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Questions and Answers of
Corporate Finance
Assume that you have a logarithmic utility function for wealth U (W) = ln(W) and that you are faced with a 50/50 chance of winning or losing $1,000. How much will you pay to avoid risk if your
Given the exponential utility function U (W) = - e-aW: (a) Graph the function, assuming a < 0. (b) Does the function exhibit positive marginal utility and risk aversion? (c) Does the function have
What kind of utility function of wealth might be consistent with an individual gambling and paying insurance at the same time?
Suppose that A > B > C > D and that the utilities of these alternatives satisfy U(A) + U(D) = U(B) + U(C). Is it true that U(1/2B + 1/2C) is greater than U(1/2 A + 1/2D) because the former has a
A small businesswoman faces a 10% chance of having a fire that will reduce her net worth to $1.00, a 10% chance that fire will reduce it to $50,000, and an 80% chance that nothing detrimental will
If you are exposed to a 50/50 chance of gaining or losing $1,000 and insurance that removes the risk costs $500, at what level of wealth will you be indifferent relative to taking the gamble or
Security A pays $30 if state 1 occurs and $10 if state 2 occurs. Security B pays $20 if state 1 occurs and $0 if state 2 occurs. The price of security A is $5, and the price of security B is $10.(a)
You are given the following information:(a) What are the prices of pure security 1 and pure security 2? (b) What is the initial price of a third security i, for which the payoff in state 1 is $6 and
Interplanetary starship captain Jose Ching has been pondering the investment of his recent pilot's bonus of 1,000 stenglers. His choice is restricted to two securities: Galactic Steel, selling for 20
Ms. Mary Kelley has initial wealth W0 = $1,200 and faces an uncertain future that she partitions into two states, s = 1 and s = 2. She can invest in two securities, j and k, with initial prices of pj
Two securities have the following payoffs in two equally likely states of nature at the end of one year:Security j costs $8 today, whereas k costs $9, and your total wealth is currently $720. (a) If
Suppose that there are only two possible future states of the world, and the utility function is logarithmic.20 Let the probability of state 1, π equal 2/3, and the prices of the pure securities, p1
Historically, the empirical distributions of stock prices on the NYSE have been skewed right. Why?
(Our thanks to Nils Hakannson, University of California, Berkeley, for providing this problem.) Two securities have the following joint distribution of returns, r1 and r2: P{r1 = - 1.0 and r2 = .15}
Suppose a risk-averse investor can choose a portfolio from among N assets with independently distributed returns, all of which have identical means [E(Rj) = E(Rj)] and identical variances {σ2j =
Given decreasing marginal utility, it is possible to prove that in a mean-variance framework no individual will hold 100% of his or her wealth in the risk-free asset. Why?
Given that assets X and Y are perfectly correlated such that Y = 6 + .2X and the probability distribution for X
A market value balance sheet for the Carr Commercial Bank is given below in millions of dollars:The standard deviations and correlations between returns on asset and liability categories (excepting
Given the following relationship between x and y, y = a + bx b < 0, prove that x and y are perfectly negatively correlated.
Given the following hypothetical end-of-period prices for shares of the Drill-On Corporation,and assuming a current price of $50 per share: (a) Calculate the rate of return for each probability. What
Derive an expression for the expectation of the product of two random variables:
Using the definition of portfolio variance, prove that a perfectly hedged stock portfolio that is 100 shares long and 100 shares short is perfectly risk free.
Given Professor Singer's variance-covariance matrix:(a) Calculate the variance of an equally weighted portfolio.(b) Calculate the covariance of a portfolio that has 10% in asset 1,80% in asset 2, and
Given two random variables x and y:(a) Calculate the mean and variance of each of these variables, and the covariance between them. (b) Suppose x and y represent the returns from two assets.
Prove that for any securities X and Y:
Let R1 and R2 be the returns for two securities with E(R1) = .03 and E(R2) = .08, VAR (R1) = .02, VAR(R2) = .05, and COV(R1, R2) = -.01. (a) Plot the set of feasible mean-variance combinations of
Let us assume a normal distribution of returns and risk-averse utility functions. Under what conditions will all investors demand the same portfolio of risky assets?
Given the facts of Problem 6.9, and that the common stock of the Rapid Rolling Corporation has E(Rk) - 25% and o2k = 52%, what is the systematic risk of the common stock? What is its unsystematic
(a) If the expected rate of return on the market portfolio is 14% and the risk-free rate is 6%, find the beta for a portfolio that has expected rate of return of 10%. What assumptions concerning this
You believe that the Beta Alpha Watch Company will be worth $100 per share one year from now. How much are you willing to pay for one share today if the risk-free rate is 8%, the expected rate of
Given the following variance-covariance matrix and expected returns vector (for assets X and Y, respectively) for a two-asset world:(a) What is the expected return of a zero-beta portfolio, given
Given the following variance-covariance matrix, calculate the covariance between portfolio A, which has 10% in asset 1 and 90% in asset 2, and portfolio B, which has 60% in asset 1 and 40% in asset 2:
Suppose that securities are priced as if they are traded in a two-parameter economy. You have forecast the correlation coefficient between the rate of return on Knowlode Mutual Fund and the market
You currently have 50% of your wealth in a risk-free asset and 50% in the four assets below:If you want an expected rate of return of 12%, you can obtain it by selling some of your holdings of the
The market price of a security is $40, the security's expected rate of return is 13%, the riskless rate of interest is 7%, and the market risk premium, [E(Rm) - Rj], is 8%. What will be the
Suppose you are the manager of an investment fund in a two-parameter economy. Given the following forecast: E(Rm) = .16, σ(Rm) = .20, Rf = .08 (a) Would you recommend investment in a security with
Why is the separation principle still valid in a world with (a) Nonmarketable assets? (b) A nonstochastic risk-free rate?
The following data have been developed for the Donovan Company, the manufacturer of an advanced line of adhesives:The risk-free rate is 6%. Calculate the following: (a) The expected market
Assume that the mean-variance opportunity set is constructed from only two risky assets, A and B. Their variance-covariance matrix isAsset A has an expected return of 30%, and Asset B has an
Ms. Bethel, manager of the Humongous Mutual Fund, knows that her fund currently is well diversified and that it has a CAPM beta of 1.0. The risk-free rate is 8% and the CAPM risk premium, [E(Rm) -
The following data have been developed for the Milliken Company:The yield to maturity on Treasury bills is .066 and is expected to remain at this point for the foreseeable future. Calculate the
For the data in Table Q6.4 (page 190), perform the indicated calculations.Table Q6.4
For the data in Table Q6.5 (page 191), calculate the items indicated.Table Q6.5
What are the assumptions sufficient to guarantee that the market portfolio is an efficient portfolio?
In the CAPM is there any way to identify the investors who are more risk averse? Explain. How would your answer change if there were not a riskless asset?
Given risk-free borrowing and lending, efficient portfolios have no unsystematic risk. True or false? Explain.
What is the beta of an efficient portfolio with E(Rj) = 20% if Rf = 5%, E(Rm) = 15%, and am = 20%? What is its oj? What is its correlation with the market?
What is the value of a European call option with an exercise price of $40 and a maturity date six months from now if the stock price is $28, the instantaneous variance of the return on the price is
Why will the value of an American put always be greater than or equal to the value of a corresponding European put?
Options listed for Krispy Kreme were used in the text as an example of option price estimation using implicit variance. The implicit variance from the August 35 option resulted in estimated call
The share price of Honeybear Inc. is $4.75. Call options written on Honeybear have an exercise price of $40 and mature in 71 days. The risk-free rate is 6½%, and the instantaneous price variance of
After a call contract is created, the outcome must be a zero-sum game; that is, the call writer may win or lose $N, but the call buyer will experience an opposite return of exactly $N and
Suppose that the government passes a usury law that prohibits lending at more than 5% interest, but normal market rates are much higher due to inflation. You have a customer, a Ms. Olson, who wants
What is the price of a European put if the price of the underlying common stock is $20, the exercise price is $20, the risk-free rate is 8%, the variance of the return of the underlying stock is .36
(a) Graph changes in wealth, AW, vs. changes in the prices of the underlying security, Δ S, for a portfolio where you sell one call option and sell one put option (both the same X, T, σ, and rf).
Assume you are a senior financial analyst at Morgan Stanley. You are asked by a client to determine the maximum price he or she should be willing to pay to purchase Honeywell call options having an
Given two European put options that are identical except that the exercise price of the first put, X1, is greater than the exercise price of the second put, X2, use first-order stochastic dominance
Consider a firm with current value of $5,000,000 and outstanding debt of $4,000,000 that matures in 10 years. The firm's asset rate-of-retum variance is .5. The interest on the debt is paid at
Figure 7.3 graphs the value of the call option as a function of the value of the underlying stock. Graph the value of a call option (vertical axis) against(a) Ï, the instantaneous standard
What are the conditions under which an American put would be exercised early on a stock that pays no dividends?
Consider the case of the firm with secured debt, subordinated debentures, and common stock, where the secured debt and subordinated debentures mature at the same time. Find the equations for the
The yields to maturity on five zero-coupon bonds are given below: Years to Maturity Yield
Suppose you believe your portfolio, which has a beta of 1.0, has been selected to outperform other portfolios of similar risk, but you know you cannot predict which way the market will move. If it
Suppose you are convinced that the spread between long- and short-term rates will widen, whereas everyone else thinks it will remain constant. Unfortunately, you do not know whether the general level
Your bank is exploring the possibility of using T-bond futures to minimize the exposure of shareholders to changes in the interest rate. The market value of major assets and liabilities is given in
Consider the Vasicek model where the current short-term rate is 2%, the long-run mean is 6%, the instantaneous standard deviation is 10%, and the rate of adjustment is 0.4. Derive the interest rates
Consider the Cox, Ingersoll, and Ross model where the current short-term rate is 2%, the long- run mean is 6%, the instantaneous standard deviation is 10%, and the rate of adjustment is 0.4. Derive
Consider the Ho-Lee model with π = 0.5 and δ = 0.9. Further assume that 1-, 2-, and 3-year interest rates are 4, 5, and 6%. Derive the four-period tree of bond prices.
Most futures contracts have fairly short lives, usually less than 18 months. Why are there not futures contracts with longer lives?
Suppose you observe the following yields on T-bills and T-bill futures contracts on January 5, 1991: Yield (%) March futures contract on a 90 day T-bill (futures contract
Your team of agricultural experts has observed that spot prices of rutabagas show a definite pattern, rising from January through June, then falling toward a December low. You wish to buy contracts
Suppose you can buy or sell European puts and calls on the common stock of XYZ Corporation, which has a current share price of $30, has a rate of return of standard deviation of .3, and pays no
On January 29, 1987, you could buy a March 1987 silver contract for $5,610 per ounce and at the same time sell a March 1988 contract for $6,008 an ounce. (a) Exactly what would you have done had you
A project runs for two periods and then is sold at a fair price. Its present value without flexibility is $30 million, and the initial investment is $20 million. The annual volatility of the
Assume the stochastic process for the value of the firm as shown in Fig. Q9.10 (it might be the present value of a project that has several investment phases). There are two call options in sequence.
A company operates under a hard budget constraint and has a WACC of 12%. In the current year it can spend a maximum of $80 million on a new investment. The management is considering two alternative
Two companies are developing a 50-50joint venture with an NPV of $25 million. The annual volatility of the venture is 20% and its WACC is 12%. The risk-free rate is 5%. One of the companies wants to
Using simple binomial trees, calculate the value of a European put option with the following characteristics: Underlying asset current value = 200. Abandonment value = 175. Up movement per period =
Using simple binomial trees, calculate the value of a call option with the following characteristics: Underlying asset current value = 1,000. Option exercise price = 1,250. Per-period dividends = 10%
Using simple binomial trees, calculate the value of a call option with the following characteristics: Underlying asset current value = 100. Option exercise price in period 1 = 110. Option exercise
sing simple binomial trees, calculate the value of a combined call and put option with the following characteristics: Underlying asset current value = 2,000. Contraction option = 50% reduction in
The value of a mineral extraction project depends on the inventory in the ground (12,000 tons), the price in the spot market (currently $20 per ton), the cost of capital (12%), the risk-free rate
Suppose that we have a firm whose current value is $1,000 and that (given a multiplicative stochastic process) its value could go up by 12.75% or down by 11.31%-a standard deviation of 12% per annum.
Suppose you know with certainty that the Clark Capital Corporation will pay a dividend o $10 per share on every January I forever. The continuously compounded risk-free rate is 5% (also forever). (a)
Given the following situations, determine in each case whether or not the hypothesis of an efficient capital market (semistrong form) is contradicted. (a) Through the introduction of a complex
The First National Rank has been losing money on automobile consumer loans and is considering the implementation of a new loan procedure that requires a credit check on loan applicants. Experience
Hearty Western Foods, one of the nation's largest consumer products firms, is trying to decide whether it should spend $5 million to test market a new ready-to-eat product (called Kidwich), to
The efficient market hypothesis implies that abnormal returns are expected to be zero. Yet in order for markets to be efficient, arbitrageurs must be able to force prices back into equilibrium. If
(a) Ina poker game with six players, you can expect to lose 83% of the time. How can this still be a martingale? (b) In the options market, call options expire unexercised over 80% of the time." Thus
If securities markets are efficient, what is the NPV of any security, regardless of risk?
From time to time the federal government considers passing into law an excess profits tax on U.S. corporations. Given what you know about efficient markets and the CAPM, how would you define excess
State the assumptions inherent in this statement: A condition for market efficiency is that there be no second-order stochastic dominance.
Roll's critique of tests of the CAPM shows that if the index portfolio is ex post efficient, it is mathematically impossible for abnormal returns, as measured by the empirical market line, to be
In a study on corporate disclosure by a special committee of the Securities and Exchange Commission, we find the following statement (177, D6): The "efficient market hypothesis"-which asserts that
In your own words, what does the empirical evidence on block trading tell us about market efficiency?
Which of the following types of information provides a likely opportunity to earn abnormal returns on the market? (a) The latest copy of a company's annual report. (b) News coming across the NYSE
Mr. A has received, over the last three months, a solicitation to purchase a service that claims to be able to forecast movements in the Dow Jones Industrial index. Normally, he does not believe in
The Ponzi Mutual Fund (which is not registered with the SEC) guarantees a 2% per month (24% per year) return on your money. You have looked into the matter and found that they have indeed been able
Empirical evidence indicates the mutual funds that have abnormal returns in a given year are successful in attracting abnormally large numbers of new investors the following year. Is this consistent
The Value Line Investment Survey publishes weekly stock performance forecasts. Stocks are grouped into five portfolios according to expected price performance, with Group 1 comprising the most highly
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