Chapter 10
Solutions to Questions and Problems
1.
R = .1133 or 11.33%
2.
Dividend yield = .0169 or 1.69%
Capital gains yield = .0964 or 9.64%
3.
R = –.0675 or –6.75%
Dividend yield = .0169 or 1.69%
Capital gains yield = –.0843 or –8.43%
4.A. Total dollar return = $44
The total percentage return of the bond is:
R = .0393 or 3.93%
7.
N 
.11  .06  .08  .28  .13  .1000 or 10.00%
X   xi  N 
5
 i 1 

N 
.36  .07  .21  .12  .43  .1620 or 16.20%
Y   yi  N 
5
 i 1 

N
2
2
s X   xi  x   N  1
 i 1

1
2
.11  .100 2  .06  .100 2   .08  .100 2  .28  .100 2  .13  .100 2  .016850
sX 
5 1
1
2
.36  .162 2   .07  .162 2  .21  .162 2   .12  .162 2  .43  .162 2  .061670
sY 
5 1





The standard deviation is the square root of the variance, so the standard deviation of each stock is:
sX = .1298 or 12.98%
sY = .2483 or 24.83%
8.
a.
Large company stock average return = 3.24%
T-bills average return = 6.55%
b.
Variance = 0.058136
Standard deviation = 0.2411 or 24.11%
Using the equation for variance, we find the variance for T-bills over this period was:
Variance = 0.000153
Standard deviation = 0.0124 or 1.24%
9.
c.
Average observed risk premium = –3.32%
Variance = 0.062078
Standard deviation = 0.2440 or 24.40%
d.
Before the fact, for most assets the risk premium will be positive; investors demand
compensation over and above the risk-free return to invest their money in the risky
asset. After the fact, the observed risk premium can be negative if the asset’s nominal
return is unexpectedly low, the risk-free return is unexpectedly high, or if some
combination of these two events occurs.
a.
Arithmetic average return = .0880 or 8.80%
b.
Variance = 0.023570
Standard deviation = 0.1535 or 15.35%
10. a.
b.
r = .0441 or 4.41%
RP = .0370 or 3.70%
11. r f = .0086 or 0.86%
And to calculate the average real risk premium, we can subtract the average risk-free rate
from the average real return. So, the average real risk premium was:
rp = .0355 or 3.55%
13. P1 = $163.51
There are no intermediate cash flows on a zero coupon bond, so the return is the capital
gains, or:
R = .0731 or 7.31%
14. R = .0137 or 1.37%
15. R = .0872 or 8.72%
APR = 34.88%
EAR = .3971 or 39.71%
19. R = .38 or 38%
Variance = 0.049050
Standard deviation = 0.2215 or 22.15%
20. Arithmetic average return = .0883 or 8.83%
Geometric average return = .0769 or 7.69%
21. The return for each year is:
R1 =.1507 or 15.07%
R2 =.0554 or 5.54%
R3 = –.0649 or –6.49%
R4 =.2026 or 20.26%
R5 =.2127 or 21.27%
RA = 0.1113 or 11.13%
RG = 0.1062 or 10.62%
23. P1 = $1,047.67
R = .0964 or 9.64%
And using the Fisher equation to find the real return, we get:
r = .0462 or 4.62%
Chapter 11
Solutions to Questions and Problems
1.
Total value = $7,775
WeightA = .6656
WeightB = .3344
2.
Total value = $2,600
E(Rp) = .1392 or 13.92%
3.
E(Rp) = .1330 or 13.30%
4.
wX = 0.716667
Investment in X = 0.716667($10,000) = $7,166.67
Investment in Y = (1 – 0.716667)($10,000) = $2,833.33
5.
R(R) = .1520 or 15.20%
6.
E(R) = .1005 or 10.05%
7.
E(RA) = .0860 or 8.60%
E(RB) = .1405 or 14.05%
A2 = .00125
A = .0354 or 3.54%
B2 = .02822
B = .1680 or 16.80%
8.
E(R) = .1250 or 12.50%
9.
a.
Boom: E(Rp) = .1433 or 14.33%
Bust: E(Rp) = .1067 or 10.67%
To find the expected return of the portfolio, we multiply the return in each state of the
economy by the probability of that state occurring, and then sum. Doing this, we find:
E(Rp) = .30(.1433) + .70(.1067)
E(Rp) = .1177 or 11.77%
b.
Boom: E(Rp) =.2180 or 21.80%
Bust: E(Rp) = .0400 or 4.00%
And the expected return of the portfolio is:
E(Rp) = .0934 or 9.34%
p2 = .00665
10. a.
Boom:
Good:
Poor:
Bust:
E(Rp) = .3420 or 34.20%
E(Rp) = .1280 or 12.80%
E(Rp) = –.0460 or –4.60%
E(Rp) = –.1760 or –17.60%
And the expected return of the portfolio is:
E(Rp) = .0882 or 8.82%
b.
p2 = .02590
P = .1609 or 16.09%
11. p = 1.36
12. X = 1.10
13. E(Ri) = .1460 or 14.60%
14. i = 1.235
15. E(RM) = .1376 or 13.76%
16. Rf = .0613 or 6.13%
17. a.
E(Rp) = .1025 or 10.25%
b.
wS = .6154
wRf = .3846
c.
wS = .6842
p = 0.889
d.
wS = 2
wRf = –1
22. wH = 0.4286
wL = .5714
Investment in H = $107,142.86
Investment in L = $142,857.14
24. a.
Boom:
Good:
Poor:
Bust:
E(Rp) = .2370 or 23.70%
E(Rp) = .1220 or 12.20%
E(Rp) = .0150 or 1.50%
E(Rp) = –.1400 or –14.00%
And the expected return of the portfolio is:
E(Rp) = .0859 or 8.59%
b.
p2 = .009173
P = .0958 or 9.58%
26. Portfolio value = $113,000
wW = .2177
wX = .1912
wY = .2876
wZ = .3035
E[RP] = .1425 or 14.25%
27. wF = .3125
wRf = .1875
Amount of stock F to buy = $31,250.00
28. a.
Boom: E(Rp) = .3300 or 33.00%
Normal: E(Rp) = .1430 or 14.30%
Bust:
E(Rp) = –.1630 or –16.30%
And the expected return of the portfolio is:
E(Rp) = .1252 or 12.52%
2p = .01897
p = .1377 or 13.77%
b.
RPi = .0827 or 8.27%
Chapter 12
Solutions to Questions and Problems
1.
RE = .1180 or 11.80%
2.
RE = .1305 or 13.05%
3.
RE = .04 + 1.15(.08) = .1320 or 13.20%
RE = [$1.80(1.05)/$34] + .05 = .1056 or 10.56%
RE = (.1320 + .1056)/2 = .1188 or 11.88%
5.
RP = .0806 or 8.06%
6.
YTM = 6.52%
RD = .0404 or 4.04%
7.
a.
YTM = 8.61%
b.
RD = .0560 or 5.60%
c.
The after-tax rate is more relevant because that is the actual cost to the company.
a.
WACC = .0949 or 9.49%
b.
RD = .0488 or 4.88%
9.
10. WACC = .1157 or 11.57%
12. a.
BVE = 10,000,000($5) = $50,000,000
BVD = $75,000,000 + 40,000,000 = $115,000,000
So, the total value of the company is:
V = $50,000,000 + 115,000,000 = $165,000,000
And the book value weights of equity and debt are:
E/V = $50,000,000/$165,000,000 = .3030
D/V = 1 – E/V = .6970
b.
MVE = 10,000,000($49) = $490,000,000
MVD = 1.02($75,000,000) + 1.04($40,000,000) = $118,100,000
This makes the total market value of the company:
V = $490,000,000 + 118,100,000 = $608,100,000
And the market value weights of equity and debt are:
E/V = $490,000,000/$608,100,000 = .8058
D/V = 1 – E/V = .1942
c.
The market value weights are more relevant.
13. RE = .1268 or 12.68%
Next, we need to find the YTM on both bond issues. Doing so, we find:
P1 = $1,020 = $37.50(PVIFAR%,20) + $1,000(PVIFR%,20)
R = 3.608%
YTM = 3.608% × 2
YTM = 7.22%
P2 = $1,040 = $35(PVIFAR%,12) + $1,000(PVIFR%,12)
R = 3.096%
YTM = 3.096% × 2
YTM = 6.19%
wD1 = .648
wD2 =.352
RD = .0456 or 4.56%
WACC = .1108 or 11.08%
14. a.
b.
RD = .0942 or 9.42%
RE = .1370 or 13.70%
15. MVD = $7,280,000
MVE = $9,840,000
MVP = $800,000
V = $17,920,000
RE = .1290 or 12.90%
YTM = 7.61%
RD = .0494 or 4.94%
RP = .0656 or 6.56%
WACC = .0939 or 9.39%
16. a.
b.
MVD = $141,000,000
MVE = $456,000,000
MVP = $31,200,000
V = $628,200,000
D/V = 2245
P/V =.0497
E/V =.7259
RE = .1550 or 15.50%
YTM = 7.16%
RD = .0472 or 4.72%
RP = .0641 or 6.41%
WACC = .1263 or 12.63%
18. MVD = $4,560,000
MVE = $7,500,000
MVP = $768,000
V = $12,828,000
RE1 = .1238 or 12.38%
RE2 = .1150 or 11.50%
RE = (.1238 + .1150)/2
RE = .1194 or 11.94%
YTM = 6.72%
RD = .0437 or 4.37%
RP = .0542 or 5.42%
WACC = .0886 or 8.86%
19. WACC = .0972 or 9.72%
21. g1 = .1167 or 11.67%
g2 = .1045 or 10.45%
g3 = .0338 or 3.38%
g4 = .0588 or 5.88%
So, the average arithmetic growth rate in dividends was:
g = .0784 or 7.84%
RE = .1127 or 11.27%
g = .0779 or 7.79%
RE = .1122 or 11.22%
22. MVD = $82,500,000
MVE = $156,000,000
V = $238,500,000
RE1 = .1268 or 12.68%
YTM = 7.95%
RD = .0518 or 5.18%
WACC = .1008 or 10.08%
23. WACC = .0899 or 8.99%
Adjusting for risk, the project discount rate is:
Project discount rate = .0899 + .03
Project discount rate = .1199 or 11.99%
24. WACC = .1238 or 12.38%
Project discount rate = .1238 + .02
Project discount rate = .1438 or 14.38%
PV = [$5M/(.1438 – .04)] = $48,192,771.08
The project should only be undertaken if its cost is less than $48,192,771.08.
25. WACC = .1019 or 10.19%
Project discount rate = .1019 + .02
Project discount rate = .1219 or 12.19%
PVA = $320,000(PVIFA12.195,6)
PVA = $1,308,600.96
The project should only be undertaken if its cost is less than $1,308,600.96.
27. a. RE = .0617 or 6.17%
b. RE = .1240 or 12.40%
c. When using the dividend growth model or the CAPM, you must remember that both are
estimates for the cost of equity. Additionally, and perhaps more importantly, each method
of estimating the cost of equity depends upon different assumptions.