Chapter 10
Valuation and Rates of Return
Discussion Questions
10-1. How is valuation of any financial asset related to future cash flows?
The valuation of a financial asset is equal to the present value of future
cash flows.
10-2. Why might investors demand a lower rate of return for an investment in
Microsoft as compared to United Airlines?
Because Microsoft has less risk than United Airlines, Microsoft has
relatively high returns and a strong market position; United Airlines has
had financial difficulties and emerged from bankruptcy in 2006.
10-3. What are the three factors that influence the required rate of return by
investors?
The three factors that influence the demanded rate of return are:
The real rate of return
The inflation premium
The risk premium
10-4. If inflationary expectations increase, what is likely to happen to yield to
maturity on bonds in the marketplace? What is also likely to happen to the
price of bonds?
If inflationary expectations increase, the yield to maturity (the required rate
of return) will increase. This will mean a lower bond price.
10-5. Why is the remaining time to maturity an important factor in evaluating the
impact of a change in yield to maturity on bond prices?
The longer the time period remaining to maturity, the greater the impact of
a difference between the rate the bond is paying and the current yield to
maturity (required rate of return). For example, a 2 percent ($20)
differential is not very significant for one year, but very significant for
20 years. In the latter case, it will have a much greater effect on the bond
price.
10-6. What are the three adjustments that have to be made in going from annual
to semiannual bond analysis?
The three adjustments in going from annual to semiannual bond analysis
are:
Divide the annual interest rate by two.
Multiply the number of years by two.
Divide the annual yield to maturity by two.
10-7. Why is a change in required yield for preferred stock likely to have a
greater impact on price than a change in required yield for bonds?
The longer the life of an investment, the greater the impact of a change in
the required rate of return. Since preferred stock has a perpetual life, the
impact is likely to be at a maximum.
10-8. What type of dividend pattern for common stock is similar to the dividend
payment for preferred stock?
The no-growth pattern for common stock is similar to the dividend on
preferred stock.
10-9. What two conditions must be met to go from Formula 10-7 to
Formula 10-8 in using the dividend valuation model?
( )
1
0
10-8
e
D
PK g
=–
To go from Formula (10-7) to Formula (10-8):
The firm must have a constant growth rate (g).
The discount rate (Ke) must exceed the growth rate (g).
10-10. What two components make up the required rate of return on common
stock?
The two components that make up the required rate of return on common
stock are:
The dividend yield D1/P0.
b. The growth rate (g). This actually represents the anticipated growth in
dividends, earnings, and stock price over the long term.
10-11. What factors might influence a firm’s price-earnings ratio?
The price-earnings ratio is influenced by the earnings and sales growth of the
firm, the risk (or volatility in performance), the debt-equity structure
of the firm, the dividend policy, the quality of management, and a number of
other factors. Firms that have bright expectations for the future tend to trade at
high P/E ratios while the opposite is true of low P/E firms.
10-12. How is the supernormal growth pattern likely to vary from the normal, constant
growth pattern?
A supernormal growth pattern is represented by very rapid growth in the early
years of a company or industry that eventually levels off to more normal
growth. The supernormal growth pattern is often experienced by firms in
emerging industries, such as in the early days of electronics or microcomputers.
10-13. What approaches can be taken in valuing a firm’s stock when there is no cash
dividend payment?
In valuing a firm with no cash dividend, one approach is to assume that at some
point in the future a cash dividend will be paid. You can then take the present
value of future cash dividends.
A second approach is to take the present value of future earnings as well as a
future anticipated stock price. The discount rate applied to future earnings is
generally higher than the discount rate applied to future dividends.
Chapter 10
Problems
(For the first 20 bond problems, assume interest payments are on an annual basis.)
1. Bond value (LO10-3) The Lone Star Company has $1,000 par value bonds outstanding at
10 percent interest. The bonds will mature in 20 years. Compute the current price of the
bonds if the present yield to maturity is
a. 6 percent.
b. 9 percent.
c. 13 percent.
10-1. Solution:
Loan Star Company
Calculator Solution:
(a) 6 percent yield to maturity
N I/Y PV PMT FV
20 6 CPT PV −1,458.80 100 1,000
Answer: $1,458.80 Current bond price
(b) 9 percent yield to maturity
N I/Y PV PMT FV
20 9 CPT PV −1,091.29 100 1,000
Answer: $1,091.29 Current bond price
(c) 13 percent yield to maturity
N I/Y PV PMT FV
20 13 CPT PV −789.26 100 1,000
Answer: $789.26 Current bond price
a. 6 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 20, i = 6%) Appendix D
PVA = 100 × 11.470 = $1,147.00
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 20, i = 6%) Appendix B
PV = 1,000 × .312 = $312
Total Present Value
Present Value of Interest Payments $1,147.00
Present Value of Principal Payment 312.00
Total Present Value or Price of the Bond $1,459.00
10-1. (Continued)
b. 9 percent yield to maturity
PVA = A × PVIFA (n = 20, i = 9%) Appendix D
PVA = $100 × 9.129 = $912.90
PV = FV × PVIF (n = 20, i = 9%) Appendix B
PV = $1,000 × .178 = $178.00
$ 912.90
178.00
$1,090.90
c. 13 percent yield to maturity
PVA = A × PVIFA (n = 20, i = 13%) Appendix D
PVA = $100 × 7.025 = $702.50
PV = FV × PVIF (n = 20, i = 13%) Appendix B
PV = $1,000 × .087 = $87.00
$702.50
87.00
$789.50
2. Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds will
mature in 25 years. Compute the current price of the bonds if the present yield to maturity
is
a.7 percent.
b. 10 percent.
c. 13 percent.
10-2. Solution:
Midland Oil
Calculator Solution:
(a) 7 percent yield to maturity
N I/Y PV PMT FV
25 7 CPT PV −1,116.54 80 1,000
Answer: $1,116.54 Current bond price
(b) 10 percent yield to maturity
N I/Y PV PMT FV
25 10 CPT PV −818.46 80 1,000
Answer: $ 818.46 Current bond price
(c) 13 percent yield to maturity
N I/Y PV PMT FV
25 13 CPT PV −633.50 80 1,000
Answer: $633.50 Current bond price
a. 7 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 25, i = 7%) Appendix D
PVA = $80 × 11.654 = $932.32
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 25, i = 7%) Appendix B
PV = $1,000 × .184 = $184
Total Present Value
Present Value of Interest Payments $ 932.32
Present Value of Principal Payments 184.00
Total Present Value or Price of the Bond $1,116.32
b. 10 percent yield to maturity
PVA = A × PVIFA (n = 25, i = 10%) Appendix D
PVA = $80 × 9.077 = $726.16
PV = FV × PVIF (n = 25, i = 10%) Appendix B
PV = $1,000 × .092 = $92
$726.16
92.00
$818.16
10-2. (Continued)
c. 13 percent yield to maturity
PVA = A × PVIFA (n = 25, i = 13%) Appendix D
PVA = $80 × 7.330 = $586.40
PV = FV × PVIF (n = 25, i = 13%) Appendix B
PV = $1,000 × .047 = $47
$586.40
47.00
$633.40
3. Exodus Limousine Company has $1,000 par value bonds outstanding at 10 percent interest.
The bonds will mature in 50 years. Compute the current price of the bonds if the percent
yield to maturity is
a.5 percent.
b. 15 percent.
10-3. Solution:
Exodus Limousine Company
Calculator Solution:
(a) 5 percent yield to maturity
N I/Y PV PMT FV
50 5 CPT PV −1,912.80 100 1,000
Answer: $1,912.80 Current bond price
(b) 15 percent yield to maturity
N I/Y PV PMT FV
50 15 CPT PV −666.97 100 1,000
Answer: $666.97 Current bond price
a. 5 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 50, i = 5%) Appendix D
PVA = $100 × 18.256 = $1,825.60
Present Value of Principal Payment
PV = FV × PVIF (n = 50, i = 5%) Appendix B
PV = $1,000 × .087 = $87
Present Value of Interest Payment $1,825.60
Present Value of Principal Payment 87.00
Total Present Value or Price of the Bond $1,912.60
10-3. (Continued)
b. 15 percent yield to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 50, i = 15%) Appendix D
PVA = $1,000 × 6.661 = $666.10
PV = FV × PVIF (n = 50, i = 15%) Appendix B
PV = $1,000 × .001 = $1
Present Value of Interest Payment $666.10
Present Value of Principal Payment 1.00
Total Present Value or Price of the Bond $667.10
4. Bond value (LO10-3) Barry’s Steroids Company has $1,000 par value bonds outstanding
at 16 percent interest. The bonds will mature in 40 years. If the percent yield to maturity is
13 percent, what percent of the total bond value does the repayment of principal represent?
10-4. Solution:
Barry’s Steroids
Calculator Solution:
13 percent yield to maturity
N I/Y PV PMT FV
40 13 CPT PV −1,229.03 160.0 1,000
Answer: $1,229.03 Total present value of the bond
N I/Y PV PMT FV
40 13 CPT PV −7.53 0 1,000
Answer: $7.53 Present value of the principal payment
PV of principal payment =$7.53 = .613%
Bond value $1,229.03
Present Value of Interest Payments
PVA = A × PVIFA (n = 40, i = 13%) Appendix D
PVA = $160 × 7.634 = $1,221.44
Present Value of Principal Payment
PV = FV × PVIF (n = 40, i = 13%) Appendix B
PV = $1,000 × .008 = $8.00
Present Value of Interest Payments $1,221.44
Present Value of Principal Payment 8.00
Total Present Value or Price of the Bond $1,229.44
PV of Principal Payment $8.00 .651%
Bond Value $1,229.44
= =
5. Bond value (LO10-3) Essex Biochemical Co. has a $1,000 par value bond outstanding that
pays 15 percent annual interest. The current yield to maturity on such bonds in the market
is 17 percent. Compute the price of the bonds for the following maturity dates:
a.30 years
b. 20 years
c. 4 years