Exemption Exam - Finance
Show all work clearly, if you desire partial credit for incomplete answers. If you need to
make any extra assumptions to answer any of the questions, do so. However, state the
additional assumptions clearly.
Present Value
You plan to retire in 30 years, and you anticipate the need for an annual pre-tax retirement
income of $200,000 per year, in today's dollars.
a. Assuming an expected inflation rate of 4% over the next 30 years, what is your annual
retirement income needs in 2027 dollars?
b. Assume your life expectancy from today is 60 years. What is the present value of the
cost of your retirement, under the assumption that the discount rate is 7% for all future
cash flows?
c. Would the answer to (b) be very different if you assumed that you would live forever,
upon retirement?
d. Assume that you may save tax-free in a personal retirement account, and that you will
only be taxed upon the money you withdraw annually upon retirement. You have two
investment choices for the account. You may invest in stocks with an expected return of
12% per year, or you may invest in bonds with an expected return of 7% per year.
Compare how much you will have to contribute to your retirement account each year for
the next 30 years to meet your income goal, under the two investment policies. Assume
inflation will be 4% indefinitely.
e. Is there a simple mathematical expression that approximates the relationship between
savings each year for the next 30 years, and the future annual retirement income required?
Asset Allocation
Suppose you have two stocks in your portfolio, Max and Min. The expected return of Max
is 10% and the expected return of Min is 7%. The standard deviation of Max is 30% and
the standard deviation of Min is 20%. The correlation between the two securities is .3.
Suppose the riskless asset has an expected return of 5%.
a. What is the mean and the standard deviation of a portfolio composed of 50% Max and
50% Min?
b. Which has the highest Sharpe ratio, Max, Min or the 50/50 portfolio?
c. Suppose the correlation between Max and Min was -1. Could you identify an arbitrage
opportunity, and if so, what credit conditions would allow the investor to exploit this
opportunity? No need to calculate exact portfolio weights for the opportunity. Simply
explain the positions required.
Asset Pricing
Suppose the expected return to the market portfolio was 12%, and the standard deviation
of the market portfolio was 20%. Further, assume that all of the conditions in the previous
question hold.
a. Assuming for a moment that market prices are efficient, and that the CAPM holds, what
is the CAPM beta of the Max company?
b Now consider what you might do if the price of the Max company were lower, such that
the firm had an expected return of 12%, however the beta remained the same. Construct
a portfolio (with positive and negative weights) of the market security, the riskless asset
and shares of Max such that the portfolio has an expected return greater than the riskless
rate, but zero beta.
Capital Structure
Carbon Monoxide Unlevered Inc. (CUI) & Carbon Dioxide Levered Inc. (CLI) are two
environmentally conscious socially responsible companies manufacturing the same line
of pollution control equipment. The two firms are identical in every way except in their
capital structures: CUI is unlevered while CLI has debt of $ 30 mm yielding 10% p.a. Both
firms have expected EBIT of $ 20 mm p.a. Each firm has 2 million common shares
outstanding. CLI's shares trade at $ 20/share.
1) Suppose that corporate income is taxed @ 30%. There are no personal taxes.
1a) What should CUI's share trade at?
1b) Compute the WACC of each firm. Are the WACCs different? Why (not)?
2) Suppose that in addition to corporate taxes, ordinary income is taxed at 20%. Dividends
and capital gains are assumed to be tax exempt. At what price should CUI's shares trade
in the market?
3) We are back in the no personal tax scenario. Consider a project that costs $50 mm,
having the same risk as that of the existing business of the two firms. The project yields an
annual pre-tax cashflow of $ 15 mm p.a. What would the new share price of CLI be if it
accepted this project? What would CUI's price be, if it took this project?
Option Pricing
The following price data pertain to American options on the stock of a high tech company
Escape Inc. The options have 90 days to expiry. Assume that the borrowing/lending rate
equals 5% p.a. (Note: For those unfamiliar with how to read option price data (you are
supposed to know this but anyway....), we have explained the content of each column, i.e.,
what the number in each column below represents.
Escape Inc.
25.25 30 Jul 210 3.5 45 2.0
Stock Strike Expiry --CALL DATA-- --PUT DATA--
Open Price Open Price
Interest Interest
(a) Is there an arbitrage opportunity implicit in the option prices? If there is one, describe how you would exploit it and give the resulting payoffs.
(b) Ignore the put price (assume it is no longer traded in the market), and answer
the following questions
(b1) Would the price of an otherwise identical 180 day european call option be greater than, lesser than or equal to $ 3.5? Why?
(b2) Suppose that the riskless rate increases to 14.5% from 5%. Would the
price of the call option increase, decrease or remain the same? Why?
Qualitative Question
Shareholders of diversified tobacco companies (DTCs) in the US often argue that the tobacco and non-tobacco operations must be spun off into separate companies in order to increase shareholder wealth. Explain why share prices of DTCs might increase upon announcement of spinoffs. If spinoffs are value increasing in the above sense, why do tobacco companies remain diversified?
Note: This is a finance exam and is only intended to test your knowledge of the finance area. Hence, cast your answer in terms of finance theory.