# AGEC 424 Lab 8 10/14/2004 ```AGEC 424 Lab 8
Bond Problems
1. Smith Blarney is trying to sell my grandmother a semiannual, 10% coupon, \$1000 face value bond with 12 years to
maturity. Currently the market requires a 6% rate of return on bonds of this risk. What is this bond worth?
1a. Smith Blarney is also trying to sell my grandmother a semiannual, 6% coupon, \$1000 face value bond with 12 years to
maturity. Currently the market requires a 6% rate of return on bonds of this risk. What is this bond worth? Do you need to
2. Smith Blarney is also trying to sell Grandma a semiannual, 4% coupon, \$1000 face value bond priced at \$1075. The bond
has 5 years to maturity. What yield to maturity would Grandma earn if she buys this bond?
2b. Smith Blarney is also trying to sell Grandma a semiannual, 9% coupon, \$1000 face value bond priced at \$1000. The bond
has 5 years to maturity. What yield to maturity would Grandma get if she buys this bond? Do you need to do calculations
3. What is the current yield of the above bond (in number 2a)? Why is the current yield greater than the YTM of the bond?
4. Thompson Tires Inc. has an outstanding semiannual, 12% coupon, \$1000 face value bond that is selling for \$1185 and has
10 years to maturity. What is the YTM?
5. Assume the Thompson Tires bond in #4 is callable in 5 years with a \$50 call premium. What is the YTC?
6. Smith Blarney is back trying to sell Grandma a 10 year, callable, semiannual, \$1000 face value, 12% coupon bond. It is
callable in 1 year with a \$100 call premium. If comparable bonds of this risk yield 6% and you expect this bond to be called,
what is its value?
Key Lab 8 bond problems
1. N=24
I=3
Compute PV=1338.71
PMT=50
FV=1000
1a. N=24
I=3
Compute PV=1000
PMT=30
FV=1000
No computation is required because
when the coupon rate and required
return (YTM) are the same the bond
value will be its par value.
2. N=10
Compute I=1.19963x2=2.399%
PV= -1075
PMT=20
FV=1000
2b. N=10
Compute I=4.5x2=9%
PV= -1000
PMT=45
FV=1000
No, you do not need to do
computations. If a bond is priced at
par, its YTM is the same as its coupon
rate.
3. 40/1075 = 3.72%. The current yield
is above the YTM because the
expected capital gains are negative
(the bond is priced above par).
4. N=20
Compute I=4.569x2= 9.14%
PV= -1185
PMT=60
FV=1000
5. N=10
Compute I=4.11966x2= 8.24%
PV= -1185
PMT=60
FV=1050
6. N=2
I=3
Compute PV= 1151.66
PMT= 60
FV=1100
1
Stock Problems (constant growth model)
1. Assume a dividend today of \$2.50 with anticipated growth over the next three years of 10%. The estimated dividend
at the third year is:
a. \$3.25
b. \$3.28
c. \$3.33
d. none of the above
2. Sharbaugh Inc.’s most recent dividend was \$2.00 per share. The dividend is expected to grow at a rate of 4% per year
for the foreseeable future. If the market return is 13% on investments with comparable risk, what should the stock sell
for today?
a. \$16.00
c. \$23.11
e. \$52.00
b. \$22.22
d. \$50.00
3. A stock just paid a \$2.00 dividend that is anticipated to grow at 6% indefinitely. Similar stocks are returning about
13%. The estimated selling price of this stock is:
a. \$30.29
b. \$15.38
c. \$16.31
d. \$28.57
4. A stock just paid an annual dividend of \$2.00, which is expected to remain constant indefinitely. The market return is
14%. The estimated selling price of the stock is:
a. \$1.76
b. \$14.29
c. \$10.43
d. none of the above
5. A share of stock is currently selling for \$20.80. If the dividend just paid is \$2.00 and investors are seeking a 14%
return, what is the anticipated rate of constant growth?
a. 1%
b. 4%
c. 0%
d. none of the above
6. A share of stock is currently selling for \$31.80. If the anticipated constant growth rate for dividends is 6% and
investors are seeking a 16% return, what is the dividend just paid?
a. \$1.91
b. \$3.18
c. \$3.00
d. \$5.09
1. ANS:
C
2.50(1.1)3 = \$3.33
2. ANS:
C
(2.00  1.04)/(.13 – .04) = \$23.11
3. ANS:
A
P0 = D0(1 + g)/(k – g) = 2(1.06)/(.13 – .06) = \$30.29
4. ANS:
2/.14 = \$14.29
B
5. ANS:
B
P0 = D0(1 + g)/(k – g)
20.80 = 2(1 + g)/(.14 – g)
g = 4%
6. ANS:
C
P0 = D0(1 + g)/(k – g)
31.80 = D0(1 + .06)/(.16 – .06)
D0 = \$3
1. You are considering investing in B &amp; B, Inc.’s stock and your broker has told you that you can purchase it for \$72.
You require a return 12% for this type of investment. The last dividend (D0) that B &amp; B paid was \$4 and a 6%
constant growth rate is anticipated. Should you purchase B &amp; B, Inc.?
a. No, because the stock is overpriced by \$1.33.
b. No, because the stock is overpriced by \$3.33.
c. Yes, because the stock is underpriced by \$1.33.
d. Yes, because the stock is underpriced by \$3.33.
2
2. You are considering investing in ABC, Inc.’s stock which is selling at \$45.95. Similar stocks return 16%. ABC’s last
dividend was \$4.50 and a 6% constant growth rate is anticipated. Should you purchase ABC, Inc.?
a. No, because the stock is overpriced by \$1.75.
b. No, because the stock is overpriced by \$3.85.
c. Yes, because the stock is underpriced by \$1.75.
d. Yes, because the stock is underpriced by \$3.85.
3. Toys-r-Cool Inc.’s constant growth stock’s last dividend was \$1.50. It is selling for \$30.20 in a market in
which similar stocks return 12%. Calculate the stock’s anticipated growth rate.
a.
b.
c.
d.
6.7%
8.7%
10.9%
12%
4. Charlie Company is expected to grow at an annual rate of 6% indefinitely. The return on similar stocks is currently
11%. Charlie’s board of directors declared a dividend of \$1.85 yesterday. What should a share of Charlie Company
sell for?
a. \$39.22
b. \$37.00
c. \$16.82
d. \$17.83
5. What is the value of a share of Henley Inc. to an investor who requires a 12 percent rate of return if Henley’s last
dividend was \$1.20? Assume earnings and dividends are expected to grow indefinitely at a rate of 7% per year.
a. \$24.00
b. \$18.34
c. \$25.68
d. None of the above
6. The current price of Zebar is \$32.00 and its last dividend was \$.60. What is its return if dividends are expected to
grow indefinitely at 8 percent?
a. 9.88%
b. 11.38%
c. 18.75%
d. none of the above
1.ANS:
A
P0 = D0(1 + g)/(k – g)
P0 = 4(1.06)/(.06) = \$70.67
\$72 – \$70.67 = \$1.33 Stock is overpriced
2. ANS:
C
P0 = D0(1 + g)/(k – g)
P0 = [4.50(1.06)]/(.10) = \$47.70
\$45.95 – \$47.70 = (\$1.75) Stock is underpriced
30.20 = [1.50(1 + g)]/(.12 – g)
g = 6.7%
4. ANS:
A
P0 = D0(1 + g)/(k –g) = 1.85(1.06)/(.11 – .06) = \$39.22
5. ANS:
C
P0 = \$1.20(1.07)/(.12 –.07) = \$25.68
6. ANS:
D
3. ANS:
A
kE = [.60(1.08)/32] + .08 = 10.03%
P0 = D0(1 + g)/k – g
Stock Problems (two stage growth)
7. Long Life Insurance Inc just paid a dividend of \$1.50, and projects supernormal growth at 12% for the next three
years. After that growth is expected to slow down to a normal 4% and go on at that rate for the foreseeable future.
Similar stocks are earning a return of 10%. How much would you pay for a share of Long Live today?
a. \$37.70
b. \$32.08
c. \$26.00
d. \$28.28
3
ANS: B
D1 = 1.50(1.12) = 1.68 D2 = 1.88 D3 = 2.11 D4 = 2.11(1.04) = 2.19168768
P3 = D4/(.10 – .04) = 36.53
CF0 = 0, C01 = 1.68, C02 = 1.88, C03 = 2.11+36.53=38.64; I = 10
Solve for NPV = \$32.11
8. Cantaloupe Growers Corp. is expanding into a new geographic area. Management expects the new market to fuel
growth of 22% for three years. After that normal growth of 6% will resume. Cantaloupe’s most recent annual
dividend was \$1.25. Other fruit companies have been returning about 12% lately. How much should a share of
Cantaloupe be worth?
a. \$33.06
b. \$38.00
c. \$40.17
d. \$68.32
ANS: A
D1 = 1.25(1.22) = 1.53 D2 = 1.86 D3 = 2.27 D4 = 2.27(1.06) = 2.4059986
P3 = D4 /(.12 – .06) = 40.10
CF0 = 0, C01 = 1.53, C02 = 1.86, C03 = 2.27+40.10=42.37; I = 12
Solve for NPV = \$33.01
9. Frazier Inc. paid a dividend of \$4 last year (D0). The firm is expecting dividends to grow at 21% in years 1–2 and 10%
in Year 3. After that growth will be constant at 8% per year. Similar investments return 14%. Calculate the value of
the stock today.
a. \$71.49
b. \$88.31
c. \$91.47
d. \$116.10
ANS: C
D1 = 4(1.21) = 4.84
D2 = D1(1.21) = 5.8564
D3 = D2(1.10) = 6.442
D4 = D3(1.08) = 6.9574032
P3 = [D4]/(.14 – .08) = 115.95672
Calculator Steps:
CF0 = 0, C01 = 4.84, C02 = 5.86, C03 = 6.44 + 115.96 = 122.40; I = 14
Solve for NPV = \$91.37
10. Williamson Metals, Inc. paid a dividend last year of \$3, and is expecting dividends to grow at an 18% rate in years 1
and 2 followed by constant growth of 6% per year thereafter. Similar stocks return 12%. Calculate the value of the
stock today.
a. \$65.37
b. \$73.85
c. \$82.91
d. \$93.76
ANS: A
D1 = 3(1.18) = 3.54
D2 = 3.54(1.18) = 4.18
P2 = [4.1772(1.06)]/(.12 -.06) = 4.427832/.06 = 73.80
4.18 + 73.80 = 77.98
Calculator Steps:
CF0 = 0, C01 = 3.54, C02 = 77.98; NPV: I = 12
NPV = \$65.33
4
```