Chapter 10: Valuation and Rates of Return
Chapter 10
Valuation and Rates of Return
(For the first 20 bond problems, assume interest payments are on an annual basis.)
1.
Bond value (LO3) The Lone Star Company has $1,000 par value bonds
outstanding at 9 percent interest. The bonds will mature in 20 years. Compute the
current price of the bonds if the present yield to maturity is:
a. 6 percent.
b. 8 percent.
c. 12 percent.
10-1. Solution:
Loan Star Company
a. 6 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 20, i = 6%)
PVA = 90 × 11.470 = $1,032.30
Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 20, i = 6%)
Appendix B
PV = 1,000 × .312 = $312
Total Present Value
Present Value of Interest Payments
Present Value of Principal Payment
Total Present Value or Price of the Bond
$1,032.30
312.00
$1,344.30
10-1. (Continued)
b. 8 percent yield to maturity
PVA = A × PVIFA (n = 20, i = 8%)
10-1
Appendix D
Chapter 10: Valuation and Rates of Return
PVA = $90 × 9.818 = $883.62
PV = FV × PVIF (n = 20, i = 8%)
PV = $1,000 × .215 = $215
Appendix B
$ 883.62
215.00
$1,098.62
c. 12 percent yield to maturity
PVA = A × PVIFA (n = 20, i = 12%)
PVA = $90 × 7.469 = $672.21
Appendix D
PV = FV × PVIF (n = 20, i = 12%)
PV = $1,000 × .104 = $104
Appendix B
$672.21
104.00
$776.21
3.
Bond value (LO3) Barry’s Steroids Company has $1,000 par value bonds
outstanding at 12 percent interest. The bonds will mature in 50 years. Compute the
current price of the bonds if the percent yield to maturity is:
a. 4 percent.
b. 14 percent.
10-3. Solution:
Barry’s Steroids Company
a. 4 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 50, i = 4%)
PVA = $120 × 21.482 = $2,577.84
Present Value of Principal Payment
PV = FV × FVIF (n = 50, i = 4%)
10-2
Appendix D
Appendix B
Chapter 10: Valuation and Rates of Return
PV = $1,000 × .141 = $141
Present Value of Interest Payments
Present Value of Principal Payment
Total Present Value or Price of the Bond
$2,577.84
141.00
$2,718.84
b. 14 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 50, i = 14%)
PVA = $120 × 7.133 = $855.96
Appendix D
Present Value of Principal Payment
PV = FV × FVIF (n = 50, i = 14%)
PV = $1,000 × .001 = $1
Appendix B
Present Value of Interest Payments
Present Value of Principal Payment
Total Present Value or Price of the Bond
13.
$855.96
1.00
$856.96
Effect of yield to maturity on bond price (LO3) Tom Cruise Lines, Inc., issued
bonds five years ago at $1,000 per bond. These bonds had a 25-year life when
issued and the annual interest payment was then 12 percent. This return was in line
with the required returns by bondholders at that point as described below:
Real rate of return ............
Inflation premium ............
Risk premium ...................
Total return ...................
3%
5
4
12%
Assume that five years later the inflation premium is only 3 percent and is
appropriately reflected in the required return (or yield to maturity) of the bonds.
The bonds have 20 years remaining until maturity. Compute the new price of the
bond.
10-13. Solution:
Tom Cruise Lines, Inc.
10-3
Chapter 10: Valuation and Rates of Return
First compute the new required rate of return (yield to
maturity).
Real rate of return
Inflation premium
Risk premium
Total return
3%
3
4
10%
Then use this value to find the price of the bond.
Present Value of Interest Payments
PVA = A × PVIFA (n = 20, i = 10%)
PVA = $120 × 8.514 = $1,021.68
Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 20, i = 10%)
Appendix B
PV = $1,000 × .149 = $149
$1,021.68
149.00
$1,170.68
18.
Approximate yield to maturity (LO3) Bonds issued by the Coleman
Manufacturing Company have a par value of $1,000, which, of course, is also the
amount of principal to be paid at maturity. The bonds are currently selling for $850.
They have 10 years remaining to maturity. The annual interest payment is 8 percent
($80).
Compute the approximate yield to maturity, using Formula 10–2.
10-18. Solution:
Coleman Manufacturing Company
Approximate Yield to Maturity is represented by Y'
10-4
Chapter 10: Valuation and Rates of Return
Principal payment  Price of the bond
Number of years to maturity
0.6 (Price of the bond)  0.4 (Principal payment)
Annual interest payment 
Y' 
$1,000  850
10

0.6 ($850)  0.4 ($1,000)
$80 
$150
10

$510  400
$80 

26.
$80  15 $95

 10.44%
$910
$910
Preferred stock rate of return (LO4) Grant Hillside Homes, Inc., has preferred
stock outstanding that pays an annual dividend of $9.80. Its price is $110. What is
the required rate of return (yield) on the preferred stock?
10-26. Solution:
Grant Hillside Homes, Inc.
Kp 
Dp
Pp

$9.80
 8.91%
$110.00
(All of the following problems pertain to the common stock section of the chapter.)
27.
Common stock value (LO5) Stagnant Iron and Steel currently pays a $4.20 annual
cash dividend (D0). They plan to maintain the dividend at this level for the
foreseeable future as no future growth is anticipated. If the required rate of return by
common stockholders (Ke) is 12 percent, what is the price of the common stock?
10-27. Solution:
10-5
Chapter 10: Valuation and Rates of Return
Stagnant Iron & Steel
P0 
28.
D0 $4.20

 $35
K e 0.12
Common stock value (LO5) Laser Optics will pay a common stock dividend of
$1.60 at the end of the year (D1). The required return on common stock (Ke) is 13
percent. The firm has a constant growth rate (g) of 7 percent. Compute the current
price of the stock (P0).
10-28. Solution:
Laser Optics
P0 
29.
D1
$1.60

 $26.67
K e  g 0.13  0.07
Common stock value under different market conditions (LO5) Ecology Labs,
Inc., will pay a dividend of $3 per share in the next 12 months (D1). The required
rate of return (Ke) is 10 percent and the constant growth rate is 5 percent.
a. Compute P0.
(For parts b, c, d in this problem, all variables remain the same except the one
specifically changed. Each question is independent of the others.)
b. Assume Ke, the required rate of return, goes up to 12 percent; what will be the
new value of P0?
c. Assume the growth rate (g) goes up to 7 percent; what will be the new value of
P0? Ke goes back to its original value of 10 percent.
d. Assume D1 is $3.50; what will be the new value of P0? Assume Ke is at its
original value of 10 percent and g goes back to its original value of 5 percent.
10-29. Solution:
Ecology Labs, Inc.
P0 
D1
Ke  g
10-6
Chapter 10: Valuation and Rates of Return
34.
a.
$3.00
$3.00

 $60.00
0.10  0.05 0.05
b.
$3.00
$3.00

 $42.86
0.12  0.05 0.07
c.
$3.00
$3.00

 $100.00
0.10  0.07 0.03
d.
$3.50
$3.50

 $70.00
0.10  0.05 0.05
Common stock value based on PV calculations (LO5) Hunter Petroleum
Corporation paid a $2 dividend last year. The dividend is expected to grow at a
constant rate of 5 percent over the next three years. The required rate of return is 12
percent (this will also serve as the discount rate in this problem). Round all values
to three places to the right of the decimal point where appropriate.
a. Compute the anticipated value of the dividends for the next three years. That is,
compute D1, D2, and D3; for example, D1 is $2.10 ($2.00 × 1.05).
b. Discount each of these dividends back to the present at a discount rate of
12 percent and then sum them.
c. Compute the price of the stock at the end of the third year (P3).
P3 
D4
Ke  g
(D4 is equal to D3 times 1.05)
d. After you have computed P3, discount it back to the present at a discount rate of
12 percent for three years.
e. Add together the answers in part b and part d to get P0, the current value of the
stock. This answer represents the present value of the first three periods of
dividends, plus the present value of the price of the stock after three periods
(which, in turn, represents the value of all future dividends).
f. Use Formula 10-9 to show that it will provide approximately the same answer
as part e.
P0 
D1
Ke  g
10-7
(10–9)
Chapter 10: Valuation and Rates of Return
For Formula 10-9 use D1 = $2.10, Ke = 12 percent, and g = 5 percent. (The slight
difference between the answers to part e and part f is due to rounding.)
10-34. Solution:
Hunter Petroleum Corporation
a.
D1= $2.00 (1.05) = $2.10
D2= $2.10 (1.05) = $2.205
D3= $2.205 (1.05) = $2.315
b.
D1
D2
D3
c.
Dividends
$2.10
$2.205
$2.315
PV(12%)
.893
.797
.712
P3 
D4
Ke  g
P3 
$2.431 $2.431

 $34.729
.12  .05
.07
PV of Dividends
$1.875
1.757
1.648
$5.280
D4  $2.315 (1.05)  $2.431
d. PV of P3 for n = 3, i = 12%
$34.729 × .712 = $24.727
e. answer to part b (PV of dividends)
answer to part d (PV of P3)
current value of the stock
f.
P0 
$ 5.280
24.727
$30.007
D1
$2.10
$2.10


 $30.00
K e  g .12  .05
.07
10-8