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fundamentals of corporate finance

Questions and Answers of Fundamentals Of Corporate Finance

66. Real versus Nominal Rates. If investors are to earn a 3% real interest rate, what nominal inter- est rate must they earn if the inflation rate isa. zero? (LO6)b. 4%? (LO6)c. 6%? (LO6)
67. Real Rates. If investors receive a 6% interest rate on their bank deposits, what real interest rate will they earn if the inflation rate over the year isa. zero? (LO6)b. 3%? (LO6)c. 6%? (LO6)
68. Real versus Nominal Rates. You will receive $100 from a savings bond in 3 years. The nomi- nal interest rate is 8%.a. What is the present value of the proceeds from the bond? (LO2)b. If the
69. Real versus Nominal Dollars. Your consulting firm will produce cash flows of $100,000 this year, and you expect cash flow to keep pace with any increase in the general level of prices. The
70. Real versus Nominal Annuities. Good news: You will almost certainly be a millionaire by the time you retire in 50 years. Bad news: The inflation rate over your lifetime will average about 3%.
71. Real versus Nominal. If the interest rate is 6% per year, how long will it take for your money to quadruple in value? If the inflation rate is 4% per year, what will be the change in the purchas-
72. Inflation. In the summer of 2007, Zimbabwe's official inflation rate was about 110% per month. What was the annual inflation rate? (LO6)
73. Perpetuities. British government 4% perpetuities pay 4 interest each year forever. Another bond, 2% perpetuities, pays 2.50 a year forever. What is the value of 4% perpetuities if the long-term
74. Real versus Nominal Annuities. (LO6)a. You plan to retire in 30 years and want to accumulate enough by then to provide yourself with $30,000 a year for 15 years. If the interest rate is 10%, how
75. Retirement and Inflation. Redo part (a) of Practice Problem 64, but now assume that the infla- tion rate over the next 50 years will average 4%. (L06)a. What is the real annual savings the couple
76. Perpetuities. What is the value of a perpetuity that pays $100 every 3 months forever? The discount rate quoted on an APR basis is 6%. (LO5)
77. Changing Interest Rates. If the interest rate this year is 8% and the interest rate next year will be 10%, what is the future value of $1 after 2 years? What is the present value of a payment of
78. Changing Interest Rates. Your wealthy uncle established a $1,000 bank account for you when you were born. For the first 8 years of your life, the interest rate earned on the account was 6%. Since
79. Real versus Nominal Cash Flows.a. It is 2010, you've just graduated college, and you are contemplating your lifetime budget. You think your general living expenses will average around $50,000 a
80. Amortizing Loans and Inflation. Suppose you take out a $100,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%, and to keep things simple, we will assume you make
1. Look up Abercrombie & Fitch (ANF). Calculate its 5-year growth rate in sales and net income, using annual income statement data. Next translate these results into the real growth rates. Use the
2. Look up the most recent stock prices and the prices 5 years earlier for the following firms: E-trade (ET), Sony (SNE), Georgia Pacific (GP), Toyota (TM), and Nordstrom (JWN). What was the compound
5.1 Value after 5 years would have been 24 (1.05) = $30.63; after 50 years, 24 x (1.05)50 = $275.22.
5.2 Call g the annual growth rate of transistors over the 36-year period between 1971 and 2007. Then 2,250X(1+g)36 = 592,000,000 (1+g) 36=263,111 1+g=263,1111/36 = 1.41 So the actual growth rate was
5.3 Multiply the $1,000 payment by the 30-year discount factor: 1 PV $1,000X- = $221.68 (1.0515)30
5.4 The $1,000 investment grew to $4,000 in 5 years. FV PVX(1+ry 4,000 1,000 (1+r)5 (1+r)=4.0 (1+r) 4.01/5 r=.32, or 32% 1.32
5.5 Gift at Year Present Value 1 10,000/(1.07) = $9,345.79 2 10,000/(1.07)2= 8,734.39 3 10,000/(1.07) 38,162.98 4 10,000/(1.07)47,628.95 $33,872.11 Gift at Year Future Value 1 10,000 x (1.07) =
5.6 The rate is 4/48=.0833, about 8.3%.
5.7 The 4-year discount factor is 1/(1.08)4.7350. The 4-year annuity factor is [1/.08 - 1/(.08 x 1.084)] = 3.3121. This is the difference between the present value of a $1 perpetu- ity starting next
5.8 You will need the present value at 7% of a 20-year annuity of $55,000: Present value = annual spending annuity factor === The annuity factor is [1/.07 - 1/(.07 x 1.0720)] = 10.5940. Thus you need
5.9 Fifteen years means 180 months. Then Mortgage payment 100,000 180-month annuity factor 100,000 83.32 = $1,200.17 per month $1,000 of the payment is interest. The remainder, $200.17, is
5.10 We saw in Example 5.8 that the 25-year annuity factor for an ordinary annuity is 12.9057. Therefore, the 25-year annuity-due factor would be 12.9057 x 1.059 = 13.6672. The pres- ent value of the
5.11 If the interest rate is 5%, the future value of a 50-year, $1 annuity will be (1.05)50-1 .05 =209.348 Therefore, we need to choose the cash flow, C, so that CX 209.348 = $500,000. This requires
5.12 The quarterly rate is 8/4 = 2%. The effective annual rate is (1.02)4-1 = .0824, or 8.24%.
5.13 The cost in dollars will increase by 5% each year, to a value of $5 x (1.05)50 = $57.34. If the inflation rate is 10%, the cost will be $5 x (1.10)50 = $586.95.
5.14 The CPI in 1980 was 3.452 times its value in 1950 (see Table 5-8). Therefore, purchases that cost $250 in 1950 would have cost $250 x 3.452 = $863 in 1980. The value of a 1980 salary of $30,000,
5.15a. If there's no inflation, real and nominal rates are equal at 8%. With 5% inflation, the real rate is (1.08/1.05)-1= .02857, a bit less than 3%.b. If you want a 3% real interest rate, you need
5.16 The present value is $5,000 PV= = $4,629.63 1.08 The real interest rate is 2.857% (see Self-Test 5.15a). The real cash payment is $5,000/ (1.05) = $4,761.90. Thus, PV $4,761.90 1.02857 $4,629.63
5.17 Calculate the real annuity. The real interest rate is 1.10/1.05 1.0476. We'll round to 4.8%. The real annuity is $3,000,000 $3,000,000 Annual payment 30-year annuity factor 1 1 $3,000,000
Look at Table 28.1.a. How many rupees can you buy for one dollar?b. What is the cross exchange rate between the pound and the rupee?c. Is the rupee at a forward premium or discount on the dollar?
3. Option payoffs (S21-1) Look again at Figure 21.12. It appears that the investor in panel b can’t lose and the investor in panel a can’t win. Is that correct? Explain. (Hint: Draw a profit
4. Option payoffs (S21-1) What is a call option worth at maturity if (a) the stock price is zero?(b) the stock price is extremely high relative to the exercise price?
5. Option payoffs (S21-1) “The buyer of the call and the seller of the put both hope that the stock price will rise. Therefore the two positions are identical.” Is the speaker correct? Illustrate
6. Option combinations (S21-2) Suppose that you hold a share of stock and a put option on that share. What is the payoff when the option expires if (a) the stock price is below the exercise price?
7. Option combinations (S21-2) Dr. Livingstone I. Presume holds £600,000 in East African gold stocks. Bullish as he is on gold mining, he requires absolute assurance that at least£500,000 will be
8. Option combinations (S21-2) Suppose you buy a one-year European call option on Wombat shares with an exercise price of $100 and sell a one-year European put option with the same exercise price.
b. How much will the combined position cost you? Explain.
9. Option combinations (S21-2) Suppose that Mr. Colleoni borrows the present value of $100, buys a six-month put option on share Y with an exercise price of $150, and sells a six-month put option on
b. Suggest two other combinations of loans, options, and the underlying stock that would give Mr. Colleoni the same payoffs.
10. Option combinations (S21-2) Option traders often refer to “straddles” and “butterflies.”Here is an example of each:• Straddle: Buy one call with exercise price of $100 and
11. Option combinations (S21-2) Ms. Higden has been offered yet another incentive scheme(see Section 21-2). She will receive a bonus of $500,000 if the share price at the end of the year is $120 or
b. What combination of options would provide these payoffs? (Hint: You need to buy a large number of options with one exercise price and sell a similar number with a different exercise price.)
12. Option combinations (S21-2) Discuss briefly the risks and payoffs of the following positions:a. Buy a share and a put option on the share.b. Buy a share.c. Buy a call.Chapter 21 Understanding
13. Put–call parity (S21-2) Which one of the following statements is correct?a. Value of put + present value of exercise price = value of call + share price.b. Value of put + share price = value of
14. Put-call parity (S21-2) A European call and put option have the same maturity. Both are at-the-money, so the share price equals the exercise price. The share does not pay a dividend.Which option
15. Put–call parity (S21-2)a. If you can’t sell a share short, you can achieve exactly the same final payoff by a combination of options and borrowing or lending. What is this combination?
b. Now work out the mixture of stock and options that gives the same final payoff as investment in a risk-free loan.
16. Put–call parity (S21-2) The common stock of Triangular File Company is selling at $90. A 26-week call option written on Triangular File’s stock is selling for $8. The call’s exercise price
b. Suppose that puts are traded. What should a 26-week put with an exercise price of $100 sell for?
17. Put–call parity (S21-2) What is put–call parity and why does it hold? Could you apply the parity formula to a call and put with different exercise prices?
18. Put–call parity (S21-2) There is another strategy involving calls and borrowing or lending that gives the same payoffs as the strategy described in Problem 6. What is the alternative strategy?
19. Put–call parity (S21-1) It is possible to buy three-month call options and three-month puts on stock Q. Both options have an exercise price of $60 and both are worth $10. If the interest rate
20. Put–call parity (S21-2) In September 2020, Facebook’s share price was about $250. A ninemonth call on the stock, with an exercise price of $250, sold for $38. The risk-free interest rate was
21. Option bounds (S21-3) Pintail’s share price is currently $200. A one-year American call option has an exercise price of $50 and is priced at $75. How would you take advantage of this great
22. Option values (S21-3) How does the price of a call option respond to the following changes, other things equal? Does the call price go up or down?a. Stock price increases.b. Exercise price is
23. Option values (S21-3) Respond to the following statements.a. “I’m a conservative investor. I’d much rather hold a call option on a safe stock like Coca-Cola than a volatile stock like
24. Option values (S21-3) FX Bank has succeeded in hiring ace foreign exchange trader Lucinda Cable. Her remuneration package reportedly includes an annual bonus of 20% of the profits that she
25. Option values (S21-3) Look at actual trading prices of call options on stocks to check whether they behave as the theory presented in this chapter predicts. For example,a. Follow several options
26. Option values (S21-3) Is it more valuable to own an option to buy a portfolio of shares or to own a portfolio of options to buy each of the individual shares? Say briefly why.
27. Option values (S21-3) You’ve just completed a month-long study of energy markets and conclude that energy prices will be much more volatile in the next year than historically. Assuming you’re
28. Option values (S21-3) Table 21.4 lists some prices of options on common stocks (prices are quoted to the nearest dollar). The interest rate is 10% a year. Can you spot any mispricing?What would
29. Option payoffs (S21-1) Figure 21.13 shows some complicated payoff diagrams. Work out the combination of shares, bonds, and options that produces each of these positions.Chapter 21 Understanding
30. Option payoffs (S21-1) Some years ago the Australian firm Bond Corporation sold a share in some land that it owned near Rome for A$110 million and as a result boosted its annual earnings by A$74
b. Use payoff diagrams to show the net effect of the land sale and the option transactions.
c. Assume a one-year maturity on the options. Can you deduce the interest rate?
d. The television program argued that it was misleading to record a profit on the sale of land.What do you think?
31. Option bounds (S21-3) Problem 21 considered an arbitrage opportunity involving an American option. Suppose that this option was a European call. Show that there is a similar possible arbitrage
32. Option values (S21-3) Three six-month call options are traded on Hogswill stock:(a) (b)(c) (d)◗ FIGURE 21.13 Some complicated payoff diagrams. See Problem 29.Exercise Price Call Option Price$
How would you make money by trading in Hogswill options? (Hint: Draw a graph with the option price on the vertical axis and the ratio of stock price to exercise price on the horizontal axis. Plot the
1. One-step binomial model (S22-1) Over the coming year, Ragwort’s stock price will halve to$50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.a. What is
b. What is the amount of the loan in the replicating portfolio?
c. Use the replicating-portfolio method to value this call.
d. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
e. Use the risk-neutral method to check your valuation of the Ragwort option.
f. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.
2. One-step binomial model (S22-1) Imagine that Amazon’s stock price will either rise by 33.3% or fall by 25% over the next six months (see Section 22-1). Recalculate the value of the call option
3. Binomial model (S22-1) The share price of Heavy Metal (HM) changes only once a month:Either it goes up by 20% or it falls by 16.7%. Its price now is $40. The interest rate is 1% per month.a. What
b. What is the option delta?
c. Show how the payoffs of this call option can be replicated by buying HM’s stock and borrowing.
d. What is the value of a two-month call option with an exercise price of $40?
e. What is the option delta of the two-month call over the first one-month period?
4. One-step binomial model (S22-1) Suppose a stock price can go up by 15% or down by 13%over the next year. You own a one-year put on the stock. The interest rate is 10%, and the current stock price
b. How does this break-even exercise price change if the interest rate is increased?
5. Two-step binomial model (S22-2) Take another look at our two-step binomial trees for Amazon in Figure 22-2. Use the replicating-portfolio or risk-neutral method to value sixmonth call and put
6. Two-step binomial model (S22-2) Buffelhead’s stock price is $220 and could halve or double in each six-month period (equivalent to a standard deviation of 98%). A one-year call option on
b. Now calculate the option delta for the second six months if (1) the stock price rises to $440 and (2) the stock price falls to $110.
c. How does the call option delta vary with the level of the stock price? Explain intuitively why.
d. Suppose that in month 6, the Buffelhead stock price is $110. How, at that point, could you replicate an investment in the stock by a combination of call options and risk-free lending?Show that
7. Two-step binomial model (S22-2) Suppose that you have an option that allows you to sell Buffelhead stock (see Problem 6 ) in month 6 for $165 or to buy it in month 12 for $165. What is the value
8. Two-step binomial model (S22-2) Johnny Jones’s high school derivatives homework asks for a binomial valuation of a 12-month call option on the common stock of the Overland Railroad. The stock is
b. How would these trees change if Overland’s standard deviation were 30%? (Hint: Make sure to specify the right up and down percentage changes.)
9. Option delta (S22-1–S22-2)a. Can the delta of a call option be greater than 1.0? Explain.
b. Can it be less than zero?
c. How does the delta of a call change if the stock price rises?
d. How does it change if the risk of the stock increases?

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