gsb711-lecture-note-04-valuation-of-bonds-and-shares

GSB711 Managerial Finance – Topic 01 Page No. 1 GSB711 Managerial Finance – Topic 04 Page No. 1

Valuation of Bonds and Shares

Topic 04GSB711 – Managerial Finance

Readings: Chapter: Valuing Bonds (Pages 154 - 179)

Questions: 1, 4, 7 and Problems: 10, 14, 18, 19, 21 and 24.Chapter: Valuing Stocks (Pages 180 - 218)

Questions: 1, 3, 6 and Problems: 12, 17, 19, 24, 27 and 30.


Topics Covered….

• Valuation of Bonds– The Bond Market– Interest Rates and Bond Prices– Current Yield and Yield to Maturity– Bond Rates and Returns– The Yield Curve– Corporate Bonds and the Risk of Default


Topics Covered

• Valuation of Shares– Stocks and the Stock Market– Market Values, Book Values, and Liquidation Values– Valuing Common Stocks– Simplifying the Dividend Discount Model– Growth Stocks and Income Stocks– There Are No Free Lunches on Wall Street– Market Anomalies and Behavioral Finance


Bonds

Terminology• Bond - Security that obligates the issuer to

make specified payments to the bondholder.• Coupon - The interest payments made to the

bondholder.• Face Value (Par Value or Principal Value) -

Payment at the maturity of the bond. Please assume $1000 as Face Value unless otherwise stated.

• Coupon Rate - Annual interest payment, as a percentage of face value.


Bonds

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.

The coupon rate merely tells us what cash flow the bond will produce. Coupon payments are interest payments that we receive periodically when we invest in a bond.

Since the coupon rate is listed as a %, this misconception is quite common.


Bond Pricing

The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

PVcpn

r

cpn

r

cpn par

r t

( ) ( )

....( )

( )1 1 11 2


Bond Cash Flows


Bond Pricing

ExampleWhat is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.

95.081,1$

)0215.1(

050,1

)0215.1(

50

)0215.1(

50321

PV

PV


Bond Pricing

Example (continued)Q: How did the calculation change, given

semi-annual coupons versus annual coupon payments?


Bond Pricing

Example (continued)What is the price of the bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?

37.082,1$

)01075.1(

025,1

)01075.1(

25...

)01075.1(

25

)01075.1(

256521

PV

PV


Bond Pricing

Example (continued)What is the price of the bond if the required rate of return is 5.0 %?

000,1$

)050.1(

050,1

)050.1(

50

)050.1(

50321

PV

PV


Bond Pricing

Example (continued)What is the price of the bond if the required rate of return is 8 %?

69.922$

)08.1(

050,1

)08.1(

50

)08.1(

50321

PV

PV


Bond PricingExample (continued)Q: How did the calculation change, given

semi-annual coupons versus annual coupon payments?

Time Periods

Paying coupons twice a year, instead of once doubles the total number of cash flows to

be discounted in the PV formula.

Discount Rate

Since the time periods are now half years, the discount rate is also

changed from the annual rate to the half year rate.


Interest Rate Risk

• The value of the 5% bond falls as interest rates rise

700

800

900

1,000

1,100

1,200

0 2 4 6 8 10 12 14 16

Interest rate (%)

Bo

nd

pri

ce (

$)


Interest Rate Risk

-

500

1,000

1,500

2,000

2,500

3,000

0 2 4 6 8 10

YTM

$ B

on

d P

ric

e

30 yr bond

3 yr bond

When the interest rate equals the 5.0% coupon rate, both bonds sell at

face value


Bond Yields• Current Yield - Annual coupon payments

divided by bond price.• Yield To Maturity - Interest rate for which the

present value of the bond’s payments equal the price.


Bond Yields

Calculating Yield to Maturity (YTM=r)If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.

PVcpn

r

cpn

r

cpn par

r t

( ) ( )

....( )

( )1 1 11 2


Bond Yields

ExampleWhat is the YTM of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95.

95.081,1$

)1(

050,1

)1(

50

)1(

50321

PV

rrrPV

YTM = 2.15%


Bond Yields

WARNINGCalculating YTM by hand can be very tedious.

It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.


Bond Yields

Rate of Return - Earnings per period per dollar invested.

Rate of return =total income

investment

Rate of return =Coupon income + price change

investment


Bond Valuation Spreadsheet

Valuing bonds using a spreadsheet

5.0 % coupon 6.0% couponmaturing Feb 2011 10-year maturity

Settlement date 2/15/08 1/1/00Maturity date 2/15/11 1/1/10Annual coupon rate 0.05 0.06Yield to maturity 0.0215 0.07Redemption value (% of face value) 100 100Coupon payments per year 1 1

Bond price (% of par) 108.195 92.976

=PRICE(B7,B8,B9,B10,B11,B12)


Interest Rate Risk

600

700

800

900

1,000

1,100

1,200

1,300

1,400

0 5 10 15 20 25 30

Bo

nd

Pri

ce

Time to Maturity

Price path for Premium Bond

Price path for Discount Bond

Today Maturity


Bond Yield Spreadsheet

Finding yield to maturity using a spreadsheetFeb 2011 maturity bond, coupon rate = 5.0%, maturity = 3 years

Annual coupons Semiannual coupons

Settlement date 2/15/08 2/15/08Maturity date 2/15/11 2/15/11Annual coupon rate 0.05 0.05Bond price 108.195 108.195Redemption value (% of face value) 100 100Coupon payments per year 1 2

Yield to maturity (decimal) 0.0215 0.0216

=YIELD(B7,B8,B9,B10,B11,B12)


The Yield Curve

Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date.

Yield Curve - Graph of the term structure.


The Yield Curve

0

1

2

3

4

5

61 3 5 7 9

11

13

15

17

19

21

23

25

27

29

Maturity (years)

Yie

ld %

Treasury strips are bonds that make a single payment. The yields on Treasury strips in February 2008 show that investors received a higher yield on longer term bonds.


Corporate Bonds

• Zero coupons• Floating rate bonds• Convertible bonds


Nominal and Real rates

0

2

4

6

8

10

12

14

Per

cen

t

Year

Yield on UK nominal bonds

Yield on UK indexed bonds


Default Risk

• Credit risk• Default premium• Investment grade• Junk bonds


Default RiskStandard

Moody' s & Poor's Safety

Aaa AAA The strongest rating; ability to repay interest and principalis very strong.

Aa AA Very strong likelihood that interest and principal will berepaid

A A Strong ability to repay, but some vulnerability to changes incircumstances

Baa BBB Adequate capacity to repay; more vulnerability to changesin economic circumstances

Ba BB Considerable uncertainty about ability to repay.B B Likelihood of interest and principal payments over

sustained periods is questionable.Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal

on the debt ever to be repaid.


Valuation of Shares


Stocks & Stock MarketPrimary Market - Market for the sale

of new securities by corporations.

Initial Public Offering (IPO) - First offering of stock to the general public.

Seasoned Issue - Sale of new shares by a firm that has already been through an IPO


Stocks & Stock Market

Common Stock - Ownership shares in a publicly held corporation.

Secondary Market - Market in which previously issued securities are traded among investors.

Dividend - Periodic cash distribution from the firm to the shareholders.

P/E Ratio - Price per share divided by earnings per share.



• The difference between a firm’s actual market value and its’ liquidation or book value is attributable to its “going concern value.”

• Factors of “Going Concern Value”1. Extra earning power2. Intangible assets3. Value of future investments



Book Value - Net worth of the firm according to the balance sheet.

Liquidation Value - Net proceeds that could be realized by selling the firm’s assets and paying off its creditors.

Market Value Balance Sheet - Financial statement that uses market value of all assets and liabilities.


Valuing Common Stocks

• Stock Valuation Methods1. Valuation by comparables

• Ratios• Multiples

2. Price and Intrinsic Value3. Dividend Discount Model



Expected Return - The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR).

Expected Return

rDiv P P

P1 1 0

0



The formula can be broken into two parts.

Dividend Yield + Capital Appreciation

Expected Return

rDiv

P

P P

P1

0

1 0

0



Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

H - Time horizon for your investment.

PDiv

r

Div

r

Div P

rH H

H01

12

21 1 1

( ) ( )

...( )



ExampleCurrent forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?



ExampleCurrent forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

PV

PV

3 00

1 12

3 24

1 12

350 94 48

1 12

00

1 2 3

.

( . )

.

( . )

. .

( . )

$75.


Blue Skies Value

0

10

20

30

40

50

60

70

80

1 2 3 10 20 30 50 100

Val

ue

per

sh

are,

do

llar

s

Investment Horizon, Years

PV (Terminal Price)

PV (Dividends)



If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY.

Perpetuity PDiv

rorEPS

r 0

1 1

Assumes all earnings are paid to shareholders.



Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).

PDiv

r g01

Given any combination of variables in the equation, you can solve for the unknown variable.



ExampleWhat is the value of a stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return.

PDiv

r g01 00

12 0800

$3.

. .$75.



Example- continuedIf the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends?

$100$3.

.

.

00

12

09

g

g

Answer

The market is assuming the dividend will grow at 9% per year, indefinitely.



• Valuing Non-Constant Growth

HH

HH

r

P

r

Div

r

Div

r

DivPV

)1()1(...

)1()1( 22

11



• If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.

Payout Ratio - Fraction of earnings paid out as dividends

Plowback Ratio - Fraction of earnings retained by the firm

Sustainable Growth Rate - Steady rate at which firm can grow; return on equity x plowback ratio



Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations.

g = return on equity X plowback ratio



ExampleOur company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plowback 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?



ExampleOur company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plowback 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

P0

5

1267

.$41.

No Growth With Growth

g

P

. . .

. .$75.

20 40 08

3

12 08000



Example - continuedIf the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00.

The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).

• Present Value of Growth Opportunities (PVGO). – Net present value of a firm’s future investments.

gsb711-lecture-note-04-valuation-of-bonds-and-shares

Documents

bond market

discount bond

yr bond

bond pv

annual coupon bond

bond yield spreadsheet

bond yields rate of

bond pricing example