Chapter Six
Valuing Shares and Bonds
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-1
Chapter Organisation
6.1 Bonds and Bond Valuation
6.2 Ordinary Share Valuation
6.3 Summary and Conclusions
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-2
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-3
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-4
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-5
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-6
Bond Price Sensitivity to Interest
Rates (YTM)
Bond price
$1 800
Coupon = $100
20 years to maturity
$1000 face value
$1 600
Key Insight: Bond prices and
YTMs are inversely related.
$1 400
$1 200
$1 000
$ 800
$ 600
Yield to maturity, YTM
4%
6%
8%
10%
12%
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
14%
16%
6-7
Bond Value
V  P V of coupon payments P V of face value
1  1/ 1  r t 
F


C

r
1  r t
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-8
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?


1  1/1.1010
$1000
V  $60

0.10
1.1010
$1000
 $60 6.1446 
2.5937
 $771.10
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-9
Example 2—Bond Value
•
Assume now that the bond’s coupons are paid half-yearly.
1  1/1.0520 
$1000


V  $30

0.05
1.0520
$1000
 $30 12.4622 
2.6533
 $750.76
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-10
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-11
Interest Rate Risk and Time to
Maturity
Time to Maturity
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
Interest rate
1 year
30 years
5%
$1 047.62
$1 768.62
10
1 000.00
1 000.00
15
956.52
671.70
20
916.67
502.11
6-12
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).
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-13
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%
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-14
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-15
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-16
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.
D
P0 
r
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-17
Constant Growth Dividend
•
Dividends grow at a constant rate each time period.
•
Called the constant dividend growth model.
Dt  D0  1  g 
t
D0  1  g 
D1
P0 

rg
rg
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-18
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?
0.151.05
P0 
0.10  0.05
 $3.15
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-19
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-20
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.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-21
Solution—Non-constant Growth
Dividend
Year
Expected Dividend
1
$0.180
2
$0.216
3
$0.259
4
$0.272
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-22
Solution—Non-constant Growth
Dividend (continued)
D
4
P 
3 rg
$0.272

0.10 0.05
 $5.44
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-23
Solution—Non-constant Growth
Dividend (continued)
D3
P3
D1
D2
P0 



1
2
3
3
1  r  1  r  1  r  1  r 
$0.180 $0.216 $0.259 $5.44




2
3
3
1.10 1.10
1.10 1.10
 $0.164 $0.179 $0.195 $4.087
 $4.63
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-24
Share Price Sensitivity to Dividend
Growth, g
Share price ($)
50
45
D1 = $1
Required return, R, = 12%
40
35
30
25
20
15
10
5
0
2%
4%
6%
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
8%
10%
Dividend growth
rate, g
6-25
Share Price Sensitivity to Required
Return, r
Share price ($)
100
90
80
D1 = $1
Dividend growth rate, g, = 5%
70
60
50
40
30
20
10
Required return, R
6%
8%
10%
12%
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
14%
6-26
Components of Required Return
D
1
P 
0 r  g 
D
r  g   1
P
0
D
r 1g
P
0
r  dividend yield  capitalgains yield
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
6-27