Practice Problems – Chapter 9
1)
|
|
Yield
today |
Historical
Avg. Annual Return |
|
3-month Treasury Bills |
1.8% |
3.7% |
|
1-year Treasury Bills |
2.2% |
4.3% |
|
20-year Treasury Bonds |
4.6% |
5.7% |
|
Stock Market |
|
12.5% |
a) What is the required return for a project with a
beta of 0.9, using a short-term riskfree rate?
b) What is the required return for a project with a beta of 0.9, using a long-term riskfree rate?
c) Explain why the two methods yield different
numbers.
2) Given the following information, what is the
required return for a project with a beta of 1.25
a) using a short-term riskfree rate
b) using a long-term riskfree rate
|
|
Yield
today |
Historical
Avg. Annual Return |
| 3-month Treasury Bills |
2.00% |
3.44% |
|
6-month Treasury Bills |
2.25% |
3.89% |
|
1-year Treasury Bills |
2.50% |
4.14% |
|
5-year Treasury Bonds |
3.00% |
4.66% |
|
10-year Treasury Bonds |
4.00% |
5.04% |
|
20-year Treasury Bonds |
5.00% |
5.35% |
|
Stock Market |
|
12.12% |
3) Given the following information, what is the
required return for a project with a beta of 1.1
a) using a short-term riskfree rate
b) using a long-term riskfree rate
|
|
Yield
today |
Historical
Avg. Annual Return |
|
1-month Treasury Bills |
2.1% |
3.7% |
|
3-month Treasury Bills |
2.3% |
3.9% |
|
6-month Treasury Bills |
2.8% |
4.2% |
|
20-year Treasury Bonds |
3.3% |
5.6% |
|
Stock Market |
|
12.25% |
4) Holy Hitchcock Corp.’s stock has a beta of 1.25.
a) What is the required return for the stock, using a short-term riskfree rate?
b) What is the required return for the stock, using a long-term riskfree rate?
c) What needs to be true of the economy today in order for the two estimates to be equal?
|
|
Yield
today |
Historical
Avg. Annual Return |
|
1-month
Treasury Bills |
1.60%
|
3.33%
|
|
3-month
Treasury Bills |
1.65%
|
3.88%
|
|
6-month
Treasury Bills |
1.70%
|
4.14%
|
|
10-year
Treasury Bonds |
4.50%
|
5.14%
|
|
20-year
Treasury Bonds |
5.20%
|
5.75%
|
|
30-year
Treasury Bonds |
5.50%
|
5.98%
|
|
Stock
Market |
|
12.22%
|
5) Chicken-n-Egg Enterprises has two divisions. The Chicken division has a market value of $5m and a beta of 1.2, while the Egg division has a market value of $3m and a beta of 0.9. What is the firm's asset beta?
6) Fill in the blanks in the following table:
|
Stock |
D/V |
bd | be | ba |
| A | 0.15 | 0.22 | 1.53 | |
| B | 0.30 | 0.15 | 0.56 | |
| C |
0.25 | 0.25 | 1.22 | |
| D | 0.20 | 1.09 | 0.90 | |
| E | 0.32 | 1.76 | 1.11 |
7) The following table shows how various betas change as you take a given firm and perform a pure capital structure change. Once again, fill in the blanks.
| D/V |
bd | be | ba |
| 0.0 | |||
| 0.2 | 0.10 | 0.90 | |
| 0.4 | 0.15 | ||
| 0.20 | 1.40 | ||
| 0.7 | 1.53 |
8)
Hyper-metropic Microwaves Inc.’s equity is worth $67 million, while its
debt is worth $28 million. 70% of
the value of the firm comes from the Appliance division, which has an asset beta
of 1.1. The remaining value comes
from the Carts and Spare Parts division, which has an asset beta of 0.85.
HMI’s debt beta is 0.25
a)
What is HMI’s equity beta?
b)
Suppose they decide to double their debt-equity ratio (without any change in
their investment decisions). Making
reasonable assumptions as necessary, compute their new equity beta.
9) Millhone Publishing is a startup firm that needs to estimate the required return for its new project. A, B and C are three existing firms in the same industry.
|
Firm
|
D/V
|
ßd |
ße |
|
A |
0.30
|
0.27
|
0.999
|
|
B
|
0.45
|
0.36
|
0.869
|
|
C
|
0.20
|
0.22
|
0.945
|
a) Use the above information to estimate the project beta for Millhone's project.
b) If D is another firm in the same industry, with a debt-to-value ratio of 0.36, and a debt beta of .32, estimate its equity beta.
10)
The Warshawski Paper Works, a startup firm in the paper industry, needs
to estimate the required return for its new project.
A, B and C are three existing firms in the paper industry.
Firm
Value of Debt
ßd
Value of Equity
ße
A
$14.0m
0.2
$26.0m
1.85
B
$24.2m
0.3
$30.8m
2.16
C
$16.1m
0.15
$29.9m
1.89
a) Use the above information
to estimate the project beta for WPW's project.
b) If D is another firm in
the same industry, with a debt-to-equity ratio of 0.36, and a debt beta of .2,
estimate its equity beta.
11) To help you estimate the project beta for a new project in the computer peripherals industry, you have collected the following information for four firms in this industry. What is the estimated project beta?
| Firm |
D/V |
bd | be |
| 1 | 0.35 | 0.32 | 1.874 |
| 2 | 0.45 | 0.45 | 2.268 |
| 3 |
0.30 | 0.24 | 1.669 |
| 4 | 0.28 | 0.27 | 1.812 |
12) Mark
the following statements with a T or a F to indicate whether they
are true or false (no explanations required):
a) If you look at annual returns for 3-month t-bills and 20-year t-bonds for the last 75 years, half the years the t-bill return will be higher and half the years the t-bond return will be higher.
b)
If you look at annual returns for the last 75 years, the
average long-term riskfree rate
c)
d) If
short-term interest rates are expected to increase today, the difference between
the yield on short-term Treasuries and the yield on long-term Treasuries today
will be more than the average historical difference between these two yields.
e) Positive NPV projects plot above the SML and negative NPV projects plot below it.
f)
If you take a given firm and increase its debt ratio while holding assets
constant, debt beta goes up (since the debt becomes riskier) so equity beta has
to go down to keep asset beta constant.
g)
Even
though equity beta represents the systematic risk stockholders will
actually bear,
we still use asset beta to compute a project's required return.
h) A firm's debt beta will always be lower than its asset beta.