Principles of Finance, 6e
Besley/Brigham
Chapter 10
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-a – 5 min.
TOPICS:
Yield to Maturity
67. The current market price of Smith Corporation’s 10 percent, 10-year bonds is $1,297.58. A 10 percent coupon interest
rate is paid semiannually, and the par value is equal to $1,000. What is the YTM (stated on a simple, or annual, basis) if
the bonds mature 10 years from today?
a.
8%
b.
6%
c.
4%
d.
2%
e.
1%
ANSWER:
b
RATIONALE:
Financial calculator solution: Inputs: N = 20; PV = −1,297.58; PMT = 50; FV = 1,000.
Output: I = 3.0% per period. rd = YTM = 3.0% × 2 periods = 6%. Cash flow time line:
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-a – 5 min.
TOPICS:
Yield to Maturity
68. Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the
next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter.
The required rate of return on equity (rs) is 10 percent. What is the current price of the common stock?
a.
$53.45
b.
$60.98
c.
$64.49
d.
$67.47
e.
$69.21
ANSWER:
d
RATIONALE:
Equation solution: = $2.00 × 1.04 = $2.08 = $2.08 × 1.05 = $2.184 = $2.184 ×
1.06 = $2.315
Principles of Finance, 6e
Besley/Brigham
Chapter 10
b.
$82.84
c.
$91.88
d.
$101.15
e.
$110.37
ANSWER:
b
RATIONALE:
Equation solution: = $2.00 × 1.40 = $2.80 = $2.80 × 1.25 = $3.50
Financial calculator
solution: Inputs: CF0 = 0; CF1 = 2.80; CF2 = 95.375; I = 9. Output: NPV = $82.84; P0 =
$82.84.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Stock Valuation
74. Trickle Corporation’s 12 percent coupon rate, semiannual payment, $1,000 par value bonds mature in 25 years. The
bonds currently sell for $1,230.51 in the market, and the yield curve is flat. Assuming that the yield curve is expected to
remain flat, what is Trickle’s most likely before-tax cost of debt if it issues new bonds today?
a.
b.
c.
d.
e.
ANSWER:
d
RATIONALE:
Financial calculator solution: Inputs: N = 50; PV = −1,230.51; PMT = 60; FV = 1,000.
Output: I = 4.78 periodic rate (semiannual). The simple annual rate equals 2 × 4.78% =
9.56%. Thus, the before-tax cost of debt is 9.56%.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Bond Valuation
75. U.S. Delay Corporation, a subsidiary of the Postal Service, must decide whether to issue zero coupon bonds or
quarterly payment bonds to fund construction of new facilities. The 1,000 par value quarterly payment bonds would sell at
$795.54, have a 10 percent annual coupon rate, and mature in ten years. At what price would the zero coupon bonds with
a maturity of 10 years have to sell to earn the same effective annual rate as the quarterly payment bonds?
a.
$274.50
b.
$271.99
Principles of Finance, 6e
Besley/Brigham
Chapter 10
c.
$198.89
d.
$257.52
e.
$254.84
ANSWER:
d
RATIONALE:
Calculate PV of zero coupon bond using the effective annual rate Inputs: N = 10; I =
14.53; PMT = 0; FV = 1,000. Output: PV = −$257.518 ≈ −$257.52. Vd = $257.52. The
zero coupon bonds would have to sell at $257.52. Financial calculator solution: Calculate
simple periodic and annual interest rates Inputs: N = 40; PV = −795.54; PMT = 25; FV =
1,000. Output: I = 3.45% per period. rNominal = 4 × 3.45 = 13.80%. Calculate the effective
annual rate using interest rate conversion feature Inputs: P/YR = 4; NOM% = 13.80.
Output: EFF% = 14.53%.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Zero Coupon and Effective Annual Rate
76. A 15-year zero coupon bond has a yield to maturity of 8 percent and a maturity value of $1,000. What is the amount of
tax that an investor in the 30 percent tax bracket would pay during the first year of owning the bond?
a.
$7.57
b.
$10.41
c.
$15.89
d.
$20.44
e.
$25.22
ANSWER:
a
RATIONALE:
Step 1:
Find PV of bond:
N
= 15
I
= 8
PMT
= 0
FV
= 1,000
Solve for PV = −315.24.
Step 2:
Find interest for the first year:
Value at t = 0
Interest rate
Interest income
$ 25.22
Step 3:
Find tax due:
Interest income
$25.22
Tax rate
Tax due
$ 7.57
POINTS:
1
Principles of Finance, 6e
Besley/Brigham
Chapter 10
ANSWER:
d
RATIONALE:
Financial calculator solution: Burger King Vd Calculate the effective annual rate to apply
to Burger King bonds using interest rate conversion feature, and calculate the value, VBK,
of Burger King bonds: Inputs: P/YR = 2; NOM% = 12. Output: EFF% = rEAR = 12.36%.
Inputs: N = 20; I = 12.36; PMT = 80; FV = 1,000. Output: PV = −$681.54. McDonalds Vd
Inputs: N = 40; I = 6; PMT = 40; FV = 1,000. Output: PV = $699.07. Calculate the
difference between the two bonds’ PVs Difference: Vd(McD) −Vd(BK) = 699.07 − 681.54 =
$17.53. Cash flow time lines:
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Bond Value
80. An 8 percent annual coupon, noncallable bond has ten years until it matures and a yield to maturity of 9.1 percent.
What should be the price of a 10-year bond of equal risk which pays an 8 percent semiannual coupon? Assume both bonds
have a maturity value of $1,000.
a.
$898.64
b.
$736.86
c.
$854.27
d.
$941.08
e.
$964.23
ANSWER:
d
RATIONALE:
Step 1:
Determine the interest rate to use in order to evaluate the
semiannual bond’s price:
Principles of Finance, 6e
Besley/Brigham
Chapter 10
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Note that this is stated on an annual basis. To convert to a
semiannual basis divide it by 2:
8.9019%/2 = 4.451%.
Step 2:
Calculate the semiannual bond’s price:
N
= 20
I
= 4.451
PMT
= 40
FV
= 1,000
Solve for PV =
$941.08.
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Bond Value – Semiannual Payment
81. Fish & Chips Inc. has two bond issues outstanding, and both sell for $701.22. The first issue has a coupon rate of 8
percent and 20 years to maturity. The second has an identical yield to maturity as the first bond, but only 5 years until
maturity. Both issues pay interest annually. What is the annual interest payment on the second issue?
a.
$120.00
b.
$37.12
c.
$56.42
d.
$29.68
e.
$11.16
ANSWER:
b
RATIONALE:
Financial calculator solution: Calculate YTM or rd for first issue Inputs: N = 20; PV =
−701.22; PMT = 80; FV = 1,000. Output: I = 12%. Calculate PMT on second issue using
12% = rd = YTM Inputs: N = 5; I = 12; PV = −701.22; FV = 1,000. Output: PMT = $37.116
≈ $37.12.
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Bond Interest Payments
82. A two-year zero-coupon Treasury bond with a maturity value of $1,000 has a price of $873.4387. A one-year zero-
coupon Treasury bond with a maturity value of $1,000 has a price of $938.9671. If the pure expectations theory is correct,
for what price should one-year zero-coupon Treasury bonds sell one year from now?
a.
$798.89
Principles of Finance, 6e
Besley/Brigham
Chapter 10
c.
$938.97
d.
$945.26
e.
$950.47
ANSWER:
a
b.
$824.66
c.
$852.28
d.
$930.23
e.
$989.11
ANSWER:
d
RATIONALE:
First find the yields on one-year and two-year zero-coupon bonds, so you can find the
implied rate on a one-year bond, one year from now. Then use this implied rate to find its
price.
1-Year
2-Year
N
= 1
N
= 2
PV
= −938.9671
PV
= −873.4387
PMT
= 0
PMT
= 0
FV
= 1,000
FV
= 1,000
Solve for I
= 6.5%.
Solve for I
= 7.0%.
Therefore, if the implied rate = x Now find the price of a 1-
year zero, 1 year from now:
N
= 1
I
= 7.5
PMT
= 0
FV
= 1,000
Solve for PV = $930.23.
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Zeros and Expectations Theory
83. A four-year, zero-coupon Treasury bond sells at a price of $762.8952. A three-year, zero-coupon Treasury bond sells
at a price of $827.8491. Assuming the pure expectations theory is correct, what does the market believe the price of one-
year, zero-coupon bonds will be in three years?
a.
$921.66
b.
$934.58
Principles of Finance, 6e
Besley/Brigham
Chapter 10
Time Estimate-a – 5 min.
TOPICS:
Bond Valuation
a.
Higher coupon rate.
(assume that this rate will remain constant over the next 5 years). For you to be able to purchase this stock at the end of 5
years, how much must you deposit in your bank account today, at t = 0?
a.
$2,985.00
b.
$4,291.23
c.
$3,138.52
d.
$3,704.18
e.
$4,831.25
ANSWER:
d
RATIONALE:
Numerical solution: Amount needed to buy 100 shares:
$50(100)
= $5,000.
$5,000
= PV(1 + 0.06/365)5(365)
$5,000
= PV(1.3498)
PV
= $3,704.18.
Financial calculator solution: Convert the simple interest rate to an effective annual rate
Inputs: P/YR = 365; NOM% = 6. Output: EFF% = rEAR = 6.183%. Calculate PV of deposit
required today Inputs: N = 5; I = 6.183; FV = 5,000. Output: PV = −$3,704.205 ≈
−$3,704.21. Note: The numerical solution is used as the correct answer because of its
greater precision. If the financial calculator derived effective annual rate is expressed to
five decimal places it yields a PV = −$3,704.18.
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-01 – Stocks and Bonds
Time Estimate-b – 10 min.
TOPICS:
Preferred Stock Value
85. Which of the following statements about bonds is most correct?
a.
The current yield on a bond is fixed over the life of the bond.
b.
The coupon rate on bond changes periodically on most long-term bonds,
c.
The yield to maturity on a bond is fixed as long as the bond is held until maturity.
d.
The price of a bond increases as the market interest rates increase.
ANSWER:
c
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-3 – Comprehension
Business Program-6 – Reflective Thinking
DISC-FIN-01 – Stocks and Bonds