shares MPS Amount Βi Wiβi A 3,00,000 500 1,500L 1.4 2,100 B 4,00,000 750 3,000L 1.2 3,600 C 2,00,000 250 500L 1.6 800

` 5,000L ` 6,500L

Βp =Wi iWiβ∑

∑= 6,500L

5,000L`

` = 1.30

2. 0.91 = rfβ × rfW + pβ × pW

0.91 = (1 - pW ) × 0 + 1.30 pW

∴ pW = 0.70

rfW = 0.30


...................................................................... 94 ..............................................................

∴ Amount of risk free securities to be acquired = ` 5,000L × 0.30 = ` 1,500L

3. Stocks Wi Amount to be disposed MPS No of

stocks A 30% 1,500 × 30% = 450L 500 90,000 B 60% 1,500L × 60% = 900L 750 1,20,000 C 10% 1500L × 10% = 150L 250 60,000 ` 1,500L

4. Vp = ` 5,000L

βT = 0.91

βp

= 1.30

βF = 1

Lot 200 Futures price = ` 8,125

No of lots = T P

F

Vp[ - ] × lot × futures price

β ββ

= 5000L [0.91 - 1.30]1 × 200 × 8125

= - 120 lots 5. If nifty ↑ by 2% Cash market gain = ` 5,000 × 1.30 × 2% = ` 1,30L In future market Sell = ` 8,125 Buy = 8,125 + 2% = ` 8,287.5 = (8,125 – 8,287.5) × 120 lots × 200 = (` 39L) ∴ 130L - 39L = ` 91L

∴ % of portfolio = 91L 5,000L`

`× 100 = 1.82 %

Beta = % Δ in portfolio% Δ in market

= 1.82%2%

= 0.91


...................................................................... 95 ..............................................................

B. Arbitrage Pricing Theory By Stephen Ross (APT) Re = Rf + RP1F1 + RP2F2 + RP3F3 + RP4F4 + ……… + RPnFn 13. Mr. Tamarind intends to invest in equity shares of a company the value of which

depends upon various parameters as mentioned below : Factor Beta Expected value in % Actual value in % GNP 1.20 7.70 7.70 Inflation 1.75 5.50 7.00 Interest Rate 1.30 7.75 9.00 Stock market index 1.70 10.00 12.00

If the risk free rate of interest be 9.25%, how much is the return of the share under Arbitrage Pricing Theory?

Ans. RP = 9.25 + (7.7 - 7.7) × 1.2 + (7 - 5.50) × 1.75 + (9 - 7.75) × 1.30 + (12 - 10) × 1.70

RP = 16.9% 14. The expected return on equity shares in an economy is affected by four factors i.e.

change in GDP growth, change in oil prices, change in monsoon and change in Book value. Assume the Rf to be 10%. The values of these factors are as follows:

Macro factors Value of Macro factor Change in GDP 6% Change in Oil Prices -2% Change in Monsoon 3% Change in Book Value 10%

Given the following factor sensitivities of the equity shares of four companies, find the expected return on equity shares of each company. Factor Factor Sensitivity Madhav

Ltd. Keshav

Ltd. Krishna

Ltd. Damodar

Ltd. Change in GDP 1.50 2.00 0.50 0.20 Change in Oil prices -1.00 -0.05 -0.10 -0.90 Change in Monsoon 0.2 0.5 2.00 1.50 Change in Book Value 0.25 0.50 0.65 0.55

Murari had ` 1,00,000 to invest. He borrowed 100 shares of Damodar Ltd. and sold these at the rate of ` 500. He invested Rs. 1,50,000 in the equity shares of other three companies. Find the expected return of the portfolio. Ans. ReA = 10 + 6 × 1.5 + (-2) - 1 + 3(0.20) + 10 (0.25) = 24% ReB = 10 + 6 × 2 + (-2) - 0.05 + 3(0.50) + 10 (0.50) = 28.6% ReC = 10 + 6 × 0.5 + (-2) - 0.10 + 3(2) + 10 (0.65) = 25.7% ReD = 10 + 6 × 0.20 + (-2) - 0.90 + 3(1.50) + 10 (0.55) = 23%


...................................................................... 96 ..............................................................

WA = +50,000+150,000 - 50,000

= + 0.50

WB = +50,000+150,000 - 50,000

= + 0.50

WC = +50,000+150,000 - 50,000

= + 0.50

WD = -50,000+150,000 - 50,000

= - 0.50

Rp = (0.5 × 24.1) + (0.5 × 28.6) + (0.5 × 25.7) + (-0.5 × 23) = 27.7%

III. Efficient Market Hypothesis 15. The closing value of Sensex for the month of October,2011 is given below:

Date Closing Sensex Value

Date Closing Sensex Value

1.10.11 2800 17.10.11 3300 3.10.11 2780 18.10.11 3450 4.10.11 2795 19.10.11 3360 5.10.11 2830 20.10.11 3290 7.10.11 2760 21.10.11 3360 10.10.11 2790 24.10.11 3340 11.10.11 2880 25.10.11 3290 12.10.11 2960 27.10.11 3240 13.10.11 2990 28.10.11 3140 14.10.11 3200 31.10.11 3260

You are required to test the weak form of efficient market hypothesis by applying the

run test at 5% and 10% level of significance. Following value can be used: Value of t at 5% is 2.101 at 18 degrees of freedom. Value of t at 10% is 1.734 at 18 degrees of freedom. Value of t at 5% is 2.086 at 20 degrees of freedom. Value of t at 10% is 1.725 at 20 degrees of freedom.

Ans. 2800 3300 + 2780 - 3450 + 2795 + 3360 - 2830 + 3290 - 2760 - 3360 + 2790 + 3340 - 2880 + 3290 -


...................................................................... 97 ..............................................................

2960 + 3240 - 2990 + 3140 - 3200 + 3260 +

No. of runs = 8 No. of positive changes = n1 = 11 No. of negative changes = n2 = 8

µ = 1 2

1 2

2n n +1n + n

µ = 2 × 11 × 811 + 8

+ 1

µ = 10.26

σ = 1 2 1 2 1 22

1 2 1 2

2n n (2n n - n - n )(n + n ) (n + n -1)

σ = 2 × 11 × 8[(2 × 11 × 8) - 11 - 8](11 + 8 - 1)

σ = 2.06 df = n1 + n2 – 1 = 11 + 8 – 1 = 18 df At 5% significance, Upper limit = µ + t × σ = 10.26 + 2.101 × 2.06 = 14.59 Lower limit = µ - t × σ = 10.26 – 2.101 × 2.06 = 5.93 At 10% significance, Upper limit = µ + t × σ = 10.26 + 1.734 × 2.06 = 13.83 Lower limit = µ - t × σ = 10.26 – 1.734 × 2.06 = 6.69 Since our runs = 8 lies between the upper and lower limit, both at 5% and 10% significance, the market is weak form efficient and no one has tried to bias. 4. Mutual Fund Performance Appraisal

A. Sharpe’s Measure = Rp - Rfpσ

B. Treynor’s Measure = Rp - Rfpβ

C. Jenson’s Alpha = E(r) – CAPM 5. PORTFOLIO REBALANCING 16. Indira has a fund of Rs. 3 lacs which she wants target to invest in share market

with rebalancing target after every 10 days to start with for a period of one month from now. The present nifty is 5326. The minimum nifty within a month can at most be 4793.4. She wants to know she should rebalance the portfolio under the


...................................................................... 98 ..............................................................

following situations according to the theory of Constant Proportion Portfolio Insurance policy using 2 as multiplier.

Immediately to start with : • 10 days later being the first day of rebalancing if Nifty falls to 5122.96 • 10 days further from the above date if the Nifty touches to 5539.04.

For the sake of simplicity, assume that the value of her equity component will change in tandem with that of nifty and the risk free securities in which she is going to invest will have no beta.

Ans. a. Immediately to start with When Nifty 5326 ⟶ Portfolio = ` 3,00,000

If Nifty 4793.4 ⟶ Portfolio = 3,00,0005,326

` × 4793.4 = ` 2,70,000

Our Floor Value = ` 2,70,000 As Per CPPI, Investment in stocks = (Portfolio – Floor) × Multiplier (m) = (3,00,000 – 2,70,000) × 2 = ` 60,000 Stock Balance = ` 60,000 Cash Balance = ` 3,00,000 – ` 60,000 = ` 2,40,000

b. After 10 days = Nifty = 5,122.96 When nifty 5326 ⟶ Equity ` 60,000

When nifty 5122.96 ⟶ Equity = 60,0005326

× 5,122.96 = ` 57,712.65

Portfolio Value = ` 57,712.65 + ` 2,40,000 = ` 2,97,712.65 As Per CPPI, Investment in stocks = (297,712.65 – 270,000) × 2 = ` 55,425.31 Stock Balance = ` 55,425.31 Cash Balance = 2,97,712.65 – 55,425.31 = ` 2,42,287.34

c. After 10 days, Nifty = 5,539.04 When nifty 5122.96 ⟶ Equity ` 55,425.31

When nifty 5539.04 ⟶ Equity = 55,425.315122.96

` × 5,539.04 = ` 59,926.88

Portflio Value = ` 59,926.88 + ` 2,42,287.34 = ` 3,02,214.22 As Per CPPI, Investment in stocks = 2(302,214.22 – 270,000) = ` 64,428.44 New Stock Balance = ` 64,428.44 Cash Balance = 3,02,214.22 – 64,428.44 = ` 2,37,785.78

KHETAN EDUCATION MUTUAL FUNDS

...................................................................... 99 ..............................................................

MUTUAL FUNDS INTRODUCTION: A Mutual Fund is an organisation in the form of a ‘Trust’ which pools the savings of the

investors to invest in the capital market in a variety of securities. The returns earned on the investment are distributed among unit holders in proportion of their holding.

THERE ARE BROADLY TWO SCHEMES OF A MUTUAL FUNDS: a. Open ended scheme: This has got unlimited authorized capital with no maturity date. The investors can buy

and sell units at any point of time directly from the fund. b. Closed ended scheme: This has got limited authorised capital with a particular maturity date and lock in period

after which the fund is liquidated. Since, The fund gets closed after initial offer, it is listed in the stock market in order to provide liquidity to the investors.

Advantages of Mutual Funds: a. High Returns b. Economies of scale c. Tax benefits d. Expert Advice e. Synergy Benefits Disadvantages of Mutual Funds: a. High Cost b. Over-diversification c. Manipulation of funds d. Disturbance of tax planning ⟶ An unexpected small income from a mutual fund can

change the tax bracket of an investor, thereby spoiling the tax planning. Net Asset Value (NAV) NAV is the market value of all assets less liabilities divided among all units. NAV is

computed daily and it represents per unit of holding.

NAV = Market value of all assets-liabilitiesno.of units

Computation of return from a Mutual Fund

Return from Mutual Fund = 1 0

0

Dividend per unit + Capital gains unit + NAV - NAV × 100NAV


...................................................................... 100 ..............................................................

1. A has invested in three Mutual fund schemes as per details below: MF A MFB MFC Date of investment 01.12.03 01.01.04 01.03.04 Amount of investment ` 50,000 ` 1,00,000 ` 50,000 Net Asset Value (NAV) at entry date ` 10.50 ` 10.0 `10.0 Dividend received up to 31.03.04 ` 950 ` 1,500 Nil NAV as on 31.03.04 ` 10.40 ` 10.10 ` 9.80

Required: What is the effective yield on per annum basis in respect of each of the three schemes to Mr. A up to 31.03.04?

Ans. A. FOR MF A: Amount = ` 50,000 NAV0 = ` 10.50

No. of Units = 50,000 10.50

`

` = 4,761.90 Units

Dividend = ` 950

Dividend/Unit = 9504 761 90

`

, . = ` 0.20/unit

Return (4months) = 0.20 + 10.40 - 10.5010.50

× 100 = 0.95%

Annual Return = 0.95% × 3 = 2.85% p.a. Or, Effective Annual Return = [(1+ 0.95%)3 – 1] × 100 = 2.88% p.a. B. FOR MF B: Date of investment = 01.01.04 Maturity = 3 months Amount invested = ` 1,00,000 NAV0 = ` 10

No. of Units = 1,00,000 10

`

` = 10,000 Units

Dividend = ` 1,500

Dividend/ Unit = 1 50010 000` ,

, = ` 0.15/Unit

Return (3months) = 0.15 + 10.10 - 1010

× 100 = 2.5%

Annual Return = 2.5% × 4 = 10% p.a. Or, Effective Annual Return = [(1+ 2.5%)4 – 1] × 100 = 10.38% p.a.


...................................................................... 101 ..............................................................

C. FOR MF C: Date of investment = 01.03.04 ∴ Maturity = 1 month Amount invested = ` 50,000, NAV0 = ` 10

⇒ No. of Units = 50,000 10

`

` = 5,000 Units

Dividend = Nil

Return = 9.80 - 1010

× 100 = -2%

Annual Return = - 2% × 12 = -24% p.a. Or, Effective Annual Return = [(1- 2%)12 – 1] × 100 = -21.5% p.a. 2. Sun Moon Mutual Fund ( approved mutual fund) sponsored open-ended equity

oriented scheme “Chanakya opportunity Fund”. There were three plans – ‘A’ – Dividend Re-investment Plan, ‘B’- Bonus Plan and ‘C’- Growth plan. At the time of Initial offer on 1.4.1995, Mr. Anand, Mr. Charu and Mr. Bachhan, three investors invested ` 1,00,000 each and chose ‘B’, ‘C’ and ‘A’ plan respectively.

The history of the fund is as follows: Net Asset value per unit

Date Dividend % Bonus Plan A Plan B Plan C 28.07.1999 20 -- 30.70 31.40 33.42 31.03.2000 70 5:4 58.4 31.05 70.05 31.10.2003 40 -- 42.18 25.02 56.15 15.03.2004 25 -- 44.45 29.10 64.28 31.03.2004 -- 1:3 42.18 20.05 60.12 24.03.2005 40 1:4 48.10 19.95 72.40 31.07.2005 -- -- 53.75 22.98 82.07

On 31st July all three investors redeemed all the balance units. Calculate the annual rate of return of each of the investors.

Consider: a. Long term Capital gain is exempt from Income tax. b. Short term capital gain is subject to 10% income tax. c. STT = 0.2% only on sale/ redemption of units. d. Ignore Education Cess.


...................................................................... 102 ..............................................................

Ans. a. Dividend reinvestment plan – PLAN A

Date NAV Dividend Investment

No. of units

Cum. Units

01.04.1995 ` 10.00 ` 1,00,000 10,000 10,000 28.07.1999 ` 30.70 ` 20,000 651.470 =10,000 + 651.47 =

10,651.470 31.03.2000 ` 58.40 ` 74,560.290 1,276.720 =10,651.47 + 1,276.72 =

11,928.188 31.10.2003 ` 42.18 ` 47,712.752 1,131.170 =11,928.18 + 1,131.17 =

13,059.35 15.03.2004 ` 44.45 ` 32,648.375 734.497 =13,059.35+ 734.497 =

13,793.850 24.03.2005 ` 48.10 ` 55,175.3865 1,147.097 =13,793.85+ 1,147.097 =

14,940.95 WORKING NOTE : Since opening NAV is not provided, we assume it to equal to face value on IPO. Dividend = 20% Dividend / Unit = 10 × 20% = ` 2.0 No. of units = 10,000 Total Dividend = 10,000 × ` 2 = ` 20,000 The date from start to end = 10 years and 4 months (`) Sales Proceeds = (14,940.95 × ` 53.75) 8,03,076.06 S.T.T. proceeds @ 0.2% (1,606.15) 8,01,469.91 Short term capital gain tax (635.78) [(53.75 – 0.2%) – 48.10] × 1,147.10 × 10% 8,00,834.13

Total Return = 8,00,834.13 - 1,00,000

1,00,000 × 100 = 700.834%

Return p.a. = 700.834%

10 years and 4 months = 10.33 years = 67.84% p.a.

b. Bonus Scheme- PLAN B Date No. of units Cumulative

01.04.1995 10,000 10,000 31.03.2000 12,500 22,500 31.03.2004 7,500 30,000 24.03.2005 7,500 37,500


...................................................................... 103 ..............................................................

(`) Sale proceeds = 37,500 × 22.98 8,61,750 -S.T.T. @ 0.2% (1,723.5) 8,60,026.5 STCG [(22.98 – 0.2%)] – 19.95] × 7500× 10% (2,238.03) 8,57,788.47

Total return = 8,57,788.47 - 100,000

100,000 × 100 = 757.788%

∴ Return p.a. = 757.788 ÷ 10.33 years = 73.3580% p.a. c. Growth Scheme – PLAN C (`) Sales Proceeds = 10,000 units × ` 82.07 820,700 -S.T.T. @ 0.2% (1641.4) 8,19,058.60

Total Return = 8,19,058.60 - 1,00,000

1,00,000 × 100 = 719.06%

Return p.a. = 719.06

10.33 years = 69.61% p.a.

Bonus Plan is yielding the highest return. NOTE: Dividend Rate is applied on Face value. Dividend Yield is applied on MPS. Dividend Payout is applied on EPS. 3. Based on the following information, determine the NAV of a regular income

scheme on per unit basis : ` Crores Listed shares at Cost (ex-dividend) 20 Cash in hand 1.23 Bonds and debentures at cost 4.3 Of these, bonds not listed and quoted 1 Others fixed interest securities at cost 4.5 Dividend accrued 0.8 Amount payable on shares 6.32 Expenditure accrued 0.75 Number of units (` 10 face value) 20 Lacs Current realizable value of fixed income securities of face value of

` 100 106.5

The listed shares were purchased when Index was 1,000 Present Index is 2,300 Value of listed bonds and debentures at NAV date 8


...................................................................... 104 ..............................................................

There has been a diminution of 20% in unlisted bonds and debentures. Other fixed interest securities at cost.

Ans. Computation of NAV

Value of shares = 20 1,000`

` × 2300 46.00 Cr

+ Bonds not listed and quoted (1Cr – 20%) 0.80 Cr + Bonds listed and quoted 8.00 Cr + Dividend accrued 0.80 Cr Amount payable on shares (6.32) Expenditure accrued (0.75) + Value of fixed income securities (@ Cost) 4.50 + Cash in hand 1.23 54.26 Cr

∴ NAV = 54 260 2

` .

. = ` 271.30

4. There are two Mutual Funds viz. D Mutual Fund Ltd. and K Mutual Fund Ltd.

each having close ended equity schemes. NAV as on 31-12-2014 of equity schemes of D Mutual Fund Ltd. is ` 70.71 (consisting 99% equity and remaining cash balance) and that of K Mutual Fund Ltd. is 62.50 (consisting 96% equity and balance in cash). Following is the other information: Particular Equity Schemes D Mutual Fund Ltd. K Mutual Fund Ltd. Sharpe Ratio 2 3.3 Treynor’s Ratio 15 15 Standard deviation 11.25 5

There is no change in portfolios during the next month and annual average cost is ` 3 per unit for the schemes of both the Mutual Funds. If Share Market goes down by 5% within a month, calculate expected NAV after a month for the schemes of both the Mutual Funds. For calculation, consider 12 months in a year and ignore number of days for particular month.

Ans. Mutual Fund Performance

Sharpe’s measure : Rp - RfσP

Treynor’s measure : Rp - Rf

Pβ

In order to compute the closing NAV, we need to bifurcate the equity and cash component so that the equity can be marked to market as equity would fluctuate and cash would remain constant.


...................................................................... 105 ..............................................................

a. For MF D Ltd. Decomposition of NAV NAV on 31.12.14: ` 70.71 % Equity = 99% Equity component = ` 70 Cash component: ` 0.71 Computation of Beta

Sharpe Ratio = Rp - RfσP

2 = Rp - Rf11.25

Rp – Rf = 22.50

Treynor’s Ratio = Rp - Rf

Pβ

15 = 22.50

Pβ

βP = 1.5 Post ↓ 5% in market D MF ↓ 5% × 1.5 = 7.5% Equity value = ` 70 – 7.5% = ` 64.75 NAV Closing Equity = ` 64.75 + Cash = ` 0.71 - Expenses = (` 0.25) (` 3.0 ÷ 12) = ` 65.21 b. For MF K Ltd. Decomposition of NAV NAV on 31.12.14: ` 62.50 % Equity = 96% Equity component = ` 60 Cash component: ` 2.50 Computation of Beta

Sharpe Ratio = Rp - RfσP

3.3 = Rp - Rf5


...................................................................... 106 ..............................................................

Rp – Rf = 16.50

Treynor’s Ratio = Rp - Rf

Pβ

15 = 16.50

Pβ

βP = 1.10 Post ↓ 5% in market K MF ↓ 5% × 1.1 = 5.5% Equity value = ` 60 – 5.5% = ` 56.70 NAV Closing Equity = ` 56.70 + Cash = ` 2.50 -Expenses = (` 0.25) (` 3.0 ÷ 12) = ` 58.95 5. Govind invested ` 1,000 in a mutual fund the entry load of which is 2.25%. He got

50 units. What is the NAV at the time of investment? His investment time horizon is 6 months. The mutual fund charges exit load of 0.50% if the redemptions is done on or after the 6 months but on or before 1 year. What is annualized return to the investor if he gets his investment redeemed on expiry of 6 months assuming that NAV at that time is ` 25 per unit.

Ans. Amount = ` 1000 Entry load = 2.25% No. of units = 50 units

⇒ Cost or buy price = 1,000 50

`

` = ` 20

Buy price = NAV0 (1 + Entry load) ` 20 = NAV0 (1 + 2.25%) NAV0 = ` 19.56 Closing NAV = ` 25 (given) Sell price/ exit price = 25 – 0.50% = ` 24.875 Closing amount = 24.875 × 50 units = ` 1,243.75

6m return = 1,243.75 - 1,0001,000

× 100 = 24.375% for 6m

Annual return = 24.375 × 2 = 48.75%

KHETAN EDUCATION MERGER AND ACQUISITIONS

...................................................................... 107 ..............................................................

MERGER AND ACQUISITIONS 1. WHAT IS MERGER & ACQUISITION ? Merger and acquisition stands for combination of two entities for a mutual benefit.

It can be a combination with choice or it can be a forced activity. 2. THERE ARE THREE TYPES OF MERGER : i. Vertical Merger : When a merger takes place between two entities where there is a

buyer and seller relationship, it is called a Vertical Merger. ii. Horizontal Merger : When a merger takes place within the industry in order to

increase the market share, it is called Horizontal Merger. iii. Conglomerate Merger : When the merger takes place between two unrelated

companies, it is known as Conglomerate Merger. 3. THERE ARE TWO FORMS OF MERGER : i. Amalgamation : When a combination takes places between company ‘A’ and ‘B’, where the identity of

both the companies is lost and a third company is formed, it is called Amalgamation. For Eg: Brooke Bond India and Lipton India combined together and formed

Brooke Bond Lipton India Ltd. ii. Absorption : When company ‘A’ acquires Company ‘B’ in such a manner that the identity of

company ‘B’ is lost and only Company ‘A’ remains, it is called as Absorption. For Eg: Kotak Bank acquires ING Vysya Bank. 4. BENEFITS OF MERGER : i. Savings in cost ii. Economies of scale iii. Increase in Market share iv. Tax Benefits – A loss making but fundamentally strong company can be acquired in

order to reduce the tax bill. 5. SOME EQUATIONS RELATED TO MERGER:

i. Post Merger EPS (Without Synergy) = A B

A B

PAT + PATN + N × ER


...................................................................... 108 ..............................................................

PATA = Earnings of Acquirer PATB = Earnings of Target NA = No. Of shares of acquirer ‘A’ NB = No. Of shares of target ‘B’ ER = Exchange ratio

ii. Post Merger EPS (With synergy) = A B

A B

PAT + PAT + Synergy in earningsN + N × ER

iii. Post Merger MPS = Post merger EPS × P/E NOTE: If P/E Ratio of Combination is provided, we use the same for computing value of the Merged firm . If it’s not provided, then P/E Ratio of Acquirer.

iv. Post Merger MPS (Without Synergy) = A B

A B

V + VN + N × ER

VA = Market cap of ‘A’ = MPSA × NA

VB = Market cap of ‘B’ = MPSA × NB

v. Post Merger MPS (with Synergy) = A B

A B

V + V + Synergy in earningsN + N × ER

vi. Maximum Exchange Ratio

MPSA = A B

A B

PAT + PAT P/EN + N × ER

×

↓ Solve for ER vii. Minimum Exchange Ratio

MPSB = A B

A B


× P/E × ER

NOTE: The No. of shares of A (Acquirer), before and after, remains the same. But the No. of shares of B (Target), before and after, does not remain the same. ∴ Before Merger, it is ‘NB’ but after Merger it is ‘NB × ER’


...................................................................... 109 ..............................................................

1. The following information is provided related to the acquiring firm Mark Limited and target firm Mask Ltd.:

Mark Mask EAT (`) 2,000 Lakhs 400 Lakhs No. of shares outstanding 200 Lakhs 100 Lakhs P/E Ratio (times) 10 5

Required : (i) What is the swap ratio based on current market prices? (ii) What is the EPS of Mark Ltd after acquisition? (iii) What is the expected market price per share of Mark Ltd after acquisition,

assuming PE ratio of Mark Ltd remains unchanged? (iv) Determine the market price of the merged firm. (v) Calculate gain/loss for shareholders of the two independent companies after

acquisition.

Ans. EPSA = A

A

PATN

= 2,000L200

` = ` 10/- share

P/EA = 10 times MPSA = P/EA × EPSA = 10 times × ` 10 = ` 100/-

EPSB = B

B

PATN

= 400L100

` = ` 4/-

P/EB = 5 times MPSB = P/EB × EPSB = 5 times × ` 4 = ` 20/-

i. Swap Ratio (Based on MPS) = B

A

MPSMPS

= 20100

= 0.2

ii. Post Merger EPS = A B

A B


= 2000 + 400200 + 100 × 0.2

= ` 10.91

iii. Post Merger MPS = Post Merger EPS × P/E = ` 10.91 × 10 times = ` 109.10 iv. Post Merger Market Price = Post merger MPS × Post Merger No. of shares = ` 109.10 × [200 + (100 × 0.2)] = ` 24,002 lakhs v.

A B Wealth before ` 100 × 200 Lakhs Shares

= ` 20,000 Lakhs ` 20 × 100 Lakhs Shares

= ` 2,000 Lakhs Wealth after ` 109.10 × 200 Lakhs Shares

= ` 21,820 Lakhs ` 109.10 × (100 × 0.2) Lakhs shares

= ` 2,182 Lakhs +` 1,820 Lakhs + ` 182 Lakhs


...................................................................... 110 ..............................................................

2. The CEO of Ganga Ltd. is considering the acquisition of Yamuna Ltd. The basic data of the two companies are given as follows:

Ganga Ltd. Yamuna Ltd. No. of shares 2,00,000 1,20,000 Share price ` 450 ` 100 Expected EPS ` 25 ` 7.50 Expected Dividend per share ` 15 ` 5.25

The above data assumes 5% p.a. growth in the earnings and dividends. However, under the new management, the growth will be 7.5% without any further investment. The exchange ratio of 1 for 3 is being considered. Find the cost of acquisition. What is the gain from the acquisition?

Ans. Stock Deal: → The sum mentions ‘Expected Dividend’ which represent 5% growth for Yamuna. → Since Ke is not provided in the sum, we need to back calculate using the existing

data. → The data provided conforms to dividend discount model (DDM) and hence, we

would use the same to compute the value of Yamuna with growth rate of 7.5% Given: D1 = D0 (1+ g) ` 5.25 = D0 (1 + 0.05) ∴ D0 = ` 5 ∴ New D1 = ` 5 (1.075) = ` 5.375 Since Ke is not provided,

P0 = 1

e c

DK - g

`100 = e

5.25K - 0.05

∴ Ke = 10.25% → Computation of Value of B Post merger

P0 = 1

e c

DK - g

= 5.37510.25% - 7.5%

`

= ` 195.45

Post Merger MPS = A B

A B

V + VN + N × ER

= ( 450 × 2L) + ( 195.45 × 1.2L)2L + 1.2L × 1/3

` `

= ` 472.725


...................................................................... 111 ..............................................................

VAB = Post Merger MPS (NA + NB × ER) = ` 472.725 × (2L + 1.2L × 1/3) = ` 1134.54L Cost = VA × ∝ - VB

= ` 1134.54L × 1.2L × 1/32L + 1.2L × 1/3

- (` 100 × 1.2 L) = ` 69.09L

Gain = VAB – VA - VB = ` 1134.54 L – (` 450 × 2L) – (` 100 × 1.2 L) = ` 114.54L 3. Vishakha Ltd is considering the acquisition of Parthasarthy Ltd. The values of the

two firms as separate entities are ` 11m and ` 5m respectively. The combined business will result in cash synergy gain ` 0.70m annually for perpetuity. The cost of capital is 10%. The purchase consideration can be paid either in cash ` 14m or 48% of post merger shares of Vishakha Ltd.

(i) What is the gain from the merger? (ii) What is the cost of cash offer? (iii) What is the cost of the stock alternative? (iv) Which alternative would you recommend? Ans. VA = ` 11m VB = ` 5m Synergy gain p.a. (perpetuity) = ` 0.70m. ; Ke = 10%

→ Value of synergy = 0.70m10%

` = ` 7m = 1Dke

i. Gain from merger = VAB – VA- VB = ` 7m (Since it includes wealth of A and B + Synergy) ii. Cost of Cash offer = Cash paid – VB = ` 14m – ` 5m = ` 9m iii. Cost of Stock Offer = VAB × ∝ -VB =` (11+5+7) m ×48% - ` 5m = ` 6.04 m iv. We would recommend Vishakha ltd to go for stock offer as the cost would be relatively

lower. 4. The share capital of Companies X and Y consist of 75,000 shares of ` 100/- each

and 25,000 shares of ` 100/- each respectively. Company X plans to make an acquisition of Y Ltd. By exchange of 4 shares for every 5 shares in Y Ltd. The cost of equity for X, Y and combined entity XY Ltd. are 15%, 16% and 14% respectively.


...................................................................... 112 ..............................................................

The cash flows (EBIT (1 - t) +Depreciation) are likely to be as follows for a period of 5 year The terminal year cash flows are likely to grow by 5% annually from year 6 in each case:

Years 1 2 3 4 5 X Ltd. 15 16 17 18 19 Y Ltd. 4 5 6 7 8

XY Ltd. 20 22 24 26 28 i. Evaluate the proposal and give your comments on the scheme of merger. ii. If the shares swap exchange ratio is changed to 4.5 shares of X Ltd. for every

5 shares of Y Ltd., whether the merger scheme is viable. if so, allocate merger gain between the two companies again.

Ans. i. Nx = 75,000 ; Ny = 25,000 ; ER = 4/5 Ke(X) = 15% ; Ke(Y) = 16% ; Ke(XY) = 14% Computation of Value for X Ltd. • Value in gs:

Year CF(` ) Lakhs PV @ 15% PV 1 15 0.870 13.05 2 16 0.756 12.096 3 17 0.658 11.186 4 18 0.572 10.296 5 19 0.497 9.443

` 56.071 L • Value in gc:

VOF5 = 6

e c

CFK - g

= 5

e c

CF (1 + gc)K - g

= 19(1.05)15% - 5%

= ` 199.5 L

PV of VOF5 @ t = 0

= 5199.5

(1.15)= `199.5 L × 0.497 = ` 99.1515 L

∴ Value of X (Vx) = ` 56.071 L+ ` 99.1515 L = ` 155.2225 L

∴ MPSx = 155.2225L0.75L

= ` 206.96


...................................................................... 113 ..............................................................

Computation of Value of Y Ltd. • Value in gs

Year CF(` ) Lakhs PV @ 16% PV 1 4 0.862 3.448 2 5 0.743 3.715 3 6 0.641 3.846 4 7 0.552 3.864 5 8 0.476 3.808

` 18.681L • Value in gc

VOF5 = 6

e c

CFK - g

= 5

e c

CF (1 + gc)K - g

= 8(1.05)16% - 5%

= ` 76.36 L

PV of VOF5 @ t = 0

= 576.36

(1.16)= ` 36.35 L

∴ Value of Y (VY) = `18.6810 L + `36.35 L = ` 55.03 L

∴ MPSY = 55.03L0.25L

= ` 220.12

→ Computation of Value of XY Ltd

• Value in gs Year CF(` ) Lakhs PV @ 14% PV

1 20 0.877 17.540 2 22 0.769 16.918 3 24 0.675 16.200 4 26 0.592 15.392 5 28 0.519 14.532 ` 80.582 L

• Value in gc

VOF5 = 6

e c

CFK - g

= 5

e c

CF (1 + gc)K - g

= 28(1.05)14% - 5%

= ` 326.67 L

PV of VOF5 @ = 0

= 5326.67(1.14)

= `169.54 L

∴ Value of X & Y (VXY) = ` 169.54 L + ` 80.582 L = ` 250.12L


...................................................................... 114 ..............................................................

Vx = ` 155.22 L MPSx= ` 206.96 Vy = ` 55.03 L MPSy = ` 220.12 Vxy = ` 250.12 L

X Y Wealth Before ` 206.96 ` 220.12 Wealth After ` 263.28 ` 263.28 × 4/5

` 56.32 (`9.5)

Since losses, Y Ltd may not be interested.

i. Post Merger MPS = xy

x y

VN + N × ER

= 250.12L0.75 + 0.25 × 4/5

`

= ` 263.28

ii. Post Merger MPS = 250.12L0.75 + 0.25 × 4.5/5

`

= ` 256.53

X Y Wealth before ` 206.96 ` 220.12 Wealth after ` 256.53 ` 256.53 ×

4.5/5 ` 49.70 ` 10.86

Here, Merger is viable. 5. Bank 'R' was established in 2005 and doing banking in India. The bank is facing

DO OR DIE Situation. There are problems of Gross NPA (Non Performing Assets) at 40% & CAR/CRAR (Capital Adequacy Ratio/ Capital Risk Weight Asset Ratio) at 4%. The net worth of the bank is not good. Shares are not traded regularly. Last week, it was traded @ ` 8 per share.

RBI Audit suggested that bank has either to liquidate or to merge with other bank. Bank 'P' is professionally managed bank with low gross NPA of 5%.It has Net NPA as 0% and CAR at 16%. Its share is quoted in the market @ ` 128 per share. The board of directors of bank 'P' has submitted a proposal to RBI for take over of bank 'R' on the basis of share exchange ratio. The Balance Sheet details of both the banks are as follows:


...................................................................... 115 ..............................................................

` In Lakhs Bank R Bank P Paid up share capital 140 500 Reserves & Surplus 70 5,500 Deposits 4,000 40,000 Other liabilities 890 2,500 Total Liabilities 5,100 48,500 Cash in hand & with RBI 400 2,500 Balance with other banks - 2,000 Investments 1,100 15,000 Advances 3,500 27,000 Other Assets 100 2,000 Total Assets 5,100 48,500

It was decided to issue shares at Book Value of Bank 'P' to the shareholders of

Bank 'R'. All assets and liabilities are to be taken over at Book Value. For the swap ratio, weights assigned to different parameters are as follows:

Gross NPA 30% CAR 20% Market price 40% Book value 10%

(a) What is the swap ratio based on above weights? (b) How many shares are to be issued? (c) Prepare Balance Sheet after merger. (d) Calculate CAR & Gross NPA % of Bank 'P' after merger. Ans. (a) COMPUTATION OF SWAP RATIO

Gross NPA = P

R

GNPAGNPA

= 540

= 0.125

CAR = R

P

CARCAR

= 416

= 0.25

Market Price = R

P

MPSMPS

= 8128

= 0.0625

WN: BVPSR = Total Book valueNo. of shares

= 140 + 7014

= ` 15

No. of shares of R = Rs.140LRs.10

= 14L

BVPSP = 500 + 550050

= ` 120


...................................................................... 116 ..............................................................

No. of shares of P = 500L 10

`

` = 50L

→ BVPS = R

P

BVPSBVPS

= 15120

= 0.125

→ Swap ratio = (0.3 × 0.125) + (0.2 × 0.25) + (0.4 × 0.0625) + (0.10 × 0.125) = 0.125 (b) NO. OF SHARES TO BE ISSUED BY ‘P’ TO BANK ‘R’ = 14L × 0.125 = 1.75L (c) COMBINED BALANCESHEET OF ‘P’ AND ‘R’ → Combined paid up capital = ` 500L + (1.75L shares × ` 10 FV) = ` 517.5L So, after acquisition, Paid up capital increases by ` 17.5L because of R’s share but the

balancesheet of R before merger is `140L → Only ` 17.5 is transferred to paid up capital.

→ Reserves and surplus = ` 5,500L Capital Reserves = ` (140 – 17.5) L + ` 70 L = ` 192.5 L

Balance sheet

Liability Amt (`) Asset Amt (`) Paid up capital 517.50 Cash in hand and with RBI 2,900 Reserves and surplus 5,500.00 Balance with other banks 2,000 Capital reserves 192.50 Investments 16,100 Deposits 44,000.00 Advances 30,500 Other liabilities 3,390.00 Other assets 2,100 53,600.00 53,600

(d) CAR = Total capitalRisk weighted assets

GNPA = Gross NPAAdvances


...................................................................... 117 ..............................................................

Particulars Bank R Bank P Total Total Capital (140 + 70) =` 210L (500 + 5,500) = `6000L ` 6210L CAR 4% 16% Risk weighted Assets

210L4%

`

= ` 5250L 6,000L

16%`

= ` 37,500L

` 42,750

∴ Combined CAR (After merger) = 6,21042,750

× 100 = 14.53%

Particulars Bank R Bank P Total

GNPA % 40% 5% Advances 3,500L 27,000L 30,500L ∴ GNPA (3,500L × 40%) =1,400 (27,000L × 5%) = 1,350 2,750

∴ Combined GNPA % = 2,750L30,500L

× 100 = 9.02%


...................................................................... 118 ..............................................................

VALUE AT RISK (VAR)

INTRODUCTION: Eg : Suppose a fund manager holds a portfolio of $ 1,00,000 and he wants to know what would be the maximum loss in a day and assume by some statistical method, he comes to know that his 5% VAR for a day = $12,500. It means: ⟶ We are 95% confident that the losses will not exceed $ 12,500 in a single day. ⟶ There is a 5% chance that portfolio losses will be $ 12,500 or more. What we learn in this chapter: a. VAR Definition b. VAR Calculation c. VAR Conversion VAR Definition: a. VAR is the Dollar/ Percentage loss to the portfolio value that will be equalled or

exceeded x% of the time. b. We can calculate 1%, 5% and 10% VAR and it can be given as VAR(1%), VAR(5%)

and VAR (10%). c. A VAR (1%) of $15,000 indicates that there is 1% chance that on any given day, the

portfolio could experience a loss of $ 15,000 or more.

VAR CALCULATION VAR can be computed by three methods: • Delta Normal Method • Monte Carlo Simulation • Historical simulation NOTE: In our curriculum we are supposed to focus on’ Delta Normal Method’ on the basis of syllabus provided by ICAI. Delta Normal Method: This method has got exhaustive application of ‘Normal Distribution Curve’ or Z Table. By this, we assume the asset returns or prices are “Normally” Distributed and it does not have Skewness or Kurtosis. VAR can be computed with the help of following equation.

KHETAN EDUCATION VALUE AT RISK

...................................................................... 119 ..............................................................

VAR = x × σ × z X = Amount on which we intend to compute VAR σ = Standard deviation z = Corresponding z factor for VAR % The Z values for: VAR (1%) = 2.33 VAR (5%) = 1.65 VAR (10%) = 1.28 VAR Conversion: Eg: Assume the daily VAR(5%) on dollar basis of a particular asset to be $17,000. Compute

the weekly (5days), Monthly (20days), Semi annual (125 days) and Annual (250 days).

⟶ Weekly VAR = $17,000 × √5

⟶ Monthly VAR = $17,000 × √20

⟶ Semi-Annually VAR = $17,000 × √125

⟶ Annual VAR = $17,000 × √250 1. A Fund is long on 250 shares trading at ` 50 each. Find out 95% daily VAR given

annual volatility = 12% p.a. Ans. VAR = x × σ × z X = Amount on which we intend to compute VAR σ = Standard deviation z = Corresponding z factor for VAR % Annual VAR = (` 50 × 250) × 1.65 × 12% = ` 2,475

Daily VAR = 2475250

` = ` 156.55

Or,

Daily VAR = (` 50 × 250) × 1.65 × 12%

250 = ` 156.75

2. Consider the data in the first sum. A person has a long call position on 250 shares.

Given N(d1) = 0.5948 . Find out 95% daily VAR on call. Ans. Delta of Call = N(d1) ‘Long Call’(C+) on 250 shares = No. of calls × Delta of call = Long stock position = 250 × 0.5948 = 148.7 Shares or 149 shares approx.


...................................................................... 120 ..............................................................

VAR = x × σ × z

VAR = (` 50 × 149) ×1.65 × 12%

250 = ` 93.30 ≈ ` 93.423

3. A portfolio contains ` 10,000 worth of stocks A and ` 6000 worth of stock B. The

annual Volatilities of stock A and B are 12% and 16% respectively. The coefficient of correlation is 0.4.

a. Calculate the 95% quarterly VAR for stock A position. b. Calculate the 95% quarterly VAR for stock B position. c. Calculate the combined VAR. Ans. a. VAR on long stock position for A = x × σ × z

= ` 10,000 × 0.12 × 62.5250

× 1.65 = ` 990

b. VAR on long stock position for B = x × σ × z

= ` 6,000 × 0.16250

× √62.5 × 1.65 = ` 792.43

c. Combined VAR Computation.

σP = 2 2 2 2AB A BW Aσ A + W Bσ B + 2 WA × WB × r × σ × σ×

σP = 2 2 2 2(10,000) + (0.12) + (6,000) (0.16) + 2 × 10,000 × 6000 × 0.4 × 0.12 × 0.16

σP = ` 1,811.96 (Annual )

VAR = x × σ × z = 1811.96

250 × 62.5 × 1.65 = 1,811.96

1,5.811 × 7.91 × 1.65 = ` 1,495.81

≈ ` 1,494.87 4. An Indian firm has $ 20,000 payable after two months. The spot rate is ` 50.00/$.

Annualised volatility = 10%. Dollar Interest Rate of 6% p.a. Find out the 95% daily VAR.

Ans. Since the sum provides spot for today, whereas payable is standing at the end of 2nd month, we need to compute 2 months PV for $ 20,000 @ 6% p.a.

PV = $ 20,000 × 121 + 0.06 ×

12

= $ 19,802

∴ VAR = ($ 19,802 × ` 50/$) × 10%

250 × 1.65 = ` 10,333.11

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