Practice
Problems – Chapters 18,
19
Note:
Problems 1 through 4 assume a one-period risk-neutral world, just like the
class examples.
1)
Teeter-Totter Inc. is a levered firm with a promised debt payment of
$10,000 at time 1. Their existing assets will generate the following cashflows at
time 1:
State of Economy Probability
Cashflows
Great
0.3
10,900
Okay
0.4
6,900
Poor
0.3
4,900
In addition, the firm has $1000 in
cash. This can be invested in a
t-bill maturing at time 1, for a return of 4%.
Alternatively, the money can be invested in a project that requires an
investment of $1,000 and generates the following expected cashflows:
State of Economy Probability
Cashflows
Great
0.3
2,200
Okay
0.4
300
Poor
0.3
500
a) What is the NPV of the project?
b) What is the value of the firm,
the value of its debt and the value of its equity if the project is not taken?
c) What is the value of the firm,
the value of its debt and the value of its equity if the project is taken?
Based on these computations, will stockholders invest in this project?
2)
See-Saw Inc. is a levered firm with a promised debt payment of $5,000 at
time 1. Their existing assets will
generate the following cashflows at time 1:
State of Economy Probability
Cashflows
Great
0.2
6,200
Okay
0.5
2,400
Poor
0.3
1,200
In addition, the firm has $750 in
cash. This can be invested in a
t-bill maturing at time 1, for a return of 5%.
Alternatively, the money can be invested in a project that requires an
investment of $750 and generates the following expected cashflows:
State of Economy Probability
Cashflows
Great
0.2
1,800
Okay
0.5
500
Poor
0.3
300
a) What is the NPV of the project?
b) What is the value of the firm,
the value of its debt and the value of its equity if the project is not taken?
c) What is the value of the firm,
the value of its debt and the value of its equity if the project is taken?
Based on these computations, will stockholders invest in this project?
3)
A levered firm has a promised debt payment of $9,000 at time 1.
Their existing assets will generate the following cashflows at time 1:
State of Economy Probability
Cashflows
Great
0.3
12,000
Okay
0.45
8,500
Poor
0.25
6,000
The firm also has a project that it
can invest in today. The project
requires an investment of $1,000 and will generate the following expected
cashflows:
State of Economy Probability
Cashflows
Great
0.3
900
Okay
0.45
1,300
Poor
0.25
1,500
Assume a discount rate of 4%.
a) What is the NPV of the project?
b) What is the value of the firm,
the value of its debt and the value of its equity if the project is not taken?
c) What is the value of the firm,
the value of its debt and the value of its equity if the project is taken?
d) What is the impact of the
project on the wealth of stockholders? Will
stockholders invest in this project?
4)
A levered firm has a promised debt payment of $6,500 at time 1.
Their existing assets will generate the following cashflows at time 1:
State of Economy Probability
Cashflows
Great
0.4
8,500
Okay
0.35
7,000
Poor
0.25
5,500
The firm also has a project that it
can invest in today. The project
requires an investment of $800 and will generate the following expected
cashflows:
State of Economy Probability
Cashflows
Great
0.4
750
Okay
0.35
1,000
Poor
0.25
1,250
Assume a discount rate of 5%.
a) What is the NPV of the project?
b) What is the value of the firm,
the value of its debt and the value of its equity if the project is not taken?
c) What is the value of the firm,
the value of its debt and the value of its equity if the project is taken?
d) What is the impact of the
project on the wealth of stockholders? Will
stockholders invest in this project?
5) A levered firm has a debt-to-value ratio of 15%.
The firm’s cost of equity is 14.5%, and its weighted average cost of
capital is 13%.
a) Assume a world with just corporate
taxes and no other imperfections. If
the firm's marginal tax rate is 35%, what is the firm’s cost of debt?
What would the firm’s cost of
capital be if the firm was unlevered?
b) Now assume that personal taxes also exist.
The marginal investor has a marginal personal tax rate of 33% on ordinary
income and 20% on equity income. What
is the firm’s cost of debt? What
would the firm’s cost of capital be if the firm was unlevered?
6)
A levered firm has a debt-equity ratio of 90%.
The firm’s cost of equity is 15.6%, and the required return on its debt
is 12%. Assume T’ is
20%.
a)
What is the firm’s weighted average cost of capital?
b)
If the firm’s debt-equity ratio falls to 2/3, what is the new WACC?
7)
A levered firm has a debt-to-value ratio of 45%.
The cost of equity is 18%, and its weighted average cost of capital is
12%. Assume T’ is 20%.
a)
What is the firm’s cost of debt?
b)
If the firm increases the debt-to-value ratio to 60%, the required return
on its debt would increase by one-fifth. At this debt ratio, what would be the firm’s weighted
average cost of capital and its cost of equity?
8) Shop-or-Rob’s debt has a market value of $800,000.
If the firm had no debt, the required return on its equity would be 11%,
and its expected cashflows would be $220,000 each year forever.
The required return on the debt is 6%.
a) Assume a world with just corporate
taxes and no other imperfections. If
the firm's marginal tax rate is 35%, what is the value of the firm, the value of
equity, the required return on its equity, and its weighted average cost of
capital?
b) Now assume that personal taxes also
exist. The marginal investor has a
marginal personal tax rate of 33% on ordinary income and 20% on equity income.
What is the value of the firm, the value of equity, the required return
on its equity, and its weighted average cost of capital?
9)
Myopic Microwaves Inc. has a total market value of $25 million, $8
million of which is the market value of its debt.
The required return on the firm’s debt is 11.5%.
The required return on equity is 16.5%.
Assume T’ is 20%. What
is MMI’s required return on assets?
10)
Tom’s Turkeys has annual expected cashflows forever of $1,250,000.
It has issued perpetual debt with annual interest payments of $300,000.
The required return on the debt is 6%.
The required return on the firm’s assets is 9.625%. Assume T’ is 20%.
a) What is the value of the TT’s
equity?
b) What is the required return on their equity?
c) What is their WACC?
11)
An unlevered firm has a cost of capital of 9.5%, and annual expected
cashflows forever of $1,500,000. Assume
T’ is 20%. If the firm decides to become a levered firm with a
debt-to-value ratio of .25, what will its WACC be?
How much will the value of the firm increase?
12) A levered
firm has annual expected cashflows forever
of $575,000. The required return on
assets is 10%. The annual interest
on its perpetual debt is $120,000, and the required return on the debt is 7.25%.
T’ is 20%.
a) What is the firm’s WACC?
b) What is the value of their equity?
c) If the firm now increases its debt-to-value ratio to 40%,
what is value of equity after this change?
13) Estimating the WACC for a new project in the computer
peripherals industry, you have come up with the following estimates/information
for other firms in this industry:
E
Re
D
Rd
Firm A
440
12.4%
115
5.99%
Firm B
560
12.8%
155
6.02%
Firm C
680
12.6%
184
6.00%
Firm D
770
13.2%
220
6.05%
Assume that T’
is 20%. If the project has a target
debt-to-value ratio of 40% (in market value terms), what is your estimate of the
project’s WACC?
14 a) Fill in the blanks in the table below (assuming that T’ is 20%):
D/V
Ra
Re
Rd
WACC
Firm A
.33 13.10%
-
9.1%
-
Firm B
.36
-
14.89% 9.4%
-
Firm C
.42
-
-
9.6%?
12.06%
Firm D
.38 13.20%
14.58%
-
12.1968%
b) Now assume
you are estimating the WACC for a new project in the computer
peripherals industry, and these are four firms in that industry.
If
the project will have a market value D/V ratio of 35%, what is your estimate of
the project’s WACC?
15) Sethlet Enterprises is a start-up firm with a new project,
which requires an investment of $111,000.
The project will generate operating cashflows of $15,900 forever.
The investment will be financed 50% by new equity, and 50% by debt.
Issue costs are 5.5% for equity and 2.5% for debt. The required return
corresponding to the project’s asset beta is 14%.
Assume that T’ is 20%.
a) Compute the adjusted NPV of the project, taking the
impact of debt financing and issue costs into account.
b) Compute
the project’s weighted average cost of capital.
16) A new project requires an investment of $2,500,000.
The project will generate operating cashflows of $305,000 forever.
The investment will be financed 60% by new equity, and 40% by debt.
Issue costs are 6% for equity and 4% for debt. If the project was
all-equity financed, its cost of capital would be 12%.
Assume that T’ is 20%.
a) Compute the adjusted NPV of the project, taking the
impact of debt financing and issue costs into account.
b) Compute
the project’s weighted average cost of capital.
17) A new project requires an investment of $1,000,000.
The project will generate operating cashflows of $110,000 forever.
The investment will be financed 75% by new equity, and 25% by debt.
Issue costs are 5% for equity and 3% for debt. The required return
corresponding to the project’s asset beta is 13%.
Assume that T’ is 20%.
a) Compute the adjusted NPV of the project, taking the
impact of debt financing and issue costs into account.
b) Compute
the project’s weighted average cost of capital.
18) A new project requires an investment of $500,000.
The project will generate operating cashflows of $70,000 forever.
The investment will be financed 80% by new equity, and 20% by debt.
Issue costs are 5% for equity and 2.5% for debt. If the project was
all-equity financed, its cost of capital would be 12%.
Assume that T’ is 20%.
a) Compute the adjusted NPV of the project, taking the
impact of debt financing and issue costs into account.
b) Compute
the project’s weighted average cost of capital.
19
Mark
the following statements with a T or an F to indicate whether they
are true or false (no explanations required or considered):
a)
If there were no bankruptcy costs, the firm’s capital structure
decision would not be affected by the probability of bankruptcy.
b)
If there were no bankruptcy costs or agency costs of debt in the real
world, the marginal benefit of issuing debt would remain constant at T’.
c)
A levered firm in financial distress may sometimes accept a negative NPV
project if the cashflows from the project are negatively correlated with
existing cashflows.
d)
When the stockholders of a levered firm end up accepting a negative NPV
project or rejecting a positive NPV project, their wealth increases by doing so;
hence, this represents a benefit of issuing debt.
e)
When a levered firm under-invests (rejects a positive NPV project), the
reason for this is that stockholders have to put up the entire investment, but
too much of the resulting cashflows go to bondholders.
f)
Different firms have different marginal costs and marginal benefits of
issuing debt, leading them to choose a different debt ratio.
g)
A more capital intensive firm will tend to have a higher debt ratio.
h)
When we use either the APV method or the WACC method to compute a
project’s NPV, we are taking the effect of debt financing into account instead
of ignoring it. Hence, interest
charges should not be ignored in computing a project’s net cashflows.
i) If
interest charges are deducted when computing net cashflows, that gives the
cashflows to stockholders, instead of the total cashflows generated by the
assets.
j)
Managers who know their shares are under-priced prefer to issue debt
rather than equity; managers who know their shares are over-priced prefer to
issue equity rather than debt.
k) Internally
generated funds represent the preferred source of capital for all firms, since
there are neither any issue costs nor any inside information problems associated
with them.