Chapter 10: Valuation and Rates of Return
10-14. Solution:
Katie Pairy Fruits Inc.
Calculator Solution:
N I/Y PV PMT FV
N I/Y PV PMT FV
a. Present Value of Interest Payments
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 20, i = 12%) Appendix B
$1,224.35
b. PVA = A × PVIFA (n = 20, i = 12%) Appendix D
Chapter 10: Valuation and Rates of Return
$1,224.07
c. The answer to part a of $1,224.35 and part b of
$1,224.07 are basically the same because in both cases
we are valuing the present value of a $30 differential
between actual return and required return for 20 years.
15. Effect of yield to maturity on bond price (LO10-2 and 3) Media Bias Inc. issued
bonds 10 years ago at $1,000 per bond. These bonds had a 40-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 in time as described next:
Real rate of return............ 2%
Inflation premium............ 5
Risk premium…………..….. 5
Total return………..…….. 12%
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 30 years remaining until maturity. Compute the new price of
the bond.
10-15. Solution:
Media Bias Inc.
Chapter 10: Valuation and Rates of Return
First compute the new required rate of return (yield to
maturity)
Real rate of return 2%
Calculator Solution:
N I/Y PV PMT FV
Present Value of Interest Payments
PVA = A × PVIFA (n = 30, i = 9%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 30, i = 9%) Appendix B
Total Present Value
Present Value of Interest Payments $1,232.88
16. Effect of yield to maturity on bond price (LO10-2 and 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 15 percent. This return was
in line with the required returns by bondholders at that point in time as described
next:
Real rate of return............ 8%
Inflation premium............ 3
Chapter 10: Valuation and Rates of Return
Risk premium…………..….. 4
Total return………………. 15%
Assume that 10 years later, due to bad publicity, the risk premium is now 7 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 8%
Calculator Solution:
N I/Y PV PMT FV
Present Value of Interest Payments
PVA = A × PVIFA (n = 15, i = 18%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 15, i = 18%) Appendix B
Chapter 10: Valuation and Rates of Return
17. Deep discount bonds (LO10-3) Lance Whittingham IV specializes in buying deep
discount bonds. These represent bonds that are trading at well below par 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 18 years remaining to maturity. The
current yield to maturity on similar bonds is 14 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
Calculator Solution:
(a)
N I/Y PV PMT FV
a. Current price of the bonds
Present Value of Interest Payments
PVA = A × PVIFA (n = 18, i = 14) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 18, i = 14%) Appendix B
b. Percent increase at maturity
Maturity Value $1,000.00
Current price – 353.68
Dollar increase $ 646.32
Dollar increase $646.32
Percent increase 182.74%
Current price 353.68
= = =
c. Compound rate of growth
The bond will grow by 182.74 percent over 18 years. Using
18. Yield to maturity – A calculator or Excel is required (LO10-3) 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 $690. They have 10 years remaining to maturity. The annual interest
payment is 13 percent ($130). Compute the approximate yield to maturity.
10-18. Solution:
Calculator Solution:
N I/Y PV PMT FV
19. Yield to maturity – A calculator or Excel is required (LO10-3) Stilley Resources
bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a
Chapter 10: Valuation and Rates of Return
$1,000 par value and a coupon rate of 5 percent. If the price of the bond is $841.51,
what is the yield to maturity?
10-19. Solution:
N I/Y PV PMT FV
20. Yield to maturity – A calculator or Excel is required (LO10-3) Evans Emergency
Response bonds have 6 years to maturity. Interest is paid semiannually. The bonds
have a $1,000 par value and a coupon rate of 8 percent. If the price of the bond is
$1,073.55, what is the annual yield to maturity?
10-20. Solution:
Semiannual:
Payment: $1000 × .08 = $80/2 = $40
n: 6 years × 2 payments per year = 12
N I/Y PV PMT FV
(For the next two problems, assume interest payments are on a semiannual basis.)
21. Bond value––semiannual analysis (LO10-3) Heather Smith is considering a bond
investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual
interest rate of 11 percent and the interest is paid semiannually. The yield to
maturity on the bonds is 14 percent annual interest. There are seven years to
maturity. Compute the price of the bonds based on semiannual analysis.
10-21. Solution:
Heather Smith and Locklear Airlines
11%/2 = 5.5% semiannual interest rate
Chapter 10: Valuation and Rates of Return
5.5% × $1,000 = $55 semiannual interest
Calculator Solution:
N I/Y PV PMT FV
Present Value of Interest Payments
PVA = A × PVIFA (n = 14, i = 7%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 14, i = 7%) Appendix B
Present Value of Interest Payments $480.98
22. Bond value––semiannual analysis (LO10-3) You are called in as a financial analyst
to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a
quoted annual interest rate of 10 percent, which is paid semiannually. The yield to
maturity on the bonds is 10 percent annual interest. There are 15 years to maturity.
a.Compute the price of the bonds based on semiannual analysis.
b. With 10 years to maturity, if yield to maturity goes down substantially to
8 percent, what will be the new price of the bonds?
10-22. Solution:
Chapter 10: Valuation and Rates of Return
Olsen’s Clothing Stores
Calculator Solution:
(a)
N I/Y PV PMT FV
(b)
N I/Y PV PMT FV
a. Present Value of Interest Payments
PVA = A × PVIFA (n = 30, i = 5%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 30, i = 5%) Appendix B
b. PVA = A × PVIFA (n = 20, i = 4%) Appendix D
PV = FV × PVIF (n = 20, i = 4%) Appendix B
Chapter 10: Valuation and Rates of Return
23. Preferred stock value (LO10-4) The preferred stock of Denver Savings and Loan
pays an annual dividend of $5.70. It has a required rate of return of 6 percent.
Compute the price of the preferred stock.
10-23. Solution:
Denver Savings and Loan
$5.70 $95
0.06
p
p
p
D
PK
= = =
24. North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed
dividend of $6 per share. With the passage of time, yields have soared from the
original 6 percent to 14 percent (yield is the same as required rate of return).
a.What was the original issue price?
b. What is the current value of this preferred stock?
c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will
the price of the preferred stock be affected?