39) In evaluating the required rate of return for equity financing of a capital project, the Beta
value is
A) the expected rate of growth in a firm’s profits.
B) the expected future value of a firm’s stock.
C) the volatility in the rate of return on a firm’s stock compared with the volatility in the rate of
return on a market portfolio of stocks.
D) None of the above
40) Probabilities, which are based on past data or experience, are called
A) a priori.
B) objective.
C) uncertain.
D) statistical.
41) The use of real options in capital budgeting
A) may raise the NPV of a capital project.
B) makes the analysis of the project considerably easier.
C) allows management to make decisions more quickly.
D) eliminates the need for calculating the project’s risk adjusted discount rate.
42) The use of sensitivity analysis will generally result in
A) the calculation of a certainty equivalent NPV.
B) the calculation of a best case, a base case and a worst case.
C) the calculation of the coefficient of variation.
D) the calculation of the probability of the maximum profit.
43) A drawback in the use of sensitivity analysis in capital budgeting decisions is that it doesn‘t
A) permit evaluating alternative outcomes.
B) provide estimates of net present values.
C) assign probability values to outcomes.
D) consider different possible rates of discount.
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44) The difference between sensitivity analysis and scenario analysis is
A) sensitivity analysis is a method for evaluating risk while scenario analysis is not.
B) sensitivity analysis is based on regression analysis while scenario analysis is not.
C) sensitivity analysis examines the impact on the overall results of a change in one variable
while scenario analysis examines the impacts on overall results of changes in several variables at
the same time.
D) None of the above
Analytical Questions
1) You deposit $10,000 in a savings account today. If the interest rate is 3%, what is the value in
20 years?
2) You start working at age 20 and you plan to deposit $5,000 in a savings account every year for
the next 45 years.
a. At the end of this time, how much money will you have if the interest rate is 5%?
b. You decide that’s not enough money. How much will you have to save every year if you wish
to have $1,000,000 when you retire?
3) An aircraft company has signed a contract to deliver a plane 3 years from now. The price they
will receive at the end of 3 years is $20 million. If the firm’s cost of capital is 6%, what is the
present value of this payment?
4) An aircraft company has signed a contract to sell a plane for $20 million. The firm buying the
plane will pay for it in 5 annual payments (at year end) of $4 million. If the firm’s cost of capital
is 6%, what is the net present value of this payment?
5) A firm must spend $10 million today on a project that is expected to bring in annual revenues
of $1.5 million for the next 10 years (beginning at the end of year 1).
a. If the firm’s cost of capital is 5%, what is the NPV of this project?
b. If the firm’s cost of capital is 10%, what is the NPV of this project?
c. What is the internal rate of return?
6) If an expansion proposal is accepted, allowing an otherwise idle (and useless) machine with a
market value and book value of $2,000 to be utilized, should it be recorded as a cash outflow,
and if so, how much?
7) You win the $20 million state lottery, and you have a choice of taking an amount of money per
year for the next 20 years or a flat payment now. The flat payment that the state offers you is
$9.82 million.
a. What discount rate is the state using?
b. Should you take the money or the annuity?
8) If the interest rate is 7% and the tax rate is 15%, what is the after -tax cost of capital for the
firm?
9) Inc.’s stock is currently $50. The last dividend that they paid was $1. If dividends are expected
to increase at a 10% annual rate, what is the firm’s equity cost of capital?
10) If a company’s stock is perceived to be more risky than average, what will happen to their
equity cost of capital? Explain using the capital asset pricing model.
11) Explain what is meant by the “weighted cost of capital” and how it is used in capital
budgeting.
12) Describe the Capital Asset Pricing Model (CAPM) and how it is used in capital budgeting
decisions.
13) What additional complexities arise when multinational corporations consider capital projects
on a global basis?
14) A firm’s most recent annual dividend was $2 per share; its shares sell for $40 in the stock
market, and the company expects its dividend to grow at a constant rate of 5% in the foreseeable
future. Using the dividend growth (Gordon) model, what would you estimate its equity cost of
capital to be?
15) What are the major sources of risk for the firm?
16) You buy a lottery ticket for $1. If you win, you receive $3 million. The odds of your numbers
coming up are 1:10,000,000. What is the expected value of this gamble?
17) Project A and Project B both have expected values of $5,000. Project A has a standard
deviation of $1,000, while Project B has a standard deviation of $3,000. Comment on the
desirability of these projects.
18) Project C has an expected value of $500 and a standard deviation of 50. Project D has an
expected value of $300 and a standard deviation of 10. Comment on the desirability of these
projects.
19) The Widget Company has estimated the following revenue possibilities for the year:
Sales Probability
100 0.15
150 0.20
220 0.30
290 0.20
310 0.15
a. Find expected revenue.
b. Find the standard deviation.
c. Find the coefficient of variation.
20) Savings accounts pay very low rates of interest. The average return on the stock market is
about 10-12%, in the long run. Why would anyone put money into a savings account?
21) A two-period project has the following probabilities and cash flows:
Probability Cash flow
Period 1: .25 500
.50 600
.25 700
Period 2: .30 300
.50 500
.20 700
The discount rate is 7%, and the initial investment is $1,000. How much is the expected NPV of
this project?
22) Two projects have the following NPVs and standard deviations:
Project A Project B
NPV 200 300
Standard deviation 75 100
Which of the two projects is more risky?
23) In terms of capital budgeting, explain the difference between risk and uncertainty.
24) Describe the real option approach to risk-adjusted capital budgeting.
25) Explain why risk can be insured against but uncertainty cannot.
26) You are given risky cash flow data for a three-year project:
Year Cash flow
1 $2,000
2 3,000
3 4,000
The initial cash outflow is $6,000; the risk-free interest rate is 6%, and the risk-adjusted discount
rate is 10%.
Calculate the NPV by both the risk-adjusted discount rate method and the certainty equivalent
method in such a way that the NPV will be the same using either method.
27) What additional sources of risk come from international investments?
28) The XYZ Company has estimated expected cash flows for 1996 to be as follows:
Probability Cash flow
.10 $120,000
.15 140,000
.50 150,000
.15 180,000
.10 210,000
Calculate:
a. expected value
b. standard deviation
c. coefficient of variation
d. the probability that the cash flow will be less than $100,000
29) You are given the following risky cash flows and certainty equivalent factors for a four-year
project:
Certainty
Period Cash Flow Equivalent
Factor
1 $2,500 .95
2 3,000 .92
3 4,000 .88
4 3,000 .84
The initial investment for this project is $8,000, and the risk-free interest rate is 6%. Calculate
the net present value of the project.