Nanyang Business School
CF—Final Exam
The following test consists of 4 questions, worth 150 points. Answer to the questions to the best of your ability. This is an
individual test. You may use any reference materials you like—lectures notes, assignments, assignment solutions, othe
course materials provided, your own notes, textbooks, notes from other courses, etc. You may also use a calculator or a
computer with appropriate software to solve these questions. The one thing you may not use is the assistance of anothe
person. If you are unsure of what the questions are asking you to do, you may ask the instructor. You should feel free
to discuss general course concepts with other members of the class (or with anyone who is willing to talk about such
things with you), but you should not discuss specific issues/questions related to this test with other members of the class
or anyone else, until after the due date. (Please note that the exam is due before midnight, Singapore time, on the due
date.)
1. [40 points] A firm has developed a COVID-19 vaccine. This vaccine is expected to be in demand for the next
four years, after which there will be no demand. The vaccine may not be stored; if not sold in the year it is
produced, the excess vaccine must be destroyed.
In order to produce the vaccine, a factory must be opened. The factory may be opened at the beginning of
Year 1 (i.e., now), or at the beginning of Years 2, 3, or 4 (if not already open). The cost of opening a factory
is e200 million, at the time it is opened. Once opened, a factory must eventually be closed. Because of the
complex chemicals and biological agents involved, closing the factory is a difficult and expensive operation,
costing e150 million. If the factory is opened, it must be closed by the end of Year 4 (or earlier). Each year that
the factory is open, a fixed operating cost (regardless of the amount of vaccine produced) of e400 million is
incu
ed, paid at the end of each year of operation. If the factory is closed, it may be reopened, but the opening
cost must be paid again (and also the closing cost, when it is closed for a second time).
The price of the vaccine is fixed by regulation at e45. Initial demand is 10 million units the first year. In each
subsequent year, the demand increases by 20%, or decreases by 10%, with equal probability. The revenues are
eceived at the end of each year of production.
Example—suppose the factory is opened immediately, operated for two years, and then closed. (This strategy
is presented only to illustrate the cash flows; it is not an optimal strategy.) The cash flows are as shown below,
occu
ing at the end of the indicated years.
Year 0 Year 1 Year 2
Opening cost −e200 million — —
Operating cost — −e400 million −e400 million
Closing cost — — −e150 million
Revenues — e450 million
e540 million
o
e405 million
Assume an appropriate discount rate for all cash flows is 12% per year. All applicable taxes are already included
in the numbers given. Assume throughout that the firm’s objective is to maximise firm value; it does not pursue
other objectives, such as making people healthy.
1(a). [10 points] Consider the strategy of opening the factory immediately, operating it for the next four years, and
closing it at the end of Year 4. What is the NPV of this strategy? Is this strategy better than never opening a
factory and never producing the vaccine?
Final Exam 1 04 December 2020
Nanyang Technological University
Nanyang Business School
Executive Education
CF—Corporate Finance
Semester 1, AY 2020–2021
Prof. Robert L. Kimmel
1(b). [15 points] Assume now the firm pursues the optimal strategy, opening and closing the factory at the times and
in the states that maximise firm value. What is the optimal strategy? Describe when and in what states the firm
should open the factory, and when and in what states it should close the factory. What is the NPV of pursuing
this strategy? How does the NPV of the optimal strategy compare to the NPV of the strategy from 1(a)?
1(c). [15 points] Now assume (contrary to the assumptions given) that demand for the vaccine each year after the
first increases 40% or decreases 30%, with equal probability. How do your answers to 1(b) change? Describe
the optimal strategy and its NPV under these alternate assumptions.
2. [40 points] There is a firm that has an all-equity capital structure, with 200 shares of stock outstanding. Based
on your macroeconomic forecasts, the value of the firm one year from now will depend on the state of the
macroeconomy, as shown in the following table.
State
Recession Stable Expansion
Probability XXXXXXXXXX
Market Return −10% +10% +30%
Firm Value $3, 380 $4, 056 $6, 084
Assume throughout that the CAPM describes the expected returns of all assets co
ectly. The risk-free rate is
4.00%. The above values are after any applicable corporate income tax is paid; assume that personal taxes on
all forms of investment income are at the same rate. The firm has no plan to pay any dividend before next year.
2(a). [10 points] What is the present value of the firm’s equity, today? (Answer in aggregate, i.e., the value of all 200
outstanding shares, not the value of a single share.)
As described above, the firm’s capital structure is cu
ently 100% equity, with 200 shares of stock outstanding.
However, the firm is considering selling some wa
ants. The sale of the wa
ants would have no immediate
effect on the cash flows of the firm, since whatever cash is raised through the sale of the wa
ants, management
plans to pay out to the equityholders as a one-time special dividend. However, the wa
antholders have the
ight to exercise their wa
ants one year from now. For each wa
ant exercised, the wa
antholder pays the
firm $23.40, and firm gives the wa
antholder a newly created share of stock. If the wa
antholder chooses
not to exercise the wa
ant one year from how, it expires worthless. The firm’s plan is to sell wa
ants for 100
additional shares. Assume the wa
ants have no effect on the amount of taxes paid.
2(b). [5 points] What is the value of a share in each of the three future states, if the wa
antholders exercise thei
wa
ants? (Note—there are two effects. The wa
antholders pay cash to the firm, and the number of outstanding
shares increases.) In which (if any) of the three future states will the wa
antholders want to exercise thei
wa
ants?
2(c). [10 points] What is the value of the wa
ants, today? (Note—value the wa
ants like you would value any othe
asset. Assume the wa
antholders will exercise their wa
ants optimally, i.e., they will exercise when and only
when the value they receive is greater than zero, the value they receive if they allow the wa
ants to expire.)
2(d). [10 points] What is the value of the existing equity, once the firm issues the wa
ants and pays out the special
dividend?
2(e). [5 points] How does the value of the firm under the new capital structure (with 200 shares of equity and
wa
ants for 100 additional shares) compare to the value under the original capital structure (with only 200
shares of equity)? Does the change in capital structure increase the firm value, decrease the firm value, or leave
it the same? Are the results consistent with Modigliani/Miller Proposition I? Explain
iefly.
3. [40 points] Assume investors are risk-neutral, and the risk-free rate is 0.00%. The future (one year from now)
values of the existing assets of a firm, and the NPV of a new project the firm is contemplating, are shown below.
Final Exam 2 04 December 2020
Nanyang Technological University
Nanyang Business School
Executive Education
CF—Corporate Finance
Semester 1, AY 2020–2021
Prof. Robert L. Kimmel
State
A B
Existing Assets £30, 940 £111, 384
NPV of New Project £3, 094 £6, 188
Management knows the true state of the firm (A or B), but has no way to credibly communicate the state to
its investors, who assign probability 0.5 to each of the states. To undertake the new project, an investment of
£15, 470 is needed, which the firm does not have—it would have to issue new securities to raise the necessary
funds. The firm’s cu
ent capital structure consists of 1, 547 shares of equity, and £23, 205 face value of debt,
which is due one year from now. Management’s objective is to maximise the welfare of its curent shareholders.
3(a). [15 points] Suppose investors believe the firm will issue equity to raise the necessary funds, and undertake
the new project, in both states. If the firm issues new equity, how many new shares are needed to raise the
necessary £15, 470? What should the price of these shares be? If management acts according to investo
eliefs, is it maximising the welfare of its existing shareholders?
3(b). [15 points] Suppose investors believe the firm will issue equity to raise the necessary funds, and undertake
the new project, only in State A. If the firm issues new equity, how many new shares are needed to raise
the necessary £15, 470? What should the price of these shares be? If management acts according to investo
eliefs, is it maximising the welfare of its existing shareholders?
3(c). [10 points] Is there an cost to asymmetric information in this scenario? Why or why not? Explain
iefly. If
there is, can the problem be resolved if the firm issues debt instead of equity? Does it matter what the priority
of the debt is? Explain
iefly.
4. [30 points] Assume the CAPM describes the expected returns of all assets co
ectly. The risk-free rate is 4%,
and the expected return of the market is 12%. An all-equity firm has cash flows that are a perpetuity; each year,
the firm generates a cash flow which has expected cash flow of S$4 million, after corporate income tax is paid.
The beta coefficient of the firm’s equity is 0.75. The corporate tax rate is 33%. Personal tax rates on debt and
equity are each 20%.
4(a). [5 points] What is the value of the firm’s equity?
4(b). [5 points] What is the WACC of the firm?
Now suppose the firm issues S$10, 000, 000 market value of debt, and pays these funds to the shareholders
(either through a special dividend, or by repurchasing shares). It is forecast that the debt will be risky, with a
eta coefficient of 0.125.
4(c). [5 points] What is the value of the equity, after the recapitalisation is completed?
4(d). [10 points]