Download A1 - JustAnswer

Solutions Guide: Please reword the answers to essay type parts so as to guarantee
that your answer is an original. Do not submit as your own.
A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and
a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this
bond?
CALC: n = 10 x 2 r = 9% / 2 PV = ? PMT = 7.4% x 1,000 / 2 = 37 FV = 1,000
PV = -$895.94
A10. (Dividend discount model) Assume RHM is expected to pay a total cash dividend
of $5.60 next year and its dividends are expected to grow at a rate of 6% per year forever.
Assuming annual dividend payments, what is the current market value of a share of RHM
stock if the required return on RHM common stock is 10%?
P0 = D1 / (r - g) = $5.60 / (0.10 - 0.06) = $140.00
A12. (Required return for a preferred stock) James River $3.38 preferred is selling for
$45.25. The preferred dividend is nongrowing. What is the required return on James
River preferred stock?
PVPerpetuity = D / r = D / PV = $3.38 / $45.25 = 7.47%
A14. (Stock valuation) Suppose Toyota has nonmaturing (perpetual) preferred stock
outstanding that pays a $1.00 quarterly dividend and has a required return of 12% APR
(3% per quarter). What is the stock worth?
PVPerpetuity = D / r = $1.00 / 0.03 = $33.33
B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York
Stock Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that
one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a
coupon payment was made yesterday. a. If the yield to maturity for all three bonds is 8%,
what is the fair price of each bond? b. Suppose that the yield to maturity for all of these
bonds changed instantaneously to 7%. What is the fair price of each bond now? c.
Suppose that the yield to maturity for all of these bonds changed instantaneously again,
this time to 9%. Now what is the fair price of each bond? d. Based on the fair prices at the
various yields to maturity, is interest-rate risk the same, higher, or lower for longerversus shorter-maturity bonds?
a.
1. CALC: n = 1 x 2 = 2 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,010.61
2. CALC: n = 7 x 2 = 14 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,059.42
3. CALC: n = 15 x 2 = 30 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,097.27
b. 1. CALC: n = 1 x 2 = 2 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,020.18
2. CALC: n = 7 x 2 = 14 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,116.03
3. CALC: n = 15 x 2 = 30 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2
= $45.625 FV = $1,000
PV = -$1,195.42
c. 1. CALC: n = 1 x 2 = 2 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,001.17
2. CALC: n = 7 x 2 = 14 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 =
$45.625 FV = $1,000
PV = -$1,006.39
3. CALC: n = 15 x 2 = 30 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2
= $45.625 FV = $1,000
PV = -$1,010.18
d. Interest-rate risk varies directly with maturity. The longer maturity of the bonds, the
larger the price change is when interest rates change.
B18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of
the $1,000 principal in 10 years. You pay only $500 for the bond. a. You receive the
coupon payments for three years and the bond defaults. After liquidating the firm, the
bondholders receive a distribution of $150 per bond at the end of 3.5 years. What is the
realized return on your investment? b. The firm does far better than expected and
bondholders receive all of the promised interest and principal payments. What is the
realized return on your investment?
a. CALC: n = 3.5x2 =7 r = ? PV = -$500 PMT = 9.5%x1,000/ 2= $47.50 FV =
$150 - 47.50 = $102.50
r = -2.8746%
APY = (1 + r)m – 1 = (1 - 0.0278)2 – 1 = -5.6666%
YTM = 2x(-2.8746) = -5.7493% APR
b. CALC: n = 10x2 =20 r = ? PV = -$500 PMT = 9.5%x1,000/2 = $47.50 FV =
$1,000 r = 11.0489%
APY = (1 + r)m – 1 = (1 + 0.110489)2 – 1 = 23.3185%
YTM = 2x11.0489 = 22.0977% APR
B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend
on its common stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans
will begin paying a $1.00 per share dividend in two years and that the dividend will
increase 6% annually thereafter. Bret Kimes, one of James’ colleagues at the same firm,
is less optimistic. Bret thinks that Medtrans will begin paying a dividend in four years,
that the dividend will be $1.00, and that it will grow at 4% annually. James and Bret
agree that the required return for Medtrans is 13%. a. What value would James estimate
for this firm? b. What value would Bret assign to the Medtrans stock?
a. P1 = D2 / (r - g) = $1.00 / (0.13 - 0.06) = $14.29
P0 = $14.29 / (1 + 0.13)1 = $12.64
b. P3 = D4 / (r - g) = $1.00 / (0.13 - 0.04) = $11.11
P0 = $11.11 / (1 + 0.13)3 = $7.70
B21. (Dividend valuation) Wichita Realty Trust is expected to pay a modest dividend
PV = $1.00 / (1 + 0.10)1 + $1.00 / (1 + 0.10)2 + $2.00 / (1 + 0.10)3 + $2.00 / (1 + 0.10)4 +
$2.00 / (1 + 0.10)5 +
+$40.00 / (1 + 0.10)6
PV = $0.91 + $0.83 + $1.50 + $1.37 + $1.24 + $22.58 = $28.43
C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has
estimated the contingent returns given here. a. Calculate the expected returns on the stock
market and on Chicago Gear stock. b. What is Chicago Gear’s beta? c. What is Chicago
Gear’s required return according to the CAPM? REALIZED RETURN State of the
Market Probability that State Occurs Stock Market Chicago Gear Stagnant 0.20 (10%)
(15%) Slow growth 0.35 10 15 Average growth 0.30 15 25 Rapid growth 0.15 25 35
a. Expected Return M = 0.20 x -.10% + 0.35 x 10% + 0.30 x 15% + 0.15 x 25% =
9.75%
Expected Return Chicago Gear = 0.20 x -.15% + 0.35 x 15% + 0.30 x 25% + 0.15 x
35% = 15.00%
b. σM2 = 0.20(-0.10 - 0.0975)2 + 0.35(0.10 - 0.0975)2 + 0.30(0.15 - 0.0975)2 + 0.15(0.25
- 0.0975)2 = 0.0121
Cov(Chicago Gear, M) = 0.20(-0.15 - 0.15)(-0.10 - 0.0975) + 0.35(0.15 - 0.15)(0.10 0.0975) +
0.30(0.25 - 0.15)(0.15 - 0.0975) + 0.15(0.35 - 0.15)(0.25 - 0.0975) = 0.018
β = Cov(j,M) / σM2
= 0.018 / 0.0121 = 1.49
c. r = rf + β(rM - rf) = 0.06 + 1.49(0.0975 - 0.06) = 0.1159 = 11.59%