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principles corporate finance

Questions and Answers of Principles Corporate Finance

20. 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. Design B is more expensive, but
21. In Chapter 4, we expressed the value of a share of stock as:P0 5EPS1 r1 PVGOwhere EPS 1 is earnings per share from existing assets, r is the expected rate of return required by investors, and
18. Consider the following capital rationing problem:Project C0 C1 C2 NPV W 10,000 10,000 0 6,700 X 0 20,000 5,000 9,000 Y 10,000 5,000 5,000 0 Z 15,000 5,000 4,000 1,500 Financing available 20,000
17. Look again at the project cash flows in Problem 10 . Calculate the modified IRR as defined in Footnote 4 in Section 5.3 . Assume the cost of capital is 12%.Now try the following variation on the
16. Some people believe firmly, even passionately, that ranking projects on IRR is OK if each project’s cash flows can be reinvested at the project’s IRR. They also say that the NPV
15. Borghia Pharmaceuticals has $1 million allocated for capital expenditures. Which of the following projects should the company accept to stay within the $1 million budget? How much does the budget
14. Look again at projects D and E in Section 5.3 . Assume that the projects are mutually exclusive and that the opportunity cost of capital is 10%.a. Calculate the profitability index for each
13. The Titanic Shipbuilding Company has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of $250,000 at the end of each of the next two years. At the end
12. Mr. Cyrus Clops, the president of Giant Enterprises, has to make a choice between two possible investments:Cash Flows ($ thousands)Project C0 C1 C2 IRR (%)A 400 250 300 23 B 200 140 179 36 The
11. Consider the following two mutually exclusive projects:Cash Flows ($)Project C0 C1 C2 C3 A 100 60 60 0 B 100 0 0 140a. Calculate the NPV of each project for discount rates of 0, 10, and 20%. Plot
10. Calculate the IRR (or IRRs) for the following project:C0 C1 C2 C3 3,000 3,500 4,000 4,000 For what range of discount rates does the project have positive NPV?
9. Respond to the following comments:a. “I like the IRR rule. I can use it to rank projects without having to specify a discount rate.”b. “I like the payback rule. As long as the minimum
8. Consider the following projects:Cash Flows ($)Project C0 C1 C2 C3 C4 C5 A 1,000 1,000 0 0 0 0 B 2,000 1,000 1,000 4,000 1,000 1,000 C 3,000 1,000 1,000 0 1,000 1,000a. If the opportunity cost of
7. Suppose you have the following investment opportunities, but only $90,000 available for investment. Which projects should you take?Project NPV Investment 1 5,000 10,000 2 5,000 5,000 3 10,000
6. Consider projects Alpha and Beta:Cash Flows ($)Project C0 C1 C2 IRR (%)Alpha 400,000 241,000 293,000 21 Beta 200,000 131,000 172,000 31 The opportunity cost of capital is 8%.Suppose you can
5. Consider a project with the following cash flows:C0 C1 C2 100 200 75a. How many internal rates of return does this project have?b. Which of the following numbers is the project IRR:(i) 50%; (ii)
4. You have the chance to participate in a project that produces the following cash flows:Cash Flows ($)C0 C1 C2 5,000 4,000 11,000 The internal rate of return is 13%. If the opportunity cost of
3.a. Calculate the net present value of the following project for discount rates of 0, 50, and 100%:Cash Flows ($)C0 C1 C2 6,750 4,500 18,000b. What is the IRR of the project?
2. Write down the equation defining a project’s internal rate of return (IRR). In practice how is IRR calculated?
1.a. What is the payback period on each of the following projects?Cash Flows ($)Project C0 C1 C2 C3 C4 A 5,000 1,000 1,000 3,000 0 B 1,000 0 1,000 2,000 3,000 C 5,000 1,000 1,000 3,000 5,000b. Given
3. Look up Intel (INTC), Dell Computer (DELL), Dow Chemical (DOW), Harley-Davidson(HOG), and Pfizer, Inc. (PFE). Look at “Financial Highlights” and “Company Profile” for each company. You
2. Look up General Mills, Inc., and Kellogg Co. The companies’ ticker symbols are GIS and K.a. What are the current dividend yield and price–earnings ratio (P/E) for each company?How do the
1. Go to www.nyse.com . Find NYSE MarkeTrac and click on the DJIA ticker tape, which shows trades for the stocks in the Dow Jones Industrial Averages. Stop the tape at GE. What are the latest price,
29. Suppose the concatenator division, which we valued based on Table 4.8 , is spun off as an independent company, Concatco, with 1 million shares of common stock outstanding.What would each share
28. Portfolio managers are frequently paid a proportion of the funds under management. Suppose you manage a $100 million equity portfolio offering a dividend yield (DIV 1 / P 0 ) of 5%. Dividends and
27. The constant-growth DCF formula:P0⫽DIV1 r ⫺ g is sometimes written as:P0⫽ROE 1 1 ⫺ b 2 BVPS r ⫺ bROE where BVPS is book equity value per share, b is the plowback ratio, and ROE is the
26. Construct a new version of Table 4.8 , assuming that competition drives down profitability(on existing assets as well as new investment) to 11.5% in year 6, 11% in year 7, 10.5% in year 8, and 8%
25. Permian Partners (PP) produces from aging oil fields in west Texas. Production is 1.8 million barrels per year in 2009, but production is declining at 7% per year for the foreseeable future.
24. Compost Science, Inc. (CSI), is in the business of converting Boston’s sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce CSI to remain in
23. Look again at the financial forecasts for Growth-Tech given in Table 4.5 . This time assume you know that the opportunity cost of capital is r ⫽ .12 (discard the .099 figure calculated in the
22. Alpha Corp’s earnings and dividends are growing at 15% per year. Beta Corp’s earnings and dividends are growing at 8% per year. The companies’ assets, earnings, and dividends per share are
21. Each of the following formulas for determining shareholders’ required rate of return can be right or wrong depending on the circumstances:a. r ⫽DIV1 P0⫹ gb. r ⫽EPS1 P0 For each formula
20. Phoenix Corp. faltered in the recent recession but has recovered since. EPS and dividends have grown rapidly since 2017.2017 2018 2019 2020 2021 EPS $.75 2.00 2.50 2.60 2.65 Dividends $ 0 1.00
19. Mexican Motors stock sells for 200 pesos per share and next year’s dividend is 8.5 pesos.Security analysts are forecasting earnings growth of 7.5% per year for the next five years.a. Assume
18. Company Q’s current return on equity (ROE) is 14%. It pays out one-half of earnings as cash dividends (payout ratio .5). Current book value per share is $50. Book value per share will grow as Q
17. Pharmecology is about to pay a dividend of $1.35 per share. It’s a mature company, but future EPS and dividends are expected to grow with inflation, which is forecasted at 2.75% per year.a.
16. Consider the following three stocks:a. Stock A is expected to provide a dividend of $10 a share forever.b. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is
15. Rework Table 4.2 under the assumption that the dividend on Fledgling Electronics is $10 next year and that it is expected to grow by 5% a year. The capitalization rate is 15%.
14. Look in a recent issue of The Wall Street Journal at “NYSE-Composite Transactions.”a. What is the latest price of IBM stock?b. What are the annual dividend payment and the dividend yield on
13. Suppose the horizon date is set at a time when the firm will run out of positive-NPV investment opportunities. How would you calculate the horizon value? ( Hint: What is the P /EPS ratio when
12. What is meant by the “horizon value” of a business? How can it be estimated?
11. What do financial managers mean by “free cash flow”? How is free cash flow calculated?Briefly explain.
10. Under what conditions does r, a stock’s market capitalization rate, equal its earnings–price ratio EPS 1 / P 0 ?
9. True or false? Explain.a. The value of a share equals the discounted stream of future earnings per share.b. The value of a share equals the PV of earnings per share assuming the firm does not
8. Consider three investors:a. Mr. Single invests for one year.b. Ms. Double invests for two years.c. Mrs. Triple invests for three years.Assume each invests in company Z (see Problem 5). Show that
7. If company Z (see Problem 5) were to distribute all its earnings, it could maintain a level dividend stream of $15 a share. How much is the market actually paying per share for growth
6. Company Z-prime is like Z in all respects save one: Its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. What is Z-prime’s stock price?Assume
5. Company Z’s earnings and dividends per share are expected to grow indefinitely by 5%a year. If next year’s dividend is $10 and the market capitalization rate is 8%, what is the current stock
4. Company Y does not plow back any earnings and is expected to produce a level dividend stream of $5 a share. If the current stock price is $40, what is the market capitalization rate?
3. Company X is expected to pay an end-of-year dividend of $5 a share. After the dividend its stock is expected to sell at $110. If the market capitalization rate is 8%, what is the current stock
2. Respond briefly to the following statement:“You say stock price equals the present value of future dividends? That’s crazy! All the investors I know are looking for capital gains.”
1. True or false?a. All stocks in an equivalent-risk class are priced to offer the same expected rate of return.b. The value of a share equals the PV of future dividends per share.
2. Log on to www.smartmoney.com and find the Living Yield Curve, which shows a picture of the yield curve. How does today’s yield curve compare with yield curves in the past? Do short-term interest
1. The Web sites of The Wall Street Journal ( www.wsj.com ) and the Financial Times ( www.ft.com )are wonderful sources of market data. You should become familiar with them. Use www.wsj.com to answer
35. Look one more time at Table 3.4.a. Suppose you knew the bond prices but not the spot interest rates. Explain how you would calculate the spot rates. ( Hint: You have four unknown spot rates, so
34.a. What spot and forward rates are embedded in the following Treasury bonds? The price of one-year strips is 93.46%. Assume for simplicity that bonds make only annual payments. ( Hint: Can you
33. What is the duration of a common stock whose dividends are expected to grow at a constant rate in perpetuity?
32. The duration of a bond that makes an equal payment each year in perpetuity is (1 ⫹ yield)/yield. Prove it.
31. Find the arbitrage opportunity (opportunities?). Assume for simplicity that coupons are paid annually. In each case the face value of the bond is $1,000.Bond Maturity (years) Coupon, $ Price, $A
30. Write a spreadsheet program to construct a series of bond tables that show the present value of a bond given the coupon rate, maturity, and yield to maturity. Assume that coupon payments are
29. A bond’s credit rating provides a guide to its price. As we write this in Spring 2009, Aaa bonds yield 5.41% and Baa bonds yield 8.47%. If some bad news causes a 10% five-year bond to be
28. Suppose that you buy a two-year 8% bond at its face value.a. What will be your nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your real
27. Look again at the spot interest rates shown in Problem 25. What can you deduce about the one-year spot interest rate in three years if . . .a. The expectations theory of term structure is
26. Look at the spot interest rates shown in Problem 25. Suppose that someone told you that the five-year spot interest rate was 2.5%. Why would you not believe him? How could you make money if he
25. Look again at Table 3.4. Suppose the spot interest rates change to the following downwardsloping term structure: r 1 ⫽ 4.6%, r 2 ⫽ 4.4%, r 3 ⫽ 4.2%, and r 4 ⫽ 4.0%. Recalculate discount
24. Look up prices of 10 U.S. Treasury bonds with different coupons and different maturities.Calculate how their prices would change if their yields to maturity increased by 1 percentage point. Are
23. The formula for the duration of a perpetual bond that makes an equal payment each year in perpetuity is (1 ⫹ yield)/yield. If each bond yields 5%, which has the longer duration—a perpetual
22. Find the “live” spreadsheet for Table 3.3 on this book’s Web site, www.mhhe.com/bma.Show how duration and volatility change if (a) the bond’s coupon is 8% of face value and(b) the
21. Calculate durations and modified durations for the 4% coupon bond and the strip in Table 3.1 . The answers for the strip will be easy. For the 4% bond, you can follow the procedure set out in
20. You have estimated spot rates as follows:r 1 ⫽ 5.00%, r 2 ⫽ 5.40%, r 3 ⫽ 5.70%, r 4 ⫽ 5.90%, r 5 ⫽ 6.00%.a. What are the discount factors for each date (that is, the present value of $1
19. Is the yield on high-coupon bonds more likely to be higher than that on low-coupon bonds when the term structure is upward-sloping or when it is downward-sloping? Explain.
18. A 6% six-year bond yields 12% and a 10% six-year bond yields 8%. Calculate the six-year spot rate. Assume annual coupon payments. (Hint: What would be your cash flows if you bought 1.2 10% bonds?)
17. A six-year government bond makes annual coupon payments of 5% and offers a yield of 3% annually compounded. Suppose that one year later the bond still yields 3%. What return has the bondholder
16. A 10-year U.S. Treasury bond with a face value of $10,000 pays a coupon of 5.5% (2.75%of face value every six months). The semiannually compounded interest rate is 5.2% (a sixmonth discount rate
15. A 10-year German government bond (bund) has a face value of €100 and a coupon rate of 5% paid annually. Assume that the interest rate (in euros) is equal to 6% per year. What is the bond’s PV?
14. The two-year interest rate is 10% and the expected annual inflation rate is 5%.a. What is the expected real interest rate?b. If the expected rate of inflation suddenly rises to 7%, what does
13. The one-year spot interest rate is r 1 ⫽ 5% and the two-year rate is r 2 ⫽ 6%. If the expectations theory is correct, what is the expected one-year interest rate in one year’s time?
12. Calculate the durations and volatilities of securities A, B, and C. Their cash flows are shown below. The interest rate is 8%.Period 1 Period 2 Period 3 A 40 40 40 B 20 20 120 C 10 10 110
11. True or false? Explain.a. Longer-maturity bonds necessarily have longer durations.b. The longer a bond’s duration, the lower its volatility.c. Other things equal, the lower the bond coupon, the
10.a. An 8%, five-year bond yields 6%. If the yield remains unchanged, what will be its price one year hence? Assume annual coupon payments.b. What is the total return to an investor who held the
9. The following table shows the prices of a sample of U.S. Treasury strips in August 2009.Each strip makes a single payment of $1,000 at maturity.a. Calculate the annually compounded, spot interest
8.a. What is the formula for the value of a two-year, 5% bond in terms of spot rates?b. What is the formula for its value in terms of yield to maturity?c. If the two-year spot rate is higher than the
7. Look again at Table 3.4 . Suppose that spot interest rates all change to 4%—a “flat” term structure of interest rates.a. What is the new yield to maturity for each bond in the table?b.
6. Which comes first in the market for U.S. Treasury bonds:a. Spot interest rates or yields to maturity?b. Bond prices or yields to maturity?
5. Construct some simple examples to illustrate your answers to the following:a. If interest rates rise, do bond prices rise or fall?b. If the bond yield is greater than the coupon, is the price of
4. Here are the prices of three bonds with 10-year maturities:Bond Coupon (%) Price (%)2 81.62 4 98.39 8 133.42 If coupons are paid annually, which bond offered the highest yield to maturity?Which
3. In February 2009 Treasury 6s of 2026 offered a semiannually compounded yield of 3.5965%. Recognizing that coupons are paid semiannually, calculate the bond’s price.
2. The following statements are true. Explain why.a. If a bond’s coupon rate is higher than its yield to maturity, then the bond will sell for more than face value.b. If a bond’s coupon rate is
1. A 10-year bond is issued with a face value of $1,000, paying interest of $60 a year. If market yields increase shortly after the T-bond is issued, what happens to the bond’sa. Coupon rate?b.
3. In 2006 the State of Indiana sold a 75-year concession to operate and maintain the East-West Toll Road. Before doing so, it commissioned a consulting report that estimated the value of the
2. Retirement planning You need to have accumulated savings of $2 million by the time that you retire in 20 years. You currently have savings of $200,000. How much do you need to save each year to
1. Amortizing loans Suppose that you take out a 30-year mortgage loan of $200,000 at an interest rate of 10%.a. What is your total monthly payment?b. How much of the first month’s payment goes to
38. You own an oil pipeline that will generate a $2 million cash return over the coming year.The pipeline’s operating costs are negligible, and it is expected to last for a very long
37. Use Excel to construct your own set of annuity tables showing the annuity factor for a selection of interest rates and years.
36. Here are two useful rules of thumb. The “Rule of 72” says that with discrete compounding the time it takes for an investment to double in value is roughly 72/interest rate (in percent).The
35. Your firm’s geologists have discovered a small oil field in New York’s Westchester County.The field is forecasted to produce a cash flow of C 1 $2 million in the first year. You estimate that
34. Dear Financial Adviser, My spouse and I are each 62 and hope to retire in three years. After retirement we will receive $7,500 per month after taxes from our employers’ pension plans and $1,500
33. The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate PV for each of the following cases.a.
32. You estimate that by the time you retire in 35 years, you will have accumulated savings of $2 million. If the interest rate is 8% and you live 15 years after retirement, what annual level of
31. A mortgage requires you to pay $70,000 at the end of each of the next eight years. The interest rate is 8%.a. What is the present value of these payments?b. Calculate for each year the loan

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