Chapter 10: Valuation and Rates of Return
10-11
7. Bond maturity effect (LO3) For problem 6 graph the relationship in a manner
similar to the bottom half of Figure 10-2. Also explain why the pattern of price
change takes place.
10–7. Solution:
Hartford Telephone Company (Continued)
closer to par value.
8. Interest rate effect (LO3) Go to Table 10-1, which is based on bonds paying 10
percent interest for 20 years. Assume interest rates in the market (yield to maturity)
go from 10 percent to 7 percent:
a. What was the bond price at 10 percent?
b. What is he bond price at 7 percent?
c. What would be your percentage return on the investment if you bought when
rates were 10 percent and sold when rates were 7 percent?
10–8. Solution:
a. $1,000
30
25
15
5
0
10
Bond Value
$1,000
Years
11% Bond, $1,000 Par Value
Chapter 10: Valuation and Rates of Return
Purchase price (10%) ………………. 1,000.00
Chapter 10: Valuation and Rates of Return
a. $735.30
b. $864.11
c. Sales price (12%) ……………………. $864.11
Chapter 10: Valuation and Rates of Return
10-14
gain.
12. Bond value (LO3) Ron Rhodes calls his broker to inquire about purchasing a bond
of Golden Years Recreation Corporation. His broker quotes a price of $1,170. Ron
is concerned that the bond might be overpriced based on the facts involved. The
$ 1,000 par value bond pays 13 percent interest, and it has 18 years remaining until
maturity. The current yield to maturity on similar bonds is 11 percent.
Do you think the bond is overpriced? Do the necessary calculations.
10–12. Solution:
Ron Rhodes – Golden Years Recreation Corporation
Present Value of Interest Payments
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 18, i = 11%) Appendix B
Chapter 10: Valuation and Rates of Return
10-15
13. Effect of yield to maturity on bond price (LO3) Tom Cruise Lines, Inc., issued
bonds five years ago at $1,000 per bond. These bonds had a 25-year life when
issued and the annual interest payment was then 12 percent. This return was in line
with the required returns by bondholders at that point as described below:
Real rate of return ……….. 3%
Inflation premium ……….. 5
Risk premium …………….. 4
Total return …………….. 12%
Assume that five years later the inflation premium is only 3 percent and is
appropriately reflected in the required return (or yield to maturity) of the bonds.
The bonds have 20 years remaining until maturity. Compute the new price of the
bond.
10–13. Solution:
Tom Cruise Lines, Inc.
First compute the new required rate of return (yield to
maturity).
Real rate of return 3%
Then use this value to find the price of the bond.
Present Value of Interest Payments
Chapter 10: Valuation and Rates of Return
10-16
14. Analyzing bond price changes (LO3) Further analysis of problem 13:
a. Find the present value of 2 percent × $1,000 (or $20) for 20 years at 10 percent.
The $20 is assumed to be an annual payment.
b. Add this value to $1,000.
c. Explain why the answers to problem 14b and problem 13 are basically the same.
(There is a slight difference due to rounding in the tables.)
10–14. Solution:
Tom Cruise Lines, Inc. (Continued)
a. PVA = A × PVIFA (n = 20, i = 10%) Appendix D
PVA = $20 × 8.514 = $170.28
for 20 years.
In problem 14 we take the present value of the $20
actual return (coupon = 12%) and required return (10%)
to arrive at $1,170.68.
Chapter 10: Valuation and Rates of Return
10-17
15. Effect of yield to maturity on bond price (LO2 & 3) Media Bias, Inc. issued
bonds 10 years ago at $1,000 per bond. These bonds had a 35-year life when issued
and the annual interest payment was then 10 percent. This return was in line with
the required returns by bondholders at that point in time as described below:
Real rate of return ……….. 2%
Inflation premium ……….. 4
Risk premium …………….. 4
Total return …………….. 10%
Assume that 10 years later, due to good publicity, the risk premium is now 2
percent and is appropriately reflected in the required return (or yield to maturity) of
the bonds. The bonds have 25 years remaining until maturity. Compute the new
price of the bond.
10–15. Solution:
Media Bias Company
First compute the new required rate of return (yield to
maturity)
Real rate of return 2%
Then use this value to find the price of the bond.
Present Value of Interest Payments
PVA = A × PVIFA (n=25, i = 8%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n=25, i = 8%) Appendix B
Total Present Value
Chapter 10: Valuation and Rates of Return
10-18
16. Effect of yield to maturity on bond price (LO2 & 3) Wilson Oil Company issued
bonds five years ago at $1,000 per bond. These bonds had a 25-year life when
issued and the annual interest payment was then 8 percent. This return was in line
with the required returns by bondholders at that point in time as described below:
Real rate of return ……….. 2%
Inflation premium ……….. 3
Risk premium …………….. 3
Total return …………….. 8%
Assume that 10 years later, due to bad publicity, the risk premium is now 6 percent
and is appropriately reflected in the required return (or yield to maturity) of the
bonds. The bonds have 15 years remaining until maturity. Compute the new price of
the bond.
10–16. Solution:
Wilson Oil Company
First compute the new required rate of return (yield to
maturity).
Real rate of return 2%
Then use this value to find the price of the bond.
Present Value of Interest Payments
PVA = A × PVIFA (n = 15, i = 11%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 15, i = 11%) Appendix B
Chapter 10: Valuation and Rates of Return
17. Deep discount bonds (LO3) Lance Whittingham IV specializes in buying deep
discount bonds. These represent bonds that are trading at well below part value. He
has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value
bond pays 4 percent annual interest and has 16 years remaining to maturity. The
current yield to maturity on similar bonds is 10 percent.
a. What is the current price of the bonds?
b. By what percent will the price of the bonds increase between now and maturity?
c. What is the annual compound rate of growth in the value of the bonds? (An
approximate answer is acceptable.)
10–17. Solution:
Lance Whittingham IV – Leisure Time Corporation
a. Current price of the bonds
Present Value of Interest Payments
PVA = A × PVIFA (n = 16, i = 10%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 16, i = 10%) Appendix B
b. Percent increase at maturity
Maturity Value $1,000.00
Chapter 10: Valuation and Rates of Return
18. Approximate yield to maturity (LO3) Bonds issued by the Coleman
Manufacturing Company have a par value of $1,000, which, of course, is also the
amount of principal to be paid at maturity. The bonds are currently selling for $850.
They have 10 years remaining to maturity. The annual interest payment is 8 percent
($80).
Compute the approximate yield to maturity, using Formula 10–2.
10–18. Solution:
Coleman Manufacturing Company
Approximate Yield to Maturity is represented by Y’
Principal payment Price of the bond
Annual interest payment Number of years to maturity
Y’ 0.6 (Price of the bond) 0.4 (Principal payment)
$1,000 850
$80 10
0.6 ($850) 0.4 ($1,000)
$150
$80 10
$510 400
$80
−
+
=
+
−
+
=
+
+
=
+
+
19. Approximate yield to maturity (LO3) Bonds issued by the Tyler Food
Corporation have a par value of $1,000, are selling for $1,080, and have 20 years
remaining to maturity. The annual interest payment is 12.5 percent ($125).
Compute the approximate yield to maturity, using Formula 10-2.
10–19. Solution: