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fundamentals of corporate finance

Questions and Answers of Fundamentals Of Corporate Finance

10. Option delta (S22-1–S22-2) Suppose you construct a risk-free investment by buying a share of stock and selling a call option. As the share price changes, the option delta changes, and you will
11. Black–Scholes model (S22-3)a. Use the Black–Scholes formula to find the value of the following call option.i. Time to expiration one year.ii. Standard deviation 40% per year.iii. Exercise
b. Now recalculate the value of this call option, but use the following parameter values. Each change should be considered independently.i. Time to expiration two years.ii. Standard deviation 50% per
c. In which case did increasing the value of the input not increase your calculation of option value?
12. Black–Scholes model (S22-3) Use the Black–Scholes formula to value the following options:a. A call option written on a stock selling for $60 per share with a $60 exercise price. The stock’s
b. A put option written on the same stock at the same time, with the same exercise price and expiration date.Now for each of these options, find the combination of stock and risk-free asset that
13. Binomial and Black–Scholes models (S22-2-S22-3) The current price of United Carbon(UC) stock is $200. The standard deviation is 22.3% a year, and the interest rate is 21% a year.A one-year call
b. Use the formula given in Section 22-2 to calculate the up and down moves that you would use if you valued the UC option with the one-period binomial method. Now value the option by using that
c. Recalculate the up and down moves and revalue the option by using the two-period binomial method.
d. Use your answer to part (c) to calculate the option delta (1) today, (2) next period if the stock price rises, and (3) next period if the stock price falls. Show at each point how you would
14. Option risk (S22-3) “A call option is always riskier than the stock it is written on.” True or false? How does the risk of an option change when the stock price changes?
15. Option risk (S22-3)a. In Section 22-3, we calculated the risk (beta) of a six-month call option on Amazon stock with an exercise price of $1,830. Now repeat the exercise for a similar option with
b. Now calculate the risk of a one-year call on Amazon stock with an exercise price of$1,500. Does the risk rise or fall as the maturity of the option lengthens?
16. Warrants (S22-3) Use the Black–Scholes program from the Beyond the Page feature to value the Owens Corning warrants described in Section 22-3. The standard deviation of Owens Corning stock was
17. Pension fund insurance (S22-3) Use the Black–Scholes program to estimate how much you should be prepared to pay to insure the value of your pension fund portfolio for the coming year. Make
18. American options (S22-4) For which of the following options might it be rational to exercise before maturity? Explain briefly why or why not.a. American put on a non-dividend-paying stock.
b. American call—the dividend payment is $5 per annum, the exercise price is $100, and the interest rate is 10%.
c. American call—the interest rate is 10%, and the dividend payment is 5% of future stock price. (Hint: The dividend depends on the stock price, which could either rise or fall.)
19. American options (S22-4) The price of Moria Mining stock is $100. During each of the next two six-month periods the price may either rise by 25% or fall by 20% (equivalent to a standard deviation
20. American options (S22-4) Suppose that you own an American put option on Buffelhead stock (see Problem 6) with an exercise price of $220.a. Would you ever want to exercise the put early?
b. Calculate the value of the put.
c. Now compare the value with that of an equivalent European put option.
21. American options (S22-4) Recalculate the value of the Buffelhead call option (see Problem 6), assuming that the option is American and that at the end of the first six months the company pays a
22. American options (S22-4) The current price of the stock of Mont Tremblant Air is C$100.During each six-month period, it will either rise by 11.1% or fall by 10% (equivalent to an annual standard
b. Recalculate the value of the Mont Tremblant put option, assuming that it is an American option.
23. American options (S22-4) Other things equal, which of these American options are you most likely to want to exercise early?a. A put option on a stock with a large dividend or a call on the same
b. A put option on a stock that is selling below exercise price or a call on the same stock.
c. A put option when the interest rate is high or the same put option when the interest rate is low.Illustrate your answer with examples.
24. Option exercise (S22-4) Is it better to exercise a call option on the with-dividend date or on the ex-dividend date? How about a put option? Explain.CHALLENGE
25. Option delta (S22-1) Use the put-call parity formula (see Section 21-2) and the one-period binomial model to show that the option delta for a put option is equal to the option delta for a call
26. Option delta (S22-2) Show how the option delta changes as the stock price rises relative to the exercise price. Explain intuitively why this is the case. (What happens to the option delta if the
27. Option risk (S22-3) Calculate and compare the risk (betas) of the following investments: (a)a share of Amazon stock; (b) a one-year call option on Amazon; (c) a one-year put option; (d)a
28. Option risk (S22-3) In Section 22-1, we used a simple one-step model to value two Amazon options each with an exercise price of $1,830. We showed that the call option could be replicated by
b. What is the beta of the put?
c. Suppose that you were to buy one call and invest the present value of the exercise price in a bank loan. What would be the beta of your portfolio?
d. Suppose instead that you were to buy one share and one put option of Amazon. What would be the beta of your portfolio now?
e. Your answers to parts (c) and (d) should be the same. Explain.
29. Option maturity (S22-3) Some corporations have issued perpetual warrants. Warrants are call options issued by a firm, allowing the warrant holder to buy the firm’s stock.a. What does the
b. Do you think this prediction is realistic? If not, explain carefully why. (Hints: What about dividends? What about bankruptcy?)
30. Dividends (S22-4) Your company has just awarded you a generous stock option scheme.You suspect that the board will either decide to increase the dividend or announce a stock repurchase program.
Look at the stocks listed in Table 7.3. Pick at least three stocks, and find call option prices for each of them on finance.yahoo.com. Now find monthly adjusted prices and calculate the standard
b. Your answer to part (a) will not exactly match the traded price. Experiment with different values for the standard deviation until your calculated values match the prices of the traded options as
1. Expansion options (S23.1) Look again at the valuation in Table 23.2 of the option to invest in the Mark II project. Consider a change in each of the following inputs. Would the change increase or
2. Expansion options (S23.1) Look again at Table 23.2. How does the value in 1982 of the option to invest in the Mark II change ifa. The investment required for the Mark II is $800 million (vs. $900
3. Expansion options (S23.1) You own a one-year call option to buy one acre of Los Angeles real estate. The exercise price is $2 million, and the current, appraised market value of the land is $1.7
4. Expansion options (S23.1) A variation on Problem 3: Suppose the land is occupied by a warehouse generating rents of $150,000 after real estate taxes and all other out-of-pocket costs. The present
5. R&D (S23.1) Construct a sensitivity analysis of the value of the pharmaceutical R&D project described in Figure 23.2. What input assumptions are most critical for the NPV of the project?Be sure to
6. Real options and put–call parity (S23.2) Redo the example in Figure 23.2, assuming that the real option is a put option allowing the company to abandon the R&D program if commercial prospects
7. Timing options (S23.2) You own a parcel of vacant land. You can develop it now, or wait.a. What is the advantage of waiting?b. Why might you decide to develop the property immediately?
8. Timing options (S23.2) Look back at the malted herring option in Section 23-3. How did the company’s analysts estimate the present value of the project? It turns out that they assumed that the
9. Timing options (S23.2) You have an option to purchase all of the assets of the Overland Railroad for $2.5 billion. The option expires in nine months. You estimate Overland’s current(month 0)
b. Suppose you can only exercise your option now, or after nine months (not at month 3 or 6).Would you exercise now?
c. Suppose you can exercise now, or at month 3, 6, or 9. What is your option worth today?Should you exercise today, or wait?
10. Abandonment options (S23.3) A start-up company is moving into its first offices and needs desks, chairs, filing cabinets, and other furniture. It can buy the furniture for $25,000 or rent it for
11. Abandonment options (S23.3) Flip back to Tables 6.3 and 6.4, where we assumed an economic life of seven years for IM&C’s guano plant. What’s wrong with that assumption? How would you
12. Abandonment options (S23.3) In Section 10-3, we considered two production technologies for a new outboard motor. Technology A was the most efficient but had no salvage value if the new outboards
b. Technology B allows abandonment in year 1 for $17 million salvage value. You also get cash flow of $1.5 million, for a total of $18.5 million. Calculate abandonment value, assuming a risk-free
13. Abandonment options (S23.3) Take another look at the perpetual crusher example in Section 23-4. Construct a sensitivity analysis showing how the value of the abandonment put changes depending on
14. Flexible production and procurement (S23.4) Gas turbines are among the least efficient ways to produce electricity, much less thermally efficient than coal or nuclear plants. Why do gas-turbine
15. Valuing real options (S23.6) Respond to the following comments.a. “You don’t need option pricing theories to value flexibility. Just use a decision tree. Discount the cash flows in the tree
b. “These option pricing methods are just plain nutty. They say that real options on risky assets are worth more than options on safe assets.”
c. “Real-options methods eliminate the need for DCF valuation of investment projects.”
16. Valuing real options (S23.6) Why is quantitative valuation of real options often difficult in practice? List the reasons briefly.
17. Real option valuation (S23.6) Josh Kidding, who has only read part of Chapter 10, decides to value a real option by (1) setting out a decision tree, with cash flows and probabilities forecasted
18. Real option valuation (S23.6) In binomial trees, risk-neutral probabilities are set to generate an expected rate of return equal to the risk-free interest rate in each branch of the tree. What do
19. Valuing real options (S23.6) Alert financial managers can create real options. Give three or four possible examples.
20. Valuing real options (S23.6) Describe each of the following situations in the language of options:a. Drilling rights to undeveloped heavy crude oil in Northern Alberta. Development and production
b. A restaurant is producing net cash flows, after all out-of-pocket expenses, of $700,000 per year. There is no upward or downward trend in the cash flows, but they fluctuate as a random walk, with
c. A variation on part (b): Assume the restaurant faces known fixed costs of $300,000 per year, incurred as long as the restaurant is operating. Thus, Net c$ a7s0h0 f,0lo0w0 == r1e,0ve0n0u,0e0 l0e
d. A paper mill can be shut down in periods of low demand and restarted if demand improves sufficiently. The costs of closing and reopening the mill are fixed.
e. A real estate developer uses a parcel of urban land as a parking lot, although construction of either a hotel or an apartment building on the land would be a positive-NPV investment.
f. Air France negotiates a purchase option for 10 Boeing 787s. Air France must confirm the order by 2024. Otherwise, Boeing will be free to sell the aircraft to other airlines.
21. Valuing real options (S23.6) True or false?a. Real-options analysis sometimes tells firms to make negative-NPV investments to secure future growth opportunities.b. Using the Black–Scholes
22. Valuing real options (S23.6) Why is quantitative valuation of real options often difficult in practice? List the reasons briefly.CHALLENGE
23. Complex real options (S23.6) Suppose you expect to need a new plant that will be ready to produce turbo-encabulators in 36 months. If design A is chosen, construction must begin immediately.
24. Options and growth (S23.6) In Chapter 4, we expressed the value of a share of stock as P 0 = EPrS 1 + PVGO where EPS1 is earnings per share from existing assets, r is the expected rate of return
b. Suppose the CAPM is used to calculate the cost of capital for a growth (high-PVGO) firm.Assume all-equity financing. Will this cost of capital be the correct hurdle rate for investments to expand
1. Expected yield (S24.1) You own a 5% bond maturing in two years and priced at 87%. Suppose that there is a 10% chance that at maturity the bond will default and you will receive only 40% of the
2. Bond ratings (S24.1) In February 2018, Aaa bonds yielded 2.36%, Baa bonds yielded 3.43%, and Treasuries with the same maturities yielded 0.676%.a. What was the credit spread on Aaa bonds?b. What
3. Bond ratings (S24.1) It is 2030 and the yields on corporate bonds are as follows:8% 10% 12%Tau Corp wishes to raise $10 million by an issue of 9% 10-year bonds. What will be the likely issue price
4. Default option (S24.2) The difference between the value of a government bond and a similar corporate bond is equal to the value of an option. What is this option, and what is its exercise price?
5. Default option (S24.2) Other things equal, would you expect the difference between the price of a Treasury bond and a corporate bond to increase or decrease witha. The company’s business risk?b.
6. Default option (S24.2) Company A has issued a single zero-coupon bond maturing in 10 years. Company B has issued a coupon bond maturing in 10 years. Explain why it is more complicated to value
7. Default option (S24.2) How much would it cost you to insure the bonds of Backwoods Chemical against default? (See Section 24-1.)
8. Default option (S24.2) Digital Organics has 10 million outstanding shares trading at $25 per share. It also has a large amount of debt outstanding, all coming due in one year. The debt pays
9. Default option (S24.2) Square File’s assets are worth $100. It has $80 of zero-coupon debt outstanding that is due to be repaid at the end of two years. The risk-free interest rate is 5%, and
10. Predicting default probability (S24.3) A friend has mentioned that she has read somewhere that the following variables can be used to predict bankruptcy: (a) the company debt ratio;(b) the
11. Predicting default probability (S24.3) What variables are required to use the Merton model to calculate the risk-neutral probability that a company will default on its debt?
12. Predicting default probability (S24.3) Company X has borrowed $150 maturing this year and $50 maturing in 10 years. Company Y has borrowed $200 maturing in five years. In both cases, asset value
13. Predicting default probability (S24.3) Discuss the problems with developing a numerical credit scoring system for evaluating personal loans. You can only test your system using data for
14. Predicting default probability (S24.3) Look back at Section 24.3. Suppose that the standard deviation of the return on Upsilon’s assets is 50%. Recalculate the probability that the company will
15. Default option (S24.2) Look back at the first Backwoods Chemical example at the start of Section 24-1. Suppose that the firm’s book balance sheet is Backwoods Chemical Company (Book Values)Net
1. Go to finance.yahoo.com and select three industrial companies that have been experiencing difficult times.a. Are the companies’ troubles reflected in their financial ratios? (You may find it
Why are borrowers happy to enter into covenants that reassure the lender but constrain the borrower?
1. Bond terms (S25.1) Use Table 25.1 (but not the text) to answer the following questions:a. Who are the principal underwriters for the AMAT bond issue?b. What is the percentage underwriting
2. Bond terms (S25.1) Look at Table 25.1:a. The AMAT bond was issued on June 8, 2011, at 99.592%. How much would you have to pay to buy one bond delivered on June 15? Don’t forget to include
3. Bond terms (S25.1) Find the terms and conditions of a recent bond issue and compare them with those of the AMAT issue.
4. Bond terms (S25.1) Select the most appropriate term from within the parentheses:a. (High-grade bonds/Low-grade bonds) generally have only light sinking-fund requirements.b. Equipment trust
5. Bond terms (S25.1) Suppose that the AMAT bond was issued at face value and that investors continue to demand a yield of 5.85%. Sketch what you think would happen to the bond price as the first
6. Bond terms (S25.1) Bond prices can fall either because of a change in the general level of interest rates or because of an increased risk of default. To what extent do floating-rate bonds protect

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