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Questions and Answers of Corporate Finance

Compute λ if the dividend on the CD is 0, the initial price is $1300, and the payoff is $1200 + λ × max(0, S5.5 − 1300).
Consider the equity-linked CD example in Section 15.3.a. What happens to the value of the CD as the interest rate, volatility, and dividend yield change? In particular, consider alternative
Use the information in Table 15.5.a. What is the price of a bond that pays one barrel of oil 2 years from now?b. What annual cash payment would the bond have to make in order to sell for $20.90?
Using the information in Table 15.5, suppose we have a bond that pays one barrel of oil in 2 years.a. Suppose the bond pays a fractional barrel of oil as an interest payment after 1 year and after 2
Using the information in Table 15.5, suppose we have a bond that after 2 years pays one barrel of oil plus λ × max(0, S2 − 20.90), where S2 is the year-2 spot price of oil. If the bond is to sell
Using the information in Table 15.5, assume that the volatility of oil is 15%.a. Show that a bond that pays one barrel of oil in 1 year sells today for $19.2454.b. Consider a bond that in 1 year has
Swaps often contain caps or floors. In this problem, you are to construct an oil contract that has the following characteristics: The initial cost is zero. Then in each period, the buyer pays the
You have been asked to construct an oil contract that has the following characteristics: The initial cost is zero. Then in each period, the buyer pays S − F, with a cap of $21.90 − F and a floor
Using Figure 3.16 on page 85 as the basis for a discussion, explain under what circumstances an investor might prefer a PEPS to the stock or vice versa.
Suppose the effective semiannual interest rate is 3%.a. What is the price of a bond that pays one unit of the S&P index in 3 years?b. What semiannual dollar coupon is required if the bond is to
Consider again the Netscape PEPS discussed in this chapter and assume the following: the price of Netscape is $39.25, Netscape is not expected to pay dividends, the interest rate is 7%, and the
A DECS contract pays two shares if ST < 27.875, 1.667 shares if the price is above ST > 33.45, and $27.875 and $55.75 otherwise. The quarterly dividend is $0.87. Value this DECS assuming that S
A stock purchase contract with a zero initial premium calls for you to pay for one share of stock in 3 years. The stock price is $100 and the 3-year interest rate is 3%.a. If you expect the
Value the M&I stock purchase contract assuming that the 3-year interest rate is 3% and the M&I volatility is 15%. How does your answer change if volatility is 35%?
Use information from Table 15.5.a. What is the price of a bond that pays one unit of the S&P index in 2 years?b. What quarterly dollar coupon is required if the bond is to sell at par?c. What
Assume that the volatility of the S&P index is 30%.a. What is the price of a bond that after 2 years pays S2 + max(0, S2 − S0)?b. Suppose the bond pays S2 + [λ × max(0, S2 − S0)]. For what
Assume that the volatility of the S&P index is 30%.a. What is the price of a bond that after 2 years pays S0 + max(0, S2 − S0)?b. Suppose the bond pays S0 + [λ × max(0, S2 − S0)] in year 2.
Assume that the volatility of the S&P index is 30% and consider a bond with the payoff S2 + λ × [max(0, S2 − S0) − max(0, S2 − K)].a. If λ = 1 and K = $1500,
Explain how to synthetically create the equity-linked CD in Section 15.3 by using a forward contract on the S&P index and a put option instead of a call option.
Consider the equity-linked CD in Section 15.3. Assuming that profit for the issuing bank is zero, draw a graph showing how the participation rate, γ , varies with the coupon, c. Repeat assuming the
Compute the required semiannual cash dividend if the expiration payoff to the CD is $1300− max(0, 1300 − S5.5) and the initial price is to be $1300.
There is a single debt issue with a maturity value of $120. Compute the yield on this debt assuming that it matures in 1 year, 2 years, 5 years, or 10 years. What debt-to-equity ratio do you observe
Assume there are 20 shares outstanding. Compute the value of the warrant and the share price for each of the following situations.a. Warrants for 2 shares expire in 5 years and have a strike price
A firm has outstanding a bond with a 5-year maturity and maturity value of $50, convertible into 10 shares. There are also 20 shares outstanding. What is the price of the warrant? The share price?
Suppose a firm has 20 shares of equity, a 10-year zero-coupon debt with a maturity value of $200, and warrants for 8 shares with a strike price of $25. Compute the value of the debt, the share
Suppose a firm has 20 shares of equity and a 10-year zero-coupon convertible bond with a maturity value of $200, convertible into 8 shares. What is the value of the debt, the share price, and the
Using the assumptions of Example 16.4, and the stock price derived in Example 16.5 suppose you were to perform a "naive" valuation of the convertible as a risk free bond plus 50 call options on the
Consider Panels B and D in Figure 16.4. Using the information in each panel, computer the share price at each node for each bond issue.
As discussed in the text, compensation options are prematurely exercised or canceled for a variety of reasons. Suppose that compensation options both vest and expire in 3 years and that the
XYZ Corp. compensates executives with 10-year European call options, granted at the money. If there is a significant drop in the share price, the company's board will reset the strike price of the
Suppose that top executives of XYZ are told they will receive at-the-money call options on 10,000 shares each year for the next 3 years. When granted, the options have 5 years to maturity. XYZ's
Suppose that S = $100, σ = 30%, r = 6%, t = 1, and δ = 0. XYZ writes a European put option on one share with strike price K = $90.a. Construct a two-period binomial tree for the stock and
There is a single debt issue. Compute the yield on this debt assuming that it matures in 1 year and has a maturity value of $127.42, 2 years with a maturity value of $135.30, 5 years with a maturity
Firm A has a stock price of $40 and has made an offer for firm B where A promises to pay $60/share for B, as long as A's stock price remains between $35 and $45. If the price of A is below $35, A
Firm A has a stock price of $40, and has made an offer for firm B where A promises to pay 1.5 shares for each share of B, as long as A's stock price remains between $35 and $45. If the price of A is
The strike price of a compensation option is generally set on the day the option is issued. On November 10, 2000, the CEO of Analog Devices, Jerald Fishman, received 600,000 options. The stock price
Four years after the option grant, the stock price for Analog Devices was about $40. Using the same input as in the previous problem, compute the market value of the options granted in 2000, assuming
Suppose that a firm offers a 3-year compensation option that vests immediately. An employee who resigns has two years to decide whether to exercise the option. Compute annual compensation option
There are four debt issues with different priorities, each promising $30 at maturity.a. Compute the yield on each debt issue assuming that all four mature in 1 year, 2 years, 5 years, or 10
Suppose there is a single 5-year zero-coupon debt issue with a maturity value of $120. The expected return on assets is 12%. What is the expected return on equity? The volatility of equity? What
Repeat the previous problem for debt instead of equity.
In this problem we examine the effect of changing the assumptions in Example 16.1.a. Compute the yield on debt for asset values of $50, $100, $150, $200, and $500. How does the yield on debt change
The firm is considering an investment project costing $1. What is the amount by which the project's value must exceed its cost in order for shareholders to be willing to pay for it? Repeat for
Now suppose the firm finances the project by issuing debt that has lower priority than existing debt. How much must a $1, $10, or $25 project be worth if the shareholders are agreed to fund it?
Now suppose the firm finances the project by issuing debt that has higher priority than existing debt. How much must a $10 or $25 project be worth if the shareholders are agreed to fund it?
Suppose you have a project that will produce a single widget. Widgets today cost $1 and the project costs $0.90. The risk-free rate is 5%. Under what circumstances would you invest immediately in the
Consider a project that in one year pays $50 if the economy performs well (the stock market goes up) and that pays $100 if the economy performs badly (the stock market goes down). The probability of
Verify the binomial calculations in Figure 17.3.
A project costing $100 will produce perpetual net cash flows that have an annual volatility of 35% with no expected growth. If the project existed, net cash flows today would be $8. The project beta
A project has certain cash flows today of $1, growing at 5% per year for 10 years, after which the cash flow is constant. The risk-free rate is 5%. The project costs $20 and cash flows begin 1 year
Consider the oil project with a single barrel, in which S = $15, r = 5%, δ = 4%, and X = $13.60. Suppose that, in addition, the land can be sold for the residual value of R = $1 after the barrel of
Verify in Figure 17.2 that if volatility were 30% instead of 50%, immediate exercise would be optimal.
Consider the last row of Table 17.1. What is the solution for S*and S* when Ks = kr = 0? (This answer does not require calculation.)
A mine costing $275 will produce 1 ounce of gold on the day the cost is paid. Gold volatility is zero. What is the value of the mine?
A mine costing $1000 will produce 1 ounce of gold per year forever at a marginal extraction cost of $250, with production commencing 1 year after the mine opens. Gold volatility is zero. What is the
Repeat Problems 17.17 and 17.18 assuming that the annual volatility of gold is 20%.
You have a project costing $1.50 that will produce two widgets, one each the first and second years after project completion. Widgets today cost $0.80 each, with the price growing at 2% per year. The
Repeat Problem 17.18 assuming that the volatility of gold is 20% and that once opened, the mine can be costlessly shut down forever. What is the value of the mine? What is the price at which the mine
Repeat Problem 17.18 assuming that the volatility of gold is 20% and that once opened, the mine can be costlessly shut down once, and then costlessly reopened once. What is the value of the mine?
Consider again the project in Problem 17.2, only suppose that the widget price is unchanging and the cost of investment is declining at 2% per year. When will you invest? What is the value today of
Consider the widget investment problem outlined in Section 17.1. Show the following in a spreadsheet.a. Compute annual widget prices for the next 50 years.b. For each year, compute the net present
Again consider the widget investment problem in Section 17.1. Verify that with S = $50, K = $30, r = 0.04879, σ = 0, and δ = 0.009569, the perpetual call price is $30.597 and exercise optimally
The stock price of XYZ is $100. One million shares of XYZ (a negligible fraction of the shares outstanding) are buried on a tiny, otherwise worthless plot of land in a vault that would cost $50
Repeat Problem 17.6, only assume that after the stock is excavated, the land has an alternative use and can be sold for $30m.
Consider the widget investment problem of Section 17.1 with the following modification.The expected growth rate of the widget price is zero. (This means there is no reason to consider project delay.)
To answer this question, use the assumptions of Example 17.1 and the risk-neutral valuation method (and risk-neutral probability) described in Example 17.2.a. Compute the value of a claim that
You drawthese five numbers randomly from a normal distribution with mean−8 and variance 15: {−7, −11, −3, 2, −15}. What are the equivalent draws from a standard normal distribution?
What is Pr(St < $98) for t = 1? How does this probability change when you change t?
Let t = 1. What is E(St |St < $98)? What is E(St |St < $120)? How do both expectations change when you vary t from 0.05 to 5? Let σ = 0.1. Does either answer change? How?
Let KT = S0erT. Compute Pr(St KT ) for a variety of T s from 0.25 to 25 years. How do the probabilities behave? How do you reconcile your answer with the fact that both call and put prices increase
Consider Pr(St <K), equation (18.23), and E(St |St < K), equation (18.28). Verify that it is possible to pick parameters such that changes in t can have ambiguous effects on Pr(St
You drawthese five numbers from a standard normal distribution: {−1.7, 0.55, −0.3, −0.02, .85}. What are the equivalent draws from a normal distribution with mean 0.8 and variance 25?
Suppose x1∼ N(1, 5) and x2 ∼ N(−2, 2). The covariance between x1 and x2 is 1.3. What is the distribution of x1+ x2? What is the distribution of x1− x2?
Suppose x1∼ N(2, 0.5) and x2 ∼ N(8, 14). The correlation between x1 and x2 is −0.3. What is the distribution of x1+ x2? Compute the distribution of x1− x2?
Suppose x1∼ N(1, 5), x2 ∼ N(2, 3), and x3 ∼ N(2.5, 7), with correlations ρ1, 2 = 0.3, ρ1, 3 = 0.1, and ρ2,3 = 0.4. What is the distribution of x1+ x2 + x3? x1+ (3× x2) + x3? x1+ x2 + (0.5×
If x ∼ N(2, 5), what is E(ex)? What is the median of ex? Calculate.
Suppose you observe the following month-end stock prices for stocks A and B:For each stock:a. Compute the mean monthly continuously compounded return. What is the annual return?b. Compute the mean
What is Pr(St > $105) for t = 1? Howdoes this probability change when you changet? How does it change when you change σ?
What is E(St |St > $105) for t = 1? How does this expectation change when you change t , σ, and r?
Let ui ∼ U(0, 1). Draw 1000 random ui and construct a histogram of the results.What are the mean and standard deviation?
For stocks 1 and 2, S1 = $40, S2 = $100, and the return correlation is 0.45. Let r = 0.08, σ1= 0.30, σ2 = 0.50, and δ1= δ2 = 0. Generate 1000 1-month prices for the two stocks. For each stock,
Assume S0 = $100, r = 0.05, σ = 0.25, δ = 0, and T = 1. Use Monte Carlo valuation to compute the price of a claim that pays $1 if ST > $100, and 0 otherwise.(This is called a cash-or-nothing
Let h = 1/52. Simulate both the continuously compounded actual return and the actual stock price, St+h. What are the mean, standard deviation, skewness, and kurtosis of both the continuously
An options trader purchases 1000 1-year at-the-money calls on a non-dividend paying stock with S0 = $100, α = 0.20, and σ = 0.25. Assume the options are priced according to the Black-Scholes
Repeat the previous problem, only assume that the options trader purchases 1000 1-year at-the-money straddles.
Refer to Table 19.1.a. Verify the regression coefficients in equation (19.12).b. Perform the analysis for t = 1, verifying that exercise is optimal on paths 4, 6, 7, and 8, and not on path 1.
Refer to Figure 19.2.a. Verify that the price of a European put option is $0.0564.b. Verify that the price of an American put option is $0.1144. Be sure to allow for the possibility of exercise at
Assume S0 = $50, r = 0.05, σ = 0.50, and δ = 0. The Black-Scholes price for a 2-year at-the-money put is $10.906. Suppose that the stock price is lognormal but can also jump, with the number of
Let ui ∼ U (0, 1). Compute _12 i=1 ui − 6, 1000 times. (This will use 12,000 random numbers.) Construct a histogram and compare it to a theoretical standard normal density. What are the mean and
Suppose that x1∼ N(0, 1) and x2 ∼ N(0.7, 3). Compute 2000 random draws of ex1 and ex2.a. What are the means of ex1 and ex2? Why?b. Create a graph that displays a frequency distribution in each
The Black-Scholes price for a European put option with S = $40, K = $40, σ = 0.30, r = 0.08, δ = 0, and t = 0.25 is $1.99. Use Monte Carlo to compute this price.Compute the standard deviation of
Let r = 0.08, S = $100, δ = 0, and σ = 0.30. Using the risk-neutral distribution, simulate 1/S1. What is E(1/S1)? Compute forward price for a contract paying 1/S1?
Suppose S0 = 100, r = 0.06, σS = 0.4 and δ = 0. Use Monte Carlo to compute prices for claims that pay the following:a. S21b.√S1c. S1-2
Suppose that ln(S) and ln(Q) have correlation ρ =−0.3 and that S0 = $100, Q0 =$100, r = 0.06, σS = 0.4, and σQ = 0.2. Neither stock pays dividends. Use Monte Carlo to find the price today of
Assume that the market index is 100. Show that if the expected return on the market is 15%, the dividend yield is zero, and volatility is 20%, then the probability of the index falling below 95 over
Suppose that on any given day the annualized continuously compounded stock return has a volatility of either 15%, with a probability of 80%, or 30%, with a probability of 20%. This is a mixture of
Use Itˆo’s Lemma to evaluate d[ln(S)].For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows (a)
The formula for an infinitely lived call is given in equation (12.18). Suppose that S follows equation (20.20), with α replaced by r, and that E* (dV ) = rV dt. Use Itˆo’s Lemma to verify that
Suppose that the processes for S1 and S2 are given by these two equations:dS1= Î±1S1dt + Ïƒ1S1dZ1dS2 = Î±2S2dt + Ïƒ2S2dZ2dQ = Î±QQdt + Q_ Î·1dZ1+ Î·2dZ2Show that, to avoid arbitrage,
Suppose that S1 follows equation (20.26) with δ = 0. Consider an asset that follows the process dS2 = α2S2 dt − σ2S2 dZ Show that (α1 − r)/σ1=−(α2 − r)/σ2. S1 and S2 that eliminates

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