Fundamentals of Corporate Finance/3e,CH06

Copyright 2004 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 3eRoss, Thompson, Christensen, Westerfield and JordanSlides prepared by Sue Wright

6-1

Chapter Six

Valuing Shares and Bonds


6-2

6.1 Bonds and Bond Valuation

6.2 Ordinary Share Valuation

6.3 Summary and Conclusions

Chapter Organisation


6-3

Chapter Objectives

• Outline the features of bonds.

• Calculate the value (price) of a bond assuming annual and semi-annual coupons.

• Understand the implications of interest rate risk for the value of a bond.

• Calculate the value of an ordinary share under different dividend growth scenarios.

• Explain the components of required return.


6-4

Debt Securities

• Debt securities are issued when an organisation wishes to borrow money from the public on a long-term basis.

• Bonds are issued by the government.

• Debentures are secured and issued by a corporation.

• Notes are unsecured debt securities issued by a corporation.

• More recently, these are all known as bonds.


6-5

Bond Features

• Coupon payments are the stated interest payments. Payment is constant and payable every year or half-year.

• Face value (par value) is the principal amount repayable at the end of the term.

• Coupon rate is the annual coupon divided by the face value.

• Maturity is the specified date at which the principal amount is payable.


6-6

Bond Yields

• Yield to maturity is the market interest rate that equates a bond’s present value of interest payments and principal repayment with its price.

• There is an inverse relationship between market interest rates and bond price.


6-7

Bond Price Sensitivity to Interest Rates (YTM)

4% 6% 8% 10% 12% 14% 16%

$1 800

$1 600

$1 400

$1 200

$1 000

$ 800

$ 600

Bond price

Yield to maturity, YTM

Coupon = $10020 years to maturity$1000 face value

Key Insight: Bond prices and YTMs are inversely related.


6-8

Bond Value

tr

F r

tr / C

1

111

valueface ofPVpaymentscoupon of PVV


6-9

Example 1—Bond Value

• A bond with a face value of $1000 and a coupon rate of 6 per cent has 10 years to maturity. What is the market price of this bond if the market interest rate is 10 per cent?

$771.10

2.5937$1000 6.1446 $60

1.10$1000

0.101.101/ 1 $60 V 10

10


6-10

Example 2—Bond Value

• Assume now that the bond’s coupons are paid half-yearly.

$750.76

2.6533$1000 12.4622 $30

201.05

$1000 0.05

201.051/ 1 $30 V


6-11

Interest Rate Risk

• Interest rate risk is the risk that arises for bond holders from changes in interest rates.

• All other things being equal, the longer the time to maturity, the greater the interest rate risk.

• All other things being equal, the lower the coupon rate, the greater the interest rate risk.


6-12

Interest Rate Risk and Time to Maturity

Interest rate 1 year 30 years 5% $1 047.62$1 768.62 10 1 000.001 000.00 15 956.52 671.70 20 916.67 502.11

Time to Maturity


6-13

Computing Yield to Maturity

• Yield to maturity (YTM) is the rate implied by the current bond price.

• Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity.

• If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign).


6-14

YTM with Annual Coupons

• Consider a bond with a 10 per cent annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09.

– Will the yield be more or less than 10 per cent?

– N = 15; PV = 928.09; FV = 1000; PMT = 100

– CPT I/Y = 11%


6-15

Ordinary Share Valuation

Share valuation is more difficult than debenture valuation for a number of reasons:

– uncertainty of promised cash flows

– shares have no maturity

– observing the market rate of return is not easy.


6-16

Ordinary Share Valuation

• The market value of a share is the present value of all expected net cash flows to be received from the share, discounted at a rate of return that reflects the riskiness of those cash flows.

• The expected net cash flows to be received from a share are all future dividends.

• Dividend growth is an important aspect of share valuation.


6-17

Zero Growth Dividend

• Shares have a constant dividend into perpetuity, with no growth in dividends.

• The value of a share is then the same as the value of an ordinary perpetuity.

rD P 0


6-18

gr

D gr

g D P

g D D tt

100

0

1

1

Constant Growth Dividend

• Dividends grow at a constant rate each time period.

• Called the constant dividend growth model.


6-19

Example—Constant Growth Dividend

Company XYZ has just paid a dividend of 15 cents per share, which is expected to grow at 5 per cent per annum. What price should you pay for the share if the required rate of return on the investment is 10 per cent?

15.3$0.050.10

1.050.150

P


6-20

Non-constant Growth Dividend

• The growth rate cannot exceed the required rate of return indefinitely but can do so for a number of years.

• Allows for ‘super normal’ growth rates over some finite length of time.

• The dividends have to grow at a constant rate at some point in the future.


6-21

Example—Non-constant Growth Dividend

• A company has just paid a dividend of 15 cents per share and that dividend is expected to grow at a rate of 20 per cent per annum for the next three years, and at a rate of 5 per cent per annum forever after that.

• Assuming a required rate of return of 10 per cent, calculate the current market price of the share.


6-22

Solution—Non-constant Growth Dividend


6-23

Solution—Non-constant Growth Dividend (continued)

$5.440.050.10

$0.272

43

g r

D P


6-24

$4.63$4.087$0.195$0.179$0.164

1.10$5.44

1.10$0.259

1.10$0.216

1.10$0.180

1111

332

33

33

22

11

0

r P

r D

r D

r D P

Solution—Non-constant Growth Dividend (continued)


6-25

Share Price Sensitivity to Dividend Growth, g

0 2% 4% 6% 8% 10%

50

45

40

35

30

25

20

Share price ($)

Dividend growth rate, g

D1 = $1Required return, R, = 12%

15

10

5


6-26

Share Price Sensitivity to Required Return, r

6% 8% 10% 12% 14%

100

90

80

70

60

50

40

Share price ($)

Required return, R

D1 = $1Dividend growth rate, g, = 5%

30

20

10


6-27

Components of Required Return

yield gains capitalyield dividend0

1

0

1

10

r

g P

D r

P

D g r

g r

D P

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Fundamentals of Corporate Finance/3e,CH06

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