1)
LeGuin’s Leggings Inc. has a new project
that will generate real cashflows of $9,000 per year for 4 years (starting at
the end of the first year). Inflation
is expected to be 3% per year for the first 2 years, and 4% per year for the
next 2 years. The nominal discount
rate for the project is 7%.
a)
Compute the project’s nominal cashflows each year.
b)
Compute the present value of the nominal cashflows using the nominal discount
rate.
b)
Compute the present value of the real cashflows using the real discount rate.
(15 points)
2) Lathen’s Walls and Streets Inc.’s existing assets are expected to generate cashflows per share of $0.44 each quarter forever.a)
What is the PV of this cashflow stream today if the discount rate is 8% per year
compounded annually?
b)
What is the PV of this cashflow stream today if the discount rate is 8% per year
compounded monthly?
(12
points)
Revenue
255,000
Manufacturing Cost
- 136,000
Allocated overheads
- 15,000
Incremental overheads
- 11,000
Depreciation
- 30,000
Interest
- 13,000
PBT
50,000
Tax (@ 35%)
- 17,500
N.I.
32,500
The
working capital required for the first year is $15,000; working capital
requirements will increase by 6% each year.
The income statement assumes straight line depreciation; the tax
depreciation for the year will be $49,000.
a)
What is the project’s net cashflow at time 0?
b)
What is the project’s net cashflow at time 1?
c)
When the project ends at time 4, what is the working capital you will recover at
that time?
(15
points)
Cash
$13,000
Other
Assets
$60,000
Project
with Investment of
$ 8,000
and an NPV of
$ 2,000
a) Firm D pays a dividend of 80 cents per share and invests
in the project today, issuing new shares to raise whatever capital it needs.
Assume that all these actions occur simultaneously.
Compute the following (where cum-dividend means before these actions and
ex-dividend means after these actions):
cum-dividend
stock price and value of equity
ex-dividend
stock price and value of equity
number
of new shares issued
the
fraction of the shares the original stockholders own at the end
If
the firm changes the dividend per share, which of these numbers will change?
b) Firm R repurchases shares worth $9,000 at the current market price and invests in the project, once again by issuing new shares to raise whatever capital it needs. Assume that all these actions occur simultaneously. Compute the following (where initial means before these actions and final means after these actions):
initial
and final stock price
number
of shares repurchased and number of new shares issued
initial
and final value of equity
the
fraction of the shares the original stockholders own at the end
(10 points)
5)
The TLC
Talcum Powder Co. is a levered firm operating in perfect capital markets, and
has expected cashflows of $8,000,000 each year forever.
The required return on its equity is 15.5% per year, and interest
payments are $4,000,000 per year forever.
a)
Without any further information, can you tell which is worth more, debt or
equity? Explain why.
b)
Now assume that if the firm were unlevered, the required return on its equity
would be 12%. What is the value of
debt, the value of equity, the required return on debt, and the weighted average
cost of capital?
c)
Suppose the debt-to-value ratio falls to 30%.
What is the new WACC?
(15
points)
6) Sadie’s Whips and Riding Supplies Inc. is a levered firm with a promised debt payment of $17,000 at time 1. Their existing assets will generate the following cashflows at time 1:
State of
Economy
Probability Cashflows
Great
0.25
24,500
Okay
0.35
9,200
Poor
0.40
8,100
In
addition, the firm has $3,000 in cash. This
can be invested in a t-bill maturing at time 1, for a return of 3%.
Alternatively, the money can be invested in a project that requires an
investment of $2,000 and generates the following expected cashflows:
State of
Economy
Probability Cashflows
Great
0.25
3,000
Okay
0.35
3,500
Poor
0.40
2,100
a)
What is the NPV of the project?
b)
How is the value of debt affected if the project is taken?
c)
Will stockholders invest in this project?
d)
What assumptions did you make, if any, to compute your answers?
(15
points)
7) Zelazny’s Gems and Fossils is a levered firm with expected annual
cashflows of $3,300,000 forever and a value of $25,875,000.
It has issued perpetual debt with annual interest payments of $1,350,000. If the firm were unlevered, its WACC would be 14.5%.
The company’s marginal tax rate is 35% and the
marginal investor has a marginal personal tax rate of 32% on ordinary
income and 19% on equity income.
a) What is the value of the firm’s debt?
b) What are the cashflows to stockholders?
c) What is the cost of debt, cost of equity and WACC?
d) If they decide to increase their debt-to-value ratio to 40%, what are the new values of cost of debt, cost of equity and WACC?
(20 points)
8) Sethlet
Enterprises is a start-up firm which plans to launch twin projects.
The total investment in both projects is $300,000.
The projects will generate operating cashflows of $39,500 forever.
The investment will be financed 20%
by internal funds, 50% by new debt and 30% by new equity.
Issue costs are 5.5% for equity and 3.5% for debt. The required return
corresponding to the projects’ asset beta is 13%.
Assume that
T’ is 20%.
a)
What is the projects’ weighted average cost of capital?
b)
What is the adjusted NPV of the project, taking the impact of debt financing and
issue costs into account?
(15
points)
9) Extra Credit Big Dividends Inc. can enter a new market today with a first generation product.
The project requires an investment of $400 million and has a required
return of 14% per year. It will generate cashflows that will start next year with
$32.5 million and grow at 5% per year forever.
The riskfree rate is 8% per year. Entering
the market today would position them to make a follow-on investment at the end
of two years (with a second-generation product).
The time 2 investment in this project will be $1000 million.
It will have the same required return as the first generation project. Cashflows are expected to start at time 3 with $76 million,
and grow at an expected rate of 6% per year forever. However, there is considerable uncertainty about the time 2
PV of the cashflows resulting from the second-generation project.
With a probability of 0.5 the PV could be $310 million more than
expected, and with a probability of 0.5 the PV could be $310 million less than
expected. These numbers correspond
to an annual standard deviation of returns of 30%.
a) What is the project’s NPV taking the
value of the real option into account using the decision tree approach?
b)
What is the project’s NPV taking the value of the real option into account
using the option pricing approach?
(20 points)
10)
Mark the following statements with a T
or an F to indicate whether they are true or false (no explanations
required or considered):
(40 points)
a)
If the actual rate is 2% each
quarter, the stated rate is a little more than 8% per year compounded quarterly.
b)
Nominal cashflows are
inflation-adjusted cashflows; real cashflows are not.
c)
How much is credited to a project in its last year for the salvage value
of assets depends on their original purchase price, the depreciation charged on
them over the life of the project and their market value at the end of the
project.
d)
If
land that was bought 10 years ago for $90,000 is used for a project today, when
its value is $50,000, the amount we should charge the project for use of the
land is $90,000.
e)
If something done by a firm is irrelevant in perfect capital markets,
then in the real world it can be relevant only for two reasons: taxes or
transaction costs.
f)
Corporations prefer dividend income to capital gains income.
g)
A pure dividend policy change can be made without changing capital
structure, but a pure capital structure change cannot be made without changing
dividend policy.
h)
If a firm pays a dividend of $5,000 or uses the same $5,000 for a share
repurchase, the
fraction of the firm’s shares held by the original stockholders at the end
will be the same.
i)
When a firm increases its dividend, stockholders are receiving a higher
return; hence the firm’s cost of equity increases.
j)
If capital gains income was effectively taxed at the same rate as
ordinary income, every dollar of debt a firm issued would increase its value by
the corporate tax rate, Tc.
k) Borrowing
an amount equal to 3% of the levered firm’s debt to buy 3% of the shares of
the levered firm provides an identical investment to buying 3% of the shares of
an otherwise identical unlevered firm.
l)
In the real world the marginal benefit of issuing debt
starts to decrease as you issue more and more debt, because beyond some point
the costs of financial distress come into play.
m)
In perfect capital markets, firms do not make themselves better off by
issuing debt rather than equity, even though the cost of debt is always less
than the cost of equity.
n) If the absence of bankruptcy costs, capital structure
decisions would be irrelevant in the real world.
o)
Firms with a relatively high
proportion of intangible assets should have a lower debt ratio.
p)
An unlevered firm would accept all positive NPV projects and reject all
negative NPV projects; a levered firm might sometimes reject a positive NPV
project or accept a negative NPV project.
q)
According to the pecking order theory of capital structure, firms that
are doing well should have high debt-equity ratios, since they will always issue
debt rather than equity.
r)
The timing option is like an American call option on a dividend paying
stock because a project produces cashflows just like a stock pays dividends.
s)
When we use the Black-Scholes formula
to value the abandonment option, X is the investment required for the project.