Chapter 10 Solution: Lone Star Company a. 6 percent yield to

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Chapter 10
Problems
(For the first 11 bond problems, assume interest payments are on an annual
basis.)
10-1.
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.
Solution:
Lone 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 Payments
Total Present Value or Price of the Bond
S-298
$1,032.30
312.00
$1,344.30
b. 8 percent yield to maturity
PVA = A * PVIFA (n = 20, I = 8%)
PVA = $90 * 9.818 = $883.62
Appendix D
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
10-24.
Justin Cement Company has had the following pattern of earnings per share
over the last five years:
Year
Earnings per Share
1997........................................
$4.00
1998........................................
4.20
1999........................................
4.41
2000........................................
4.63
2001........................................
4.86
The earnings per share have grown at a constant rate (on a rounded basis) and
will continue to do so in the future. Dividends represent 40 percent of earnings.
Project earnings and dividends for the next year (2002).
S-299
If the required rate of return (K e) is 13 percent, what is the anticipated stock
price (P0 ) at the beginning of 2002?
Solution:
Justin Cement Company
Earnings have been growing at a rate of 5 percent per year.
1998
1999
2000
2001
Base Period
$4.20/4.00
$4.41/4.20
$4.63/4.41
$4,86/4.63
5% growth
5% growth
5% growth
5% growth
The projected EPS for 2002 is $5.10 ($4.86 * 1.05)
Dividends for 2002 represent 40% of earnings or $2.04
($5.10 * 40%)
This is the value for D1 .
Ke (required rate of return) is 13% and the growth rate is
5%.
P0 (2002) =
10-27.
D1
$2. 04
$2. 04
=
=
= $25.50
K e - g 0.13 − 0. 05 0. 08
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 D , D , and D ; for example, D is $2.10 ($2.00 * 1.05).
S-300
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 your 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
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.)
Solution:
Hunter Petroleum Corporation
a. D1
D2
D3
$2.00 (1.05) = $2.10
$2.10 (1.05) = $2.205
$2.205 (1.05) = $2.315
b.
Dividends
$2.10
$2.205
$2.315
D1
D2
D3
PV(12%)
.893
.797
.712
S-301
PV of Dividends
$1.875
1.757
1.648
$5.280
c. P3 =
P3 =
D4
K e -g
D4 = $2. 315 (1.05) = $2.431
$2.431 2.431
=
= $34.729
.12 − .05
.07
d. PV of P 3 for n = 3, i = 12%
$34.729 * .712 = $24.727
e. answer to part b (PV of dividends)
answer to part d (PV of P 3)
current value of the stock
f. P0 =
D1
$2. 10
$2.10
=
=
= $30.00
K e - g .12 − .05
.07
S-302
$ 5.280
24.727
$30.007
S-303
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