of 48
Chapter 10: Valuation and Rates of Return
Chapter 10
Valuation and Rates of Return
Discussion Questions
10-1.
How is valuation of any financial asset related to future cash flows?
10-2.
Why might investors demand a lower rate of return for an investment in
Microsoft as compared to United Airlines?
10-3.
What are the three factors that influence the required rate of return by
investors?
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?
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?
Chapter 10: Valuation and Rates of Return
10-6.
What are the three adjustments that have to be made in going from annual
to semiannual bond analysis?
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?
10-8.
What type of dividend pattern for common stock is similar to the dividend
payment for 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?
( )
010-8
e
10-10.
What two components make up the required rate of return on common
stock?
Chapter 10: Valuation and Rates of Return
10-11.
What factors might influence a firm’s price-earnings ratio?
10-12.
How is the supernormal growth pattern likely to vary from the normal,
constant growth pattern?
10-13.
What approaches can be taken in valuing a firm’s stock when there is no
cash dividend payment?
Chapter 10: Valuation and Rates of Return
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
10-1. Solution:
Loan Star Company
N
I/Y
PV
PMT
FV
20
6
CPT PV −1,458.80
100
1,000
Chapter 10: Valuation and Rates of Return
Chapter 10: Valuation and Rates of Return
2. Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds
Midland Oil
N
I/Y
PV
PMT
FV
25
7
CPT PV −1,116.54
80
1,000
Chapter 10: Valuation and Rates of Return
10-3. Solution:
Chapter 10: Valuation and Rates of Return
Exodus Limousine Company
N
I/Y
PV
PMT
FV
50
5
CPT PV −1,912.80
100
1,000
Chapter 10: Valuation and Rates of Return
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?
Barry’s Steroids
N
I/Y
PV
PMT
FV
40
13
CPT PV −1,229.03
160.0
1,000
PVA = A × PVIFA (n = 40, i = 13%) Appendix D
PVA = $160 × 7.634 = $1,221.44
Chapter 10: Valuation and Rates of Return
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
10-5. Solution:
30
17
CPT PV −883.41
150.0
1,000
20
17
CPT PV −887.44
150.0
1,000
4
17
CPT PV −945.14
150.0
1,000
Chapter 10: Valuation and Rates of Return
Chapter 10: Valuation and Rates of Return
6. Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 9 percent
10-6. Solution:
Kilgore Natural Gas
N
I/Y
PV
PMT
FV
30
12
CPT PV −758.34
90
1,000
a. 30 years to maturity
Present Value of Interest Payments
PVA = A × PVIFA (n = 30, i = 12%) Appendix D
PVA = $90 × 8.055 = $724.95
Chapter 10: Valuation and Rates of Return
PV = FV × PVIF (n = 30, i = 12%) Appendix B
PV = $1,000 × .033 = $33
Total Present Value
Present Value of Interest Payments $724.95
Present Value of Principal Payment 33.00
Total Present Value or Price of the Bond $757.95
10-6. (Continued)
b. 15 years to maturity
$795.99
c. 1 year to maturity
7. Bond maturity effect (LO10-3) Toxaway Telephone Company has a $1,000 par
value bond outstanding that pays 6 percent annual interest. If the yield to maturity is
Toxaway Telephone Company
As the time to maturity becomes less and less, the
importance of the difference between the rate the bond
pays and the yield to maturity becomes less significant.
Therefore, the bond trades closer to par value.
8. 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) decline from 11 percent to
8 percent:
Chapter 10: Valuation and Rates of Return
b. $1,196.80
c. Sales price (8%) ............................ $1,196.36
Purchase price (11%) .................... 920.30
Profit ............................................. $ 275.99
Profit $275.99 29.99%
Purchase Price $920.37
==
9. Interest rate effect (LO10-3) Go to Table 10-1, which is based on bonds paying 10
c. Purchase price (9%) ...................... $1,091.29
Sales Price (12%) .......................... 850.61
Loss .............................................. ($240.68)
Purchase Price $1,091.29
−
= = −
10. Interest rate effect (LO10-3) Using Table 10-1, assume interest rates in the market
(yield to maturity) are 14 percent for 20 years on a bond paying 10 percent.
a. What is the price of the bond?
c. Sales price (12%) .......................... $863.78
Purchase Price (14%) .................... 735.07
Profit ............................................. $128.71
Profit $128.71 17.51%
Purchase Price $735.07
==
11. Effect of maturity on bond price (LO10-3) Using Table 10-2:
a. Assume the interest rate in the market (yield to maturity) goes down to 8
percent for the 10 percent bonds. Using column 2, indicate what the bond price
will be with a 10-year, a 15-year, and a 20-year time period.
a.
Maturity
Bond price
Chapter 10: Valuation and Rates of Return
c. Based on information in part a, you would want to
own the longest-term bond possible to maximize your
gain.
d. Based on information in part b, you would want to
own the shortest-term bond possible to minimize your
loss.
12. Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage
10-12. Solution:
Jim Busby – Disk Storage Systems
N
I/Y
PV
PMT
FV
25
12
CPT PV −1,156.86
140
1,000
Present Value of Interest Payments
PVA = A × PVIFA (n = 25, i = 12%) Appendix D
PVA = $140 × 7.843 = $1,098.02
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 25, i = 12%) Appendix B
PV = $1,000 × .059 = $59
Chapter 10: Valuation and Rates of Return
$1,157.02
The bond has a value of $1,157.02. This indicates his broker is
quoting too high a price at $1,180.
13. Effect of yield to maturity on bond price (LO10-3) 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 15 percent. This return was in line
with the required returns by bondholders at that point as described next:
First compute the new required rate of return (yield to
maturity).
Real rate of return 4%
Inflation premium 3
Risk premium 5
Total return 12%
Then, use this value to find the price of the bond.
N
I/Y
PV
PMT
FV
20
12
CPT PV −1,224.08
150
1,000
Chapter 10: Valuation and Rates of Return
14. Analyzing bond price changes (LO10-3) Katie Pairy Fruits Inc. has a $1,000, 20-
year bond outstanding with a nominal yield of 15 percent (coupon equals 15% ×
Katie Pairy Fruits Inc.
N
I/Y
PV
PMT
FV
20
12
CPT PV −1,224.08
150
1,000
N
I/Y
PV
PMT
FV
20
12
CPT PV −224.08
30
0
a. Present Value of Interest Payments
PVA = A × PVIFA (n = 20, i = 12%) Appendix D
PVA = $150 × 7.469 = $1,120.35
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 20, i = 12%) Appendix B
PV = $1,000 × .104 = $104
$1,224.35
b. PVA = A × PVIFA (n = 20, i = 12%) Appendix D
Chapter 10: Valuation and Rates of Return
PVA = $30 × 7.469 = $224.07
$1,000.00
224.07
$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.
In part b, we take the present value of the $30
Chapter 10: Valuation and Rates of Return
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:
First compute the new required rate of return (yield to
maturity)
Real rate of return 2%
Inflation premium 5%
Risk premium 2%
9% Total required return
Then, use this value to find the price of the bond.
N
I/Y
PV
PMT
FV
30
9
CPT PV −1,308.21
120
1,000
Present Value of Interest Payments
PVA = A × PVIFA (n = 30, i = 9%) Appendix D
PVA = $120 × 10.274 = $1,232.88
Chapter 10: Valuation and Rates of Return
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 30, i = 9%) Appendix B
PV = $1,000 × .075 = $75.00
Total Present Value
Present Value of Interest Payments $1,232.88
Present Value of Principal Payment 75.00
Total Present Value or Price of the Bond $1,307.88
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:
First compute the new required rate of return (yield to
maturity).
Real rate of return 8%
Inflation premium 3%
Risk premium 7%
18% Total required return
Then, use this value to find the price of the bond.
Chapter 10: Valuation and Rates of Return
N
I/Y
PV
PMT
FV
15
18
CPT PV −847.25
150
1,000
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
10-17. Solution:
Lance Whittingham IV – Leisure Time Corporation
N
I/Y
PV
PMT
FV
18
14
CPT PV −353.26
40
1,000
a. Current price of the bonds
Chapter 10: Valuation and Rates of Return
Present Value of Interest Payments
PVA = A × PVIFA (n = 18, i = 14) Appendix D
PVA = $40 × 6.467 = $258.68
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 18, i = 14%) Appendix B
$353.68
b. Percent increase at maturity
Maturity Value $1,000.00
Current price – 353.68
Dollar increase $ 646.32
10-18. Solution:
N
I/Y
PV
PMT
FV
10
CPT I/Y 20.53
−690
130
1,000
Chapter 10: Valuation and Rates of Return
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
$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?
Answer: 10%
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?
Semiannual:
Payment: $1000 × .08 = $80/2 = $40
n: 6 years × 2 payments per year = 12
N
I/Y
PV
PMT
FV
12
CPT I/Y 3.25
−1,073.55
40
1,000
3.25% × 2 = 6.5% annual rate
Chapter 10: Valuation and Rates of Return
7 × 2 = 14 number of periods (n)14%/2 = 7% yield to
maturity expressed on a semiannual basis
N
I/Y
PV
PMT
FV
14
7
CPT PV −868.82
55
1,000
Answer: $868.82 Bond price
Present Value of Interest Payments
PVA = A × PVIFA (n = 14, i = 7%) Appendix D
PVA = $55 × 8.745 = $480.98
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 14, i = 7%) Appendix B
PV = $1,000 × .388 = $388
Present Value of Interest Payments $480.98
Present Value of Principal Payment 388.00
Total Present Value or Price of the Bond $868.98
Chapter 10: Valuation and Rates of Return
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?
Olsen’s Clothing Stores
N
I/Y
PV
PMT
FV
a. Present Value of Interest Payments
PVA = A × PVIFA (n = 30, i = 5%) Appendix D
PVA = $50 × 15.372 = $768.60
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
PVA = $50 × 13.590 = $679.50
Chapter 10: Valuation and Rates of Return
PV = FV × PVIF (n = 20, i = 4%) Appendix B
24. North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed
$6.00 $42.86
.14 =
Chapter 10: Valuation and Rates of Return
25. Preferred stock value (LO10-4) X-Tech Company issued preferred stock many
years ago. It carries a fixed dividend of $12.00 per share. With the passage of time,
0.17 =
c. The price of preferred stock will increase as yields
Chapter 10: Valuation and Rates of Return
discount rate declines, and a lower present value as the
discount rate increases.
26. Analogue Technology has preferred stock outstanding that pays a $9 annual
dividend. It has a price of $76. What is the required rate of return (yield) on the
preferred stock?
Analogue Technology
$76
p
pp
KP
= = =
(All of the following problems pertain to the common stock section of the chapter.)
27. Common stock value (LO10-5) Stagnant Iron and Steel currently pays a $12.25
annual cash dividend (D0). The company plans to maintain the dividend at this level
for the foreseeable future as no future growth is anticipated. If the required rate of
return by common stockholders (Ke) is 18 percent, what is the price of the common
stock?
Stagnant Iron and Steel
e
D
BioScience Inc.
Chapter 10: Valuation and Rates of Return
D
29. Common stock value under different market conditions (LO10-5) Ecology Labs
Inc. will pay a dividend of $6.40 per share in the next 12 months (D1). The required
rate of return (Ke) is 14 percent and the constant growth rate is 5 percent.
a. Compute P0.
Ecology Labs Inc.
1
0e
D
PKg
=−
−
−
30. Maxwell Communications paid a dividend of $3 last year. Over the next 12
months, the dividend is expected to grow at 8 percent, which is the constant
Chapter 10: Valuation and Rates of Return
Maxwell Communications
1
0e
D
PKg
=−
−
31. Common stock value based on determining growth rate (LO10-5) Justin Cement
Company has had the following pattern of earnings per share over the last five years:
Year Earnings per Share
20X1 ........................... $5.00
(P0) at the beginning of 20X6?
Justin Cement Company
Earnings have been growing at a rate of 6 percent per year.
Base Period
(20X2/20X1) – 1 = 6% growth ($5.30/$5.00)
(20X3/20X2) – 1 = 6% growth ($5.62/$5.30)
Chapter 10: Valuation and Rates of Return
(20X4/20X3) – 1 = 6% growth ($5.96/$5.62)
(20X5/20X4) – 1 = 6% growth ($6.32/$5.96)
The projected EPS for 20X6 is $6.70 = ($6.32 × 1.06).
Dividends for 20X6 represent 40 percent of earnings or
$2.68 ($6.70 × 40%).
This is the value for D1.
e
10-32. Solution:
33. Common stock required rate of return (LO10-5) A firm pays a $1.50 dividend at
the end of year one (D1), has a stock price of $155 (P0), and a constant growth rate
(g) of 10 percent.
a. Compute the required rate of return (Ke).
Chapter 10: Valuation and Rates of Return
10-33. Solution:
$155.00
e
b. If the dividend payment increases, the dividend yield
(D1/P0) will go up, and the required rate of return (Ke)
will also go up. This assumes that the stock price
34. Trump Office Supplies paid a $3 dividend last year. The dividend is expected to
grow at a constant rate of 7 percent over the next four years. The required rate of
return is 14 percent (this will also serve as the discount rate in this problem). Round
all values to three places to the right of the decimal point where appropriate.
a. Compute the anticipated value of the dividends for the next four years. That is,
compute D1, D2, D3, and D4—for example, D1 is $3.21 ($3.00 × 1.07).
b. Discount each of these dividends back to the present at a discount rate of 14
percent and then sum them.
c. Compute the price of the stock at the end of the fourth year (P4).
5
4e
D
PKg
=−
Chapter 10: Valuation and Rates of Return
(D5 is equal to D4 times 1.07)
Chapter 10: Valuation and Rates of Return
$60.10 × .592 = 35.579
Chapter 10: Valuation and Rates of Return
g. Price = P/E × EPS
P/E = 8 × 1.1 = 8.8
Price = 8.8 × $5.32 = $46.816
.959
3) g increases, stock price increases
1
14
CPT PV −2.816
0
3.210
2
14
CPT PV −2.643
0
3.435
3
14
CPT PV −2.481
0
3.675
4
14
CPT PV −2.328
0
3.932
4
14
CPT PV −35.584
0
60.10
Chapter 10: Valuation and Rates of Return
35. Common stock value based on PV calculations (LO10-5) Beasley Ball Bearings
paid a $4 dividend last year. The dividend is expected to grow at a constant rate of 2
percent over the next four years. The required rate of return is 15 percent (this will
also serve as the discount rate in this problem). Round all values to three places to
the right of the decimal point where appropriate.
a. Compute the anticipated value of the dividends for the next four years. That is,
compute D1, D2, D3, and D4—for example, D1 is $4.08 ($4 × 1.02).
b. Discount each of these dividends back to present at a discount rate of 15 percent
and then sum them.
c. Compute the price of the stock at the end of the fourth year (P4).
5
4e
D
PKg
=−
(D5 is equal to D4 times 1.02.)
Beasley Ball Bearings
Chapter 10: Valuation and Rates of Return
$11.966
$33.977 × .572 = $19.435
.15 .02 .13
e
−−
10-35. (Continued)
Chapter 10: Valuation and Rates of Return
3) g increases, stock price increases
1
15
CPT PV −3.550
0
4.080
2
15
CPT PV −3.146
0
4.162
3
15
CPT PV −2.793
0
4.245
4
15
CPT PV −2.477
0
4.330
4
15
CPT PV −19.426
0
33.977
Chapter 10: Valuation and Rates of Return
COMPREHENSIVE PROBLEM
Preston Products (Dividend valuation model, P/E ratio) (LO10-5)
Mel Thomas, the chief financial officer of Preston Resources, has been asked to do
an evaluation of Dunning Chemical Company by the president and Chair of the
Board, Sarah Reynolds. Preston Resources was planning a joint venture with
$1.30 and it increases by 10 percent (g) each year. Also discount back the
( )
3 4 3 1
e
Kg
−
If you have done all these steps correctly, you should get an answer approximately
equal to the answer in part a.
c. As an alternative measure, you also examine the value of the firm based on the
price-earnings (P/E) ratio times earnings per share.
Since the company is privately traded (not in the public stock market), you will
get your anticipated P/E ratio by taking the average value of five publicly traded
chemical companies. The P/E ratios were as follows during the time period under
analysis:
P/E Ratio
Dow Chemical ........... 15
DuPont ....................... 18
Georgia Gulf .............. 7
3M .............................. 19
Olin Corp ................... 21
Assume Dunning Chemical has earnings per share of $2.10. What is the stock value
based on the P/E ratio approach? Multiply the average P/E ratio you computed
Chapter 10: Valuation and Rates of Return
Preston Resources—Dunning Chemical
e
D
b. Future Value of Dividends
Chapter 10: Valuation and Rates of Return
$3.30
.14 .10 .04
−
Present Value of Future Stock Price
Chapter 10: Valuation and Rates of Return
CP 10-1. (Continued)
c. Average P/E Ratio of Five Chemical Firms
Dow Chemical 15
DuPont 18
Georgia Gulf 7
3M 19
Chapter 10: Valuation and Rates of Return
CP 10-1. (Continued)
Chapter 10: Valuation and Rates of Return
Appendix
10A–1. Valuation of supernormal growth firm (LO10-5) Surgical Supplies
Corporation paid a dividend of $1.12 per share over the last 12 months. The
dividend is expected to grow at a rate of 25 percent over the next three years
(supernormal growth). It will then grow at a normal, constant rate of 7 percent
for the foreseeable future. The required rate of return is 12 percent (this will
also serve as the discount rate).
a. Compute the anticipated value of the dividends for the next three years
(D1, D2, and D3).
10A–1. Solution
Surgical Supplies Corporation
D3 $1.75 (1.25) = $2.19
Chapter 10: Valuation and Rates of Return
$4.20
$46.80 × .712 = $33.32