finance - answers to homework assignment

Financial Management Assignment

Hussein Saad Abdulla

ID # P09000658

Chapter 1

Introduction to Corporate Finance

1. The Financial Management Decision Process What are the three types of financial

management decisions? For each type of decision, give an example of a business

transaction that would be relevant.

The three types of financial management decisions are:

a. Capital budgeting. In capital budgeting, the financial manager tries to identify

investment opportunities that are worth more to the firm than they cost to

acquire. For example, for a large retailer such as Wal-Mart, deciding whether or

not to open another store would be an important capital budgeting decision.

Similarly, for a software company such as Oracle or Microsoft, the decision to

develop and market a new spreadsheet would be a major capital budgeting

decision.

b. Capital structure. For example, what mixture of debt and equity should the firm

use to fund its operations? Also, what are the least expensive sources of funds for

the firm? Whether to issue new equity and use the proceeds to retire outstanding

debt?

c. Working capital management. The term working capital refers to a firm’s short-

term assets, such as inventory, and its short-term liabilities, such as money owed

to suppliers. An example would be modifying the firm’s credit collection policy

with its customers.

7. Primary versus Secondary Markets You’ve probably noticed coverage in the financial

press of an initial public offering (IPO) of a company’s securities. Is an IPO a primary-

market transaction or a secondary-market transaction?

An IPO is a primary-market transaction



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8. Auction versus Dealer Markets What does it mean when we say the New York Stock

Exchange is an auction market? How are auction markets different from dealer

markets? What kind of market is Nasdaq?

In auction markets like the NYSE, brokers and agents meet at a physical location (the

exchange) to match buyers and sellers of assets.

Auction markets differ from dealers market in two ways. First, an auction market or

exchange has a physical location (like Wall Street) whereas in dealers’ market, the

dealers operate at dispersed locations. Second, in auction market, the dealers try to

match buyers and sellers with each others, whereas in dealers’ market, the dealers

buy and sell assets for themselves and communicate with each other either

electronically or literally over-the-counter. NASDAQ is a dealers’ market.



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Chapter 5

Introduction to Valuation: The Time Value of Money

1. Present Value The basic present value equation has four parts. What are they?

The basic present value equation is:

PV = FV /(1 + r )t

There are only four basic parts to this equation: the present value (PV), the future

value (FV), the discount rate (r), and the life of the investment (t). Given any three of

these, we can always find the fourth.

2. Compounding What is compounding? What is discounting?

The process of reinvesting the interest earned on an investment for more than one

period is called compounding. Compounding the interest means earning interest on

interest.

The process of finding the present value of a future cash flow discounted at the

appropriate discount rate is called discounting.

3. Compounding and Period As you increase the length of time involved, what happens

to future values? What happens to present values?

As we increase the length of time involved the future values of an investment will

increase (Figure 5.2).



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However, as the length of time until payment grows, present values decline. As

illustrated in Figure 5.3, present values tend to become small as the time horizon

grows.

4. Compounding and Interest Rates What happens to a future value if you increase the

rate r? What happens to a present value?

If we increase the rate r, the future value of an investment will increase (Figure 5.2).

On the other hand, the present value of an investment will decrease with an increase

in the rate r (Figure 5.3)

6. Time Value of Money Why would TMCC be willing to accept such a small amount

today ($1,163) in exchange for a promise to repay about 9 times that amount

($10,000) in the future?

It’s a reflection of the time value of money. TMCC gets to use the $1,163

immediately. If TMCC uses the money wisely, it will be worth more than $10,000 in

thirty years.



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Questions and Problems (page 143-144)

1. Simple Interest versus Compound Interest Jaipur Bank pays 7 percent simple interest

on its savings account balances, whereas Mathura Bank pays 7 percent interest

compounded annually. If you made a 20,000 rupee deposit in each bank, how much

more money would you earn from your Mathura Bank account at the end of 15

years?

For the account with Jaipur Bank:

FV = 20,000 x (1 + 15 x 0.07) = 41,000 rupees

For the account with Mathura Bank:

FV = PV x (1 + r)t = 20,000 X (1 + 0.07)15 = 55,180.6 rupees

Difference in investment = 55,180.6 - 41,000 = 14,180.6 rupees

2. Calculating Future Values For each of the following, compute the future value:

Present Value Years Interest Rate Future Value

€ 2,250 19 10% € 13,760.8

9,310 12 8 23,444.16

76,355 4 22 169,151.87

183,796 8 7 315,795.75

To find the FV of a lump sum, we use:

FV = PV x (1 + r)t

3. Calculating Present Values For each of the following, compute the present value:


$ 11,529.8 6 5% $ 15,451

20,154.9 9 11 51,557

29,958.3 23 16 910,020

24,024.1 18 19 550,164

To find the PV of a lump sum, we use:



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PV = FV / (1 + r)t

4. Calculating Interest Rates Solve for the unknown interest rate in each of the

following:


£ 265 2 7.63% £ 307

740 9 2.15 896

39,000 15 9.97 162,181

46,523 30 8.12 483,500

To find the applicable rate for each investment, we use:

r = (FV/PV)1/t – 1

5. Calculating the Number of Periods Solve for the unknown number of years in each of

the following:


¥ 625,000 9.36 8% ¥ 1,284,000

810,000 24.81 7 4,341,000

18,400,000 16.19 21 402,662,000

21,500,000 8.2 29 173,439,000

To find the corresponding period for each investment, we use:

t = log(FV/PV)/log(1+r)

18. Calculating Future Values You have just made your first 250,000 yen contribution to

your retirement account. Assuming you earn a 10 percent rate of return and make no

additional contributions, what will your account be worth when you retire in 45

years? What if you wait 10 years before contributing? (Does this suggest an

investment strategy?)

To find the future worth of the retirement account, we use:



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FV = PV x (1 + r)t

FV = ¥250,000 x (1 + .10)45 = ¥ 18,222,620.92

If we wait 10 more years before contributing to the account, t = 35 years, then

FV = ¥250,000 x (1 + .10)35 = ¥ 7,025,609.21

It is better to invest early as the account value after 45 years is more than double its

value after 35 years.

20. Calculating the Number of Periods You expect to receive $160,000 yuan at

graduation in two years. You plan on investing it at 10 percent until you have

1,130,400 yuan. How long will you wait from now?

To find the investment period, we use:

t = log(FV/PV)/log(1+r)

t = log(1,130,400/160,000)/log(1+0.10) = 20.51 years

Total time to reach target = 20.51 + 2 = 22.51 years



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Chapter 6

Discounted Cash Flow Valuation

Questions and Problems

1. Present Value and Multiple Cash Flows Amman Beauty Products has identified an

investment project with the following cash flows, denominated in millions of dinars. If

the discount rate is 8 percent, what is the present value of these cash flows? What is

the present value at 16 percent? At 30 percent?

Year Cash Flow

1 JOD 1,200

2 600

3 855

4 1,480

To solve this problem, we must find the PV of each cash flow and add them. To find

the PV of a lump sum, we use the equation:

PV = FV / (1 + r)t

PV @ 8% = 1,200 / (1 + 8%)1 + 600 / (1 + 8%)2 + 855 / (1 + 8%)3 + 1,480 / (1 + 8%)4

PV @ 8% = 1,111.11 + 514.4 + 678.73 + 1,087.84 = JOD 3,392.08

PV @ 16% = 1,200 / (1 + 16%)1 + 600 / (1 +16%)2 + 855 / (1 + 16%)3 + 1,480 / (1 +16%)4

PV @ 16% = 1,034.48 + 445.90 + 547.76 + 817.39= JOD 2,845.53

PV @ 30% = 1,200 / (1 + 30%)1 + 600 / (1 +30%)2 + 855 / (1 + 30%)3 + 1,480 / (1 +30%)4

PV @ 30% = 923.08 + 355.03 + 389.17 + 518.19 = JOD 2,185.47

2. Present Value and Multiple Cash Flows Investment X offers to pay you 40,000 riyals

per year for nine years, whereas Investment Y offers to pay you 60,000 riyals per year

for five years. Which of these cash flow streams has the higher present value if the

discount rate is 5 percent? If the discount rate is 22 percent?

This two payment streams represent annuity payment and its present value can be

calculated using the equation:



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PV=C [ 1− 1

(1+r )t

r ]At 5% interest rate:

PV X@5%=40,000[ 1− 1

(1+5%)9

5% ]=40,000 x 7.1078=284,312.87 riyalsPV Y@5%=60,000[ 1− 1

(1+5%)5

5% ]=60,000x 4.3295=259,768.6 riyalsAt 22% interest rate:

PV X@22%=40,000[ 1− 1

(1+22%)9

22% ]=40,000 x3.7863=151,451.40 riyalsPV Y@22%=60,000 [ 1− 1

(1+22% )5

22% ]=60,000 x 2.8636=171,818.39 riyalsCash flow X has a greater Present Value at a 5 percent interest rate, but a lower PV at a

22 percent interest rate. The reason is that X has more cash flows than Y (9 vs 5). At a

lower interest rate, the total cash flow is more important since the cost of waiting (the

interest rate) is not as great. At a higher interest rate, Y is more valuable since its large

cash flows happen earlier. At the higher interest rate, having the cash flows early are

more important since the cost of waiting (the interest rate) is so much greater



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3. Future Value and Multiple Cash Flows Ridhi Sidhi Jewellers has identified an

investment project with the following cash flows, denominated in thousands of

rupees. If the discount rate is 8 percent, what is the future value of these cash flows

in Year 4? What is the future value at a discount rate of 11 percent? At 24 percent?

Year Cash Flow

1 INR 800

2 900

3 1,000

4 1,100

To solve this problem, we must find the FV of each cash flow and add them. To find

the FV of a lump sum, we use the equation:

FV = PV (1 + r)t

FV @ 8% = 800 (1 + 8%)3 + 900 (1 + 8%)2 + 1,000 (1 + 8%)1 + 1,100

PV @ 8% = 1,007.77 + 1,049.76 + 1,080 + 1,100 = 4,237.53 rupees

PV @ 11% = 800 (1 + 11%)3 + 900 (1 +11%)2 + 1,000 (1 + 11%)1 + 1,100

PV @ 11% = 1,094.1 + 1,108.89 + 1,110 + 1,100 = 4,412.99 rupees

PV @ 24% = 800 (1 + 24%)3 + 900 (1 +24%)2 + 1,000 (1 +24%)1 + 1,100

PV @ 24% = 1,525.3 + 1,383.84 + 1,240 + 1,364 = 5,513.14 rupees

The cash flow at Year 4 is simply added to the FV of the other cash flows.

4. Calculating Annuity Present Value An investment offers $3,600 per year for 15 years,

with the first payment occurring one year from now. If the required return is 12

percent, what is the value of the investment? What would the value be if the

payments occurred for 40 years? For 100 years? Forever?

To calculate the present value for this annuity payment we use the equation:

PV=C [ 1− 1

(1+r )t

r ]For t = 15 years,



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PV=$3,600[ 1− 1

(1+12%)15

12% ]=$3,600 x 6.8108=$24,519.1For t = 40 years,

PV=$3,600[ 1− 1

(1+12%)40

12% ]=$ 3,600x 8.2438=$29,677.60For t = 100 years,

PV=$3,600[ 1− 1

(1+12%)100

12% ]=$3,600 x8.333=$29,999.64For t = ∞ years,

PV=Cr=$ 3,60012%

=$ 30,000.0

As the length of the annuity payments increases, the present value of the annuity

approaches the present value of the perpetuity. The present value of the 40 year

annuity and the present value of the perpetuity imply that the value today of all

perpetuity payments beyond 40 years is only $322.4

5. Calculating Annuity Cash Flows If you put up 294,000 Egyptian pounds today in

exchange for a 7.65 percent, 14-year annuity, what will the annual cash flow be?

To calculate the annual cash flow (C) for this annuity payment we use the equation:

PV=C [ 1− 1

(1+r )t

r ]294,000=C [ 1− 1

(1+7.65%)14

7.65% ]C=294,000÷8.4145=34,939.64 Egyptian pounds



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12. Calculating EAR Find the EAR in each of the following cases:

Stated Rate (APR) Number of Times Compounded

Effective Rate (EAR)

11% Quarterly

7 Monthly

9 Daily

18 Infinite

To find the EAR, we use the equation:

EAR = [1 + (APR / m)]m – 1

EAR = [1 + (.11 / 4)]4 – 1 = .1146 or 11.46%

EAR = [1 + (.07 / 12)]12 – 1 = .0723 or 7.23%

EAR = [1 + (.09 / 365)]365 – 1 = .0942 or 9.42%

To find the EAR with continuous compounding, we use the equation:

EAR = eq – 1

EAR = e.18 – 1 = .1972or 19.72%

20. Calculating Loan Payments You want to buy a new sports coupe for €56,850, and the

finance office at the dealership has quoted you a 5.6 percent APR loan for 60 months

to buy the car. What will your monthly payments be? What is the effective annual

rate on this loan?

To calculate the monthly payment (C) for this loan we use the equation:

PV=C [ 1− 1

(1+r )t

r ]Where, r = 5.6 / 12 = 0.4667

€ 56,850=C [ 1− 1

(1+0.4667%)60

0.4667% ]



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C=€ 56,850÷52.2265=€ 1,088.52

To calculate the effective annual rate for this loan we use the equation:

EAR=[1+ rm ]m

−1=[1+5.6%12 ]12

−1=0.0575∨5.75%

21. Calculating Number of Periods One of your customers is delinquent on his accounts

payable balance. You’ve mutually agreed to a repayment schedule of 500 Sudanese

dinars per month. You will charge .9 percent per month interest on the overdue

balance. If the current balance is 22,800 dinars, how long will it take for the account

to be paid off?

To calculate the length of time (t) for this loan we use the equation:

PV=C [ 1− 1

(1+r )t

r ]22,800=500[ 1− 1

(1+0.9%)t

0.9% ]22,800x 0.9%

500=1− 1

(1+0.9% )t

1

(1+0.9% )t=1−0.41=0.59

(1+0.9% )t= 10.59

=1.696

t=ln (1.696 )ln (1.009 )

=58.96=59months∨4 years 11months

23. Valuing Perpetuities Ghana Life Insurance Co. is selling a perpetuity contract that

pays GHC 1,150 monthly. The contract currently sells for GHC 58,000. What is the

monthly return on this investment vehicle? What is the APR? The effective annual

return?



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For this perpetuity contract, we use the equation:

PV=Cr

r= CPV

= 1,15058,000

=0.0198∨1.98% permonth

APR = 12 r = 12 x 1.98% = 23.79%

EAR=[1+ rm ]m

−1=[1+1.98% ]12−1=0.2653∨26.53%

24. Calculating Annuity Future Values You are to make monthly deposits of $300 into a

retirement account that pays 11 percent interest compounded monthly. If your first

deposit will be made one month from now, how large will your retirement account be

in 20 years?

To calculate the annuity Future Value (FV), we use the equation:

FV=C [ (1+r )t−1r ]where, r = 11/12 = 0.9167% and t = 20 x 12 = 240 months

FV=$300[ (1+0.9167%)240−10.9167% ]=$ 259,691.43

28. Discounted Cash Flow Analysis If the appropriate discount rate for the following cash

flows is 9.75 percent per year, what is the present value of the cash flows?

Year Cash Flow

1 CZK 2,800

2 0

3 8,100



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4 1,940

To solve this problem, we must find the PV of each cash flow and add them. To find

the PV of a lump sum, we use the equation:

PV = FV / (1 + r)t

PV = 2,800 / (1 + 9.75%)1 + 0 / (1 + 9.75%)2 + 8,100 / (1 + 9.75%)3 + 1,940/ (1 + 9.75%)4

PV = 2,551.25 + 0 + 6,127.33 + 1,337.16 = CZK 10,015.74



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Chapter 7

Interest Rate and Bond Valuation

Questions and Problems

3. Bond Prices Borderline Co. issued 11-year bonds one year ago at a coupon rate of 8.6

percent. The bonds make semiannual payments. If the YTM on these bonds is 7.4

percent, what is the current bond price?

To find the price of this bond, we need to realize that:

The maturity of the bond is 10 years. The bond was issued one year ago, with 11

years to maturity, so there are 10 years left on the bond.

The coupons are semiannual, so we need to use the semiannual interest rate

(3.7%) and the number of semiannual periods (20).

Using par value (FV) of $1,000 for the Bond (annuity = $1,000 x 4.3% = $43), then

the price of the bond is:

P = PV of annuity + PV of Par Value

P=C [ 1− 1

(1+r )t

r ]+FV [ 1(1+r )t ]

P=$ 43[ 1− 1

(1+3.7%)20

3.7% ]+$1,000 [ 1(1+3.7%)20 ]

P = $41.00(13.9586) + $1,000(0.48353) = $558.34 + $483.53=$1,041.87

4. Bond Yields Aragorn Co. has 10 percent coupon bonds on the market with nine years

left to maturity. The bonds make annual payments. If the bond currently sells for

£884.50 what is its YTM?

To find the YTM, we need to realize that:



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The bonds make annual payment and there are 9 years left to maturity, so the

number of periods (t) is equal to 9.

Using a par value (FV) of £1,000 for the Bond (annuity = £1,000 x 10% = £100),

then the YTM of the bond is calculated from the equation:


P=C [ 1− 1

(1+YTM )t

YTM ]+FV [ 1(1+YTM )t ]

£884.50=£ 100[ 1− 1

(1+YTM )9

YTM ]+£ 1,000[ 1(1+YTM )9 ]

We can only use trial and error method to find the value of YTM as shown in the

following table:

YTM LHS RHS

10% £884.50 £100(5.759)+ £1,000(0.424)= £1,000

13% £884.50 £100(5.1316)+ £1,000(0.3329)= £846.0

12% £884.50 £100(5.328)+ £1,000(0.3606)= £893.4

12.5% £884.50 £100(5.228)+ £1,000(0.3464)= £869.30

12.18 £884.50 £100(5.292)+ £1,000(0.3554)= £884.6

The YTM for this bond is around 12.18%

16. Interest Rate Risk Both Bond Yao and Bond Ming have 10 percent coupons, make

semiannual payments, and are priced at par value. Bond Yao has 2 years to maturity,

whereas Bond Ming has 15 years to maturity. If interest rates suddenly rise by 2

percent, what is the percentage change in the price of Bond Yao? Of Bond Ming? If

rates were to suddenly fall by 2 percent instead, what would the percentage change

in the price of Bond Yao be then? Of Bond Ming? Illustrate your answers by graphing



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bond prices versus YTM. What does this problem tell you about the interest rate risk

of longer-term bonds?

Using a par value (FV) of $1,000 for both Bond Yao and Bond Ming, the coupon

annual payments would be $1,000 x 10% = $100 for both Bonds. As it is paid

semiannually, the value (C) to use in the calculations = $100 -:- 2= $50.

Both Bonds make semiannual payment, so Bond Yao the periods remaining to

maturity are 2 x 2 = 4 periods whereas for Bond Ming the periods remaining to

maturity are 15 x 2 = 30 periods.

Initially, the Bonds are priced at par, which means that YTM is equal to coupon rate of

10%. When the interest rate rise by 2%, i.e. YTM becomes 12% (applicable rate per

period is 12% -:-2 = 6%), the price of the Bonds will vary according to the equation:

P=C [ 1− 1

(1+YTM )t

YTM ]+FV [ 1(1+YTM )t ]

PYao=$50 [ 1− 1

(1+6%)4

6% ]+$ 1,000[ 1(1+6%)4 ]

PYao=$173.25+$792.1=$ 965.35

%Change∈PYao=$ 965.35−$1,000

$ 1,000=−0.0347∨−3.47%

PMing=$50 [ 1− 1

(1+6%)30

6% ]+$ 1,000[ 1(1+6%)30 ]

PMing=688.24+$174.1=$862.35

%Change∈PMing=$862.35−$ 1,000

$1,000=−0.1377∨−13.77%

When the interest rate fall by 2%, i.e. YTM becomes 8% (applicable rate per period is

8% -:-2 = 4%), the price of the Bonds will vary according to the equation:



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P=C [ 1− 1

(1+YTM )t

YTM ]+FV [ 1(1+YTM )t ]

PYao=$50 [ 1− 1

(1+4% )4

4% ]+$1,000 [ 1(1+4%)4 ]

PYao=$181.495+$ 854.804=$1,036.3

%Change∈PYao=$1,036.3−$ 1,000

$1,000=0.0363∨3.63%

PMing=$50 [ 1− 1

(1+4%)30

4% ]+$1,000 [ 1(1+4% )30 ]

PMing=864.6+$308.3=$1,172.92

%Change∈PMing=$1,172.92−$1,000

$1,000=0.1729∨17.29%

It is noted from the graph that, everything else staying the same, the longer the

maturity of a bond, the greater is its price sensitivity to changes in interest rates.

6% 8% 10% 12% 14%800

850

900

950

1,000

1,050

1,100

1,150

1,200

PYao PMing



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19. Bond Yields Asian Exporters PLC has 8.4 percent coupon bonds on the market with 10

years to maturity. The bonds make semiannual payments and currently sell for 104

percent of par. What is the current yield on the bonds? The YTM? The effective

annual yield?

For this problem we have:

Semiannual payment with 10 years to maturity, so t = 20 periods

The coupon rate is 8.4 percent, paid on semiannual basis, so the coupon payment

(C) is 4.2% of par value. Using a par value of $1,000 for the Bond, then the

semiannual coupon payment is $42.

The PV of the bond is 104% of par value, i.e. = 104% x $1,000 = $1,040

The current yield of the bond = annual coupon payment / current Bond price

Current Yield = (2 x $42) / $1,040 = 0.08077 or 8.077 %

To find the YTM for the bond we use the equation:


P=C [ 1− 1

(1+r )t

r ]+FV [ 1(1+r )t ]

$1,040=$ 42[ 1− 1

(1+r)20

r ]+$1,000 [ 1(1+r )20 ]

We can only use trial and error method to find the value of Y as shown in the

following table:

r LHS RHS

3% $1,040 $42(14.8775)+ $1,000(0.55367)=

$1,178.53

4% $1,040 $42(13.59)+ $1,000(0.45638)= $1,027.18

3.9% $1,040 $42(13.7114)+ $1,000(0.46525)= $1,041.1



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3.91% $1,040 $42(13.6992)+ $1,000(0.4644)= $1039.77

3.908 $1,040 $42(13.7017)+ $1,000(0.4645)= $1,040.0

YTM = r x 2 = 3.908% x 2 = 7.816%

Effective AnnualYield (EAY )=[1+YTMm ]m

−1

Effective AnnualYield (EAY )=[1+ 7.816%2 ]2

−1

Effective AnnualYield (EAY )=1.07969−1=0.0796∨7.96%

24. Bond Prices versus Yields

a. What is the relationship between the price of a bond and its YTM?

b. Explain why some bonds sell at a premium over par value while other bonds sell

at a discount. What do you know about the relationship between the coupon rate

and the YTM for premium bonds? What about for discount bonds? For bonds

selling at par value?

c. What is the relationship between the current yield and YTM for premium bonds?

For discount bonds? For bonds selling at par value?

a. The bond price is the present value of the cash flows from the bond. The YTM is

the interest rate used in discounting the cash flows from the bond. The

relationship between the price of a bond and its YTM is expressed as:

Bond value = C x [1 - 1/(1 + YTM)t]/r + FV/(1 + YTM)t

Where FV is the face value of the bond paid at maturity, C is the coupon payment

per period, t is number of periods to maturity, and YTM is yield to maturity.

b. If the coupon rate is higher than the prevailing interest rate, the bond will sell at a

premium, since it provides periodic income in the form of coupon payments in

excess of that required by investors on other similar bonds. If the coupon rate is

lower than the prevailing interest rate, the bond will sell at a discount since it

provides insufficient coupon payments compared to that required by investors on



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other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for

discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par,

the YTM is equal to the coupon rate.

c. Current yield is defined as the annual coupon payment divided by the current

bond price. For premium bonds, the current yield exceeds the YTM, for discount

bonds the current yield is less than the YTM, and for bonds selling at par value,

the current yield is equal to the YTM.

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