Question: Your firm’s geologists have discovered a

> The continuously compounded interest rate is 12%. a. You invest $1,000 at this rate. What is the investment worth after five years? b. What is the PV of $5 million to be received in eight years? c. What is the PV of a continuous stream of cash flows,

> Calculate durations and modified durations for the 3% bonds in Table 3.2. You can follow the procedure set out in Table 3.4 for the 9% coupon bonds. Confirm that modified duration closely predicts the impact of a 1% change in inte

> CSC is evaluating a new project to produce encapsulators. The initial investment in plant and equipment is $500,000. Sales of encapsulators in year 1 are forecasted at $200,000 and costs at $100,000. Both are expected to increase by 10% a year in line wi

> You have estimated spot rates as follows: r1 = 5.00%, r2 = 5.40%, r3 = 5.70%, r4 = 5.90%, r5 = 6.00%. a. What are the discount factors for each date (that is, the present value of $1 paid in year t) b. Calculate the PV of the following bonds assumi

> 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.

> 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 earned over the 12-month period? Now suppose that the bond yi

> A project produces a cash flow of $432 in year 1, $137 in year 2, and $797 in year 3. If the cost of capital is 15%, what is the project’s PV? If the project requires an investment of $1,200, what is its NPV?

> A 10-year U.S. Treasury bond with a face value of $1,000 pays a coupon of 5.5% (2.75% of face value every six months). The reported yield to maturity is 5.2% (a six-month discount rate of 5.2/2 = 2.6%). a. What is the present value of the bond? b. Gener

> F&H Corp. continues to invest heavily in a declining industry. Here is an excerpt from a recent speech by F&H’s CFO: We at F&H have of course noted the complaints of a few spineless investors and uninformed security analysts about the slow growth of prof

> 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 next year’s EPS is $15.

> 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 grow, plus the NPV of future growth opportunities.

> What is the payback period on each of the following projects? Given that you wish to use the payback rule with a cutoff period of two years, which projects would you accept? c. If you use a cutoff period of three years, which projects would you accept? d

> 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

> 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 higher its volatility. d. If interest rates rise, bond durations rise also.

> Restate the net cash flows in Table 6.6 in real terms. Discount the restated cash flows at a real discount rate. Assume a 20% nominal rate and 10% expected inflation. NPV should be unchanged at +3,802, or $3,802,000. Table 6.6: Period 3 4 6. Capital

> a. An 8%, five-year bond yields 6%. If this yield to maturity remains unchanged, what will be its price one year hence? Assume annual coupon payments and a face value of $100. b. What is the total return to an investor who held the bond over this year?

> What is the PV of $100 received in: a. Year 10 (at a discount rate of 1%)? b. Year 10 (at a discount rate of 13%)? c. Year 15 (at a discount rate of 25%)? d. Each of years 1 through 3 (at a discount rate of 12%)?

> If the PV of $139 is $125, what is the discount factor?

> Look at the last question where you calculated the equivalent annual cost of producing reformulated gasoline in California. Capital investment was $400 million. Suppose this amount can be depreciated for tax purposes on the 10-year MACRS schedule from Ta

> Hayden Inc. has a number of copiers that were bought four years ago for $20,000. Currently maintenance costs $2,000 a year, but the maintenance agreement expires at the end of two years and thereafter the annual maintenance charge will rise to $8,000. Th

> Mr. Cyrus Clops, the president of Giant Enterprises, has to make a choice between two possible investments: The opportunity cost of capital is 9%. Mr. Clops is tempted to take B, which has the higher IRR. a. Explain to Mr. Clops why this is not the corr

> Low-energy lightbulbs typically cost $3.60, have a life of nine years, and use about $2.00 of electricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.60. On the other hand, they last only about a year and use about $7.00 of e

> As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $50,000. Its operating costs are

> In the International Mulch and Compost example (Section 6-2), we assumed that losses on the project could be used to offset taxable profits elsewhere in the corporation. Suppose that the losses had to be carried forward and offset against future taxable

> How does the PV of depreciation tax shields vary across the recovery-period classes shown in Table 6.4? Give a general answer; then check it by calculating the PVs of depreciation tax shields in the five-year and seven-year classes. The tax rate is 35%

> Hindustan Motors has been producing its Ambassador car in India since 1948. As the company’s website explains, the Ambassador’s “dependability, spaciousness, and comfort factor have made it the most preferred car for generations of Indians.” Hindustan is

> United Pigpen is considering a proposal to manufacture high-protein hog feed. The project would make use of an existing warehouse, which is currently rented out to a neighboring firm. The next year’s rental charge on the warehouse is $100,000, and therea

> Machine C was purchased five years ago for $200,000 and produces an annual real cash flow of $80,000. It has no salvage value but is expected to last another five years. The company can replace machine C with machine B, See this problem: Machines A and

> a. If the one-year discount factor is .905, what is the one-year interest rate? b. If the two-year interest rate is 10.5%, what is the two-year discount factor? c. Given these one- and two-year discount factors, calculate the two-year annuity factor.

> Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $35,000. The object is to save on horse transporter rentals. Marsha had been renting a transporter every other week for $200 per day plus $1.00 per mile. Most o

> Reliable Electric is considering a proposal to manufacture a new type of industrial electric motor that would replace most of its existing product line. A research breakthrough has given Reliable a two-year lead on its competitors. The project proposal i

> If the cost of capital is 9%, what is the PV of $374 paid in year 9?

> A machine costs $380,000 and is expected to produce the following cash flows:
If the cost of capital is 12%, what is the machine’s NPV?

> A widget manufacturer currently produces 200,000 units a year. It buys widget lids from an outside supplier at a price of $2 a lid. The plant manager believes that it would be cheaper to make these lids rather than buy them. Direct production costs are e

> Go to the Excel spreadsheet versions of Tables 6.1, 6.5, and 6.6 and answer the following questions. a. How does the guano project’s NPV change if IM&C is forced to use the seven-year MACRS tax depreciation schedule? b. New engineering es

> Consider the following two mutually exclusive projects: a. Calculate the NPV of each project for discount rates of 0%, 10%, and 20%. Plot these on a graph with NPV on the vertical axis and discount rate on the horizontal axis. b. What is the approx

> Construct a new version of Table 4.7, 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% in year 9 and all later years. What is the val

> A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,000 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Co

> Machines A and B are mutually exclusive and are expected to produce the following real cash flows: The real opportunity cost of capital is 10%. a. Calculate the NPV of each machine. b. Calculate the equivalent annual cash flow from each machine. c. Which

> If you invest $100 at an interest rate of 15%, how much will you have at the end of eight years?

> 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 business, the Metropolitan District Commission (MDC) has agreed to pa

> Look again at the financial forecasts for Growth-Tech given in Table 4.4. This time assume you know that the opportunity cost of capital is r = .12 (discard the .099 figure calculated in the text). Assume you do not kn

> True or false? a. A project’s depreciation tax shields depend on the actual future rate of inflation. b. Project cash flows should take account of interest paid on any borrowing undertaken to finance the project. c. In the U.S., income reported to

> 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 now (at date 0) exactly the same. Yet PVGO accounts for a greater

> 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 + g b. r = EPS1 /P0 For each formula construct a simple numerical example showing that the formu

> 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.

> 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 time. Unfortunately, the volume of oil shipped is declining, and cash flow

> 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 “Rule of 69” says that with continuous compounding the time tha

> Suppose that you take out a $200,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%, and payments on the loan are made annually at the end of each year. a. What is your annual payment on the loan? b. Construct a mortgage amor

> 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 per month after taxes from Social Security. Unfortunately

> 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. The annuity payments arrive at one-year intervals. The

> 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 expenditure will those savings support? Unfortunately, inflatio

> Look again at the project cash flows in Problem 10. Calculate the modified IRR as defined in Footnote 5 in Section 5-3. Assume the cost of capital is 12%. Now try the following variation on the MIRR concept. Figure out the fraction x such that x times C1

> 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 balance that remains outstanding, the interest payment on

> Several years ago The Wall Street Journal reported that the winner of the Massachusetts State Lottery prize had the misfortune to be both bankrupt and in prison for fraud. The prize was $9,420,713, to be paid in 19 equal annual installments. (There were

> 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 lower than its yield to maturity, then the bond’s price wil

> Vocabulary test. Explain the differences between: a. Real and financial assets. b. Capital budgeting and financing decisions. c. Closely held and public corporations. d. Limited and unlimited liability.

> A leasing contract calls for an immediate payment of $100,000 and nine subsequent $100,000 semiannual payments at six-month intervals. What is the PV of these payments if the annual discount rate is 8%?

> Which would you prefer? a. An investment paying interest of 12% compounded annually. b. An investment paying interest of 11.7% compounded semiannually. c. An investment paying 11.5% compounded continuously. Work out the value of each of these investmen

> You have just read an advertisement stating, “Pay us $100 a year for 10 years and we will pay you $100 a year thereafter in perpetuity.” If this is a fair deal, what is the rate of interest?

> How much will you have at the end of 20 years if you invest $100 today at 15% annually compounded? How much will you have if you invest at 15% continuously compounded?

> Refer to Sections 2-3 through 2-4. If the rate of interest is 8% rather than 10%, how much would you need to set aside to provide each of the following? a. $1 billion at the end of each year in perpetuity. b. A perpetuity that pays $1 billion at the en

> If the interest rate is 7%, what is the value of the following three investments? a. An investment that offers you $100 a year in perpetuity with the payment at the end of each year. b. A similar investment with the payment at the beginning of each yea

> Recalculate the NPV of the office building venture in Example 2.1 at interest rates of 5, 10, and 15%. Plot the points on a graph with NPV on the vertical axis and the discount rates on the horizontal axis. At what discount rate (approximately) would the

> 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 rule “assumes that cash flows are reinvested at the opportunity cost of capi

> Kangaroo Autos is offering free credit on a new $10,000 car. You pay $1,000 down and then $300 a month for the next 30 months. Turtle Motors next door does not offer free credit but will give you $1,000 off the list price. If the rate of interest is .83

> The interest rate is 10%. a. What is the PV of an asset that pays $1 a year in perpetuity? b. The value of an asset that appreciates at 10% per annum approximately doubles in seven years. What is the approximate PV of an asset that pays $1 a year in p

> David and Helen Zhang are saving to buy a boat at the end of five years. If the boat costs $20,000 and they can earn 10% a year on their savings, how much do they need to put aside at the end of years 1 through 5?

> Siegfried Basset is 65 years of age and has a life expectancy of 12 more years. He wishes to invest $20,000 in an annuity that will make a level payment at the end of each year until his death. If the interest rate is 8%, what income can Mr. Basset expec

> Answer this question by drawing graphs like Figure 1A.1. Casper Milktoast has $200,000 on hand to support consumption in periods 0 (now) and 1 (next year). He wants to consume exactly the same amount in each period. The interest rate is 8%. There is no r

> As winner of a breakfast cereal competition, you can choose one of the following prizes: a. $100,000 now. b. $180,000 at the end of five years. c. $11,400 a year forever. d. $19,000 for each of 10 years. e. $6,500 next year and increasing thereafter by

> A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100.
What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation

> Table 7.9 shows standard deviations and correlation coefficients for eight stocks from different countries. Calculate the variance of a portfolio with equal investments in each stock.

> Calculate the beta of each of the stocks in Table 7.9 relative to a portfolio with equal investments in each stock.

> Suppose that Treasury bills offer a return of about 6% and the expected market risk premium is 8.5%. The standard deviation of Treasury-bill returns is zero and the standard deviation of market returns is 20%. Use the formula for portfolio risk to calcul

> Here are some historical data on the risk characteristics of Bank of America and Starbucks:
Assume the standard deviation of the return on the market was 23.0%. a. The correlation coefficient of Bank of America’s return versus Starbucks is .30. What i

> Borgia 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 limit cost the company in terms of its market value? The op

> A common stock will pay a cash dividend of $4 next year. After that, the dividends are expected to increase indefinitely at 4% per year. If the discount rate is 14%, what is the PV of the stream of dividend payments?

> You can form a portfolio of two assets, A and B, whose returns have the following characteristics:
If you demand an expected return of 12%, what are the portfolio weights? What is the portfolio’s standard deviation?

> There are few, if any, real companies with negative betas. But suppose you found one with β = –.25. a. How would you expect this stock’s rate of return to change if the overall market rose by an extra 5%? What if the market fell by an extra 5%? b. You h

> Your eccentric Aunt Claudia has left you $50,000 in BP shares plus $50,000 cash. Unfortunately her will requires that the BP stock not be sold for one year and the $50,000 cash must be entirely invested in one of the stocks shown in Table 7.9. What is th

> a. How many variance terms and how many different covariance terms do you need to calculate the risk of a 100-share portfolio? b. Suppose all stocks had a standard deviation of 30% and a correlation with each other of .4. What is the standard deviation

> Halcyon Lines is considering the purchase of a new bulk carrier for $8 million. The forecasted revenues are $5 million a year and operating costs are $4 million. A major refit costing $2 million will be required after both the fifth and tenth years. Aft

> Hyacinth Macaw invests 60% of her funds in stock I and the balance in stock J. The standard deviation of returns on I is 10%, and on J it is 20%. Calculate the variance of portfolio returns, assuming a. The correlation between the returns is 1.0. b. Th

> Lonesome Gulch Mines has a standard deviation of 42% per year and a beta of +.10. Amalgamated Copper has a standard deviation of 31% a year and a beta of +.66. Explain why Lonesome Gulch is the safer investment for a diversified investor.

> Hippique s.a., which owns a stable of racehorses, has just invested in a mysterious black stallion with great form but disputed bloodlines. Some experts in horseflesh predict the horse will win the coveted Prix de Bidet; others argue that it should be pu

> Each of the following statements is dangerous or misleading. Explain why. a. A long-term United States government bond is always absolutely safe. b. All investors should prefer stocks to bonds because stocks offer higher long-run rates of return. c. T

> Here are inflation rates and U.S. stock market and Treasury bill returns between 1929 and 1933:
a. What was the real return on the stock market in each year? b. What was the arithmatic average real return? c. What was the risk premium in each year? d.

> Consider the following capital rationing problem: Set up this problem as a linear program and solve it. You can allow partial investments, that is, 0 ≤ x ≤ 1. Calculate and interpret the shadow prices16 on the capi

> 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 project. b. Show how the profitability-index rule can be used to

> What is the beta of each of the stocks shown in table

> A portfolio contains equal investments in 10 stocks. Five have a beta of 1.2; the remainder have a beta of 1.4. What is the portfolio beta? a. 1.3. b. Greater than 1.3 because the portfolio is not completely diversified. c. Less than 1.3 because divers

> Suppose the standard deviation of the market return is 20%. a. What is the standard deviation of returns on a well-diversified portfolio with a beta of 1.3? b. What is the standard deviation of returns on a well-diversified portfolio with a beta of 0?

> To calculate the variance of a three-stock portfolio, you need to add nine boxes:
Use the same symbols that we used in this chapter; for example, x1 = proportion invested in stock 1 and σ12 = covariance between stocks 1 and 2. Now complete the nine bo

> In which of the following situations would you get the largest reduction in risk by spreading your investment across two stocks? a. The two shares are perfectly correlated. b. There is no correlation. c. There is modest negative correlation. d. There

> A factory costs $400,000. It will produce an inflow after operating costs of $100,000 in year 1, $200,000 in year 2, and $300,000 in year 3. The opportunity cost of capital is 12%. Show your calculations in a time line like Figures 2.4 and 2.5. Calculat

> True or false? a. Investors prefer diversified companies because they are less risky. b. If stocks were perfectly positively correlated, diversification would not reduce risk. c. Diversification over a large number of assets completely eliminates ris

> During the boom years of 2010–2014, ace mutual fund manager Diana Sauros produced the following percentage rates of return. Rates of return on the market are given for comparison.
Calculate the average return and standard deviation of Ms. Sauros’s mut

> The following table shows the nominal returns on the U.S. stocks and the rate of inflation. a. What was the standard deviation of the nominal market returns? b. Calculate the arithmetic average real return.

> In most large corporations, ownership and management are separated. What are the main implications of this separation?