Question: What is the PV of $100 received

> 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 Fisher’s theory say about how the real interest rate will c

> a. The cost of a new automobile is $10,000. If the interest rate is 5%, how much would you have to set aside now to provide this sum in five years? b. You have to pay $12,000 a year in school fees at the end of each of the next six years. If the interes

> Air conditioning for a college dormitory will cost $1.5 million to install and $200,000 per year to operate. The system should last 25 years. The real cost of capital is 5%, and the college pays no taxes. What is the equivalent annual cost?

> The one-year spot interest rate is r1 = 5% and the two-year rate is r2 = 6%. If the expectations theory is correct, what is the expected one-year interest rate in one year’s time?

> Ms. Espinoza is retired and depends on her investments for her income. Mr. Liu is a young executive who wants to save for the future. Both are stockholders in Scaled Composites, LLC, which is building SpaceShipOne to take commercial passengers into space

> Look again at Table 3.5. 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.

> The following table tracks the main components of working capital over the life of a four-year project. Calculate net working capital and the cash inflows and outflows due to investment in working capital. 2016 2017 2018 2019 2020 Accounts receivabl

> 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?

> In December 2005, Mid-American Energy brought online one of the largest wind farms in the world. It cost an estimated $386 million and the 257 turbines have a total capacity of 360.5 megawatts (mW). Wind speeds fluctuate and most wind farms are expected

> In February 2015 Treasury 4¾s of 2041 offered a semi-annually compounded yield to maturity of 2.70%. Recognizing that coupons are paid semi-annually, calculate the bond’s price.

> A 10-year bond is issued with a face value of $1,000, paying interest of $60 a year. If yields to maturity increase shortly after the T-bond is issued, what happens to the bond’s a. Coupon rate? b. Price? c. Yield to maturity?

> 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 each expects to earn a rate of return of 8% per year

> Look one more time at Table 3.5. a. Suppose you knew the bond prices but not the spot interest rates. Explain how you would calculate the spot rates. b. Suppose that you could buy bond C in large quantities at $1,040 rather than at its equ

> Pharmecology just paid an annual 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. What is Pharmecology’s current stock price? The nominal cost

> What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%. Maturity (years) Coupon Price (%) 5

> Calculate the IRR (or IRRs) for the following project: For what range of discount rates does the project have positive NPV? Co C2 -3,000 +3,500 +4,000 -4,000

> The duration of a bond that makes an equal payment each year in perpetuity is (1 + yield)/yield. Prove it.

> Which of the following statements always apply to corporations? a. Unlimited liability. b. Limited life. c. Ownership can be transferred without affecting operations. d. Managers can be fired with no effect on ownership.

> You are quoted an interest rate of 6% on an investment of $10 million. What is the value of your investment after four years if interest is compounded: a. Annually? b. Monthly? or c. Continuously?

> Find the arbitrage opportunity (opportunities?). Assume for simplicity that coupons are paid annually. In each case the face value of the bond is $1,000. Bond Maturity (years) Сoupon ($) Price ($) A 3 751.30 B. 4 50 842.30 120 1,065.28 4 100 980.57 3

> If a bond’s yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this with a simple example of a four-year bond selling at a premium to face value. Now do the same for a four-year bond sellin

> Suppose that you buy a two-year 8% bond at its face value. a. What will be your total nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your real return? b. Now suppose that the bond is a TIPS. Wh

> We can imagine the financial manager doing several things on behalf of the firm’s stockholders. For example, the manager might: a. Make shareholders as wealthy as possible by investing in real assets. b. Modify the firm’s investment plan to help shareh

> Each of the following statements is true. Use an example to explain why they are consistent. When a company introduces a new product, or expands production of an existing product, investment in net working capital is usually an important cash outflow. Fo

> 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 right? b. Investing in long-term bonds c

> New Economy Transport (A) The New Economy Transport Company (NETCO) was formed in 1959 to carry cargo and passengers between ports in the Pacific Northwest and Alaska. By 2015 its fleet had grown to four vessels, including a small dry-cargo vessel, the V

> 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 was right? What is the minimum sensible value for the five-ye

> 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 expected to be 4% a year forever. c. Stock C is expected

> The Beyond the Page feature, “Goldman Sachs Causes a Ruckus,” describes the controversial involvement of Goldman Sachs in a mortgage-backed securities deal in 2006. When this involvement was revealed, the market value of Goldman Sachs’ common stock fell

> When appraising mutually exclusive investments in plant and equipment, financial managers calculate the investments’ equivalent annual costs and rank the investments on this basis. Why is this necessary? Why not just compare the investments’ NPVs? Explai

> Look again at Table 3.5. Suppose the spot interest rates change to the following downward-sloping term structure: r1 = 4.6%, r2 = 4.4%, r3 = 4.2%,

> 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 bond or a 15-year zero-coupon bond? What if the yield is 10%?

> Find the spreadsheet for Table 3.4. in Connect. Show how duration and volatility change if (a) the bond’s coupon is 8% of face value and (b) the bond’s yield is 6%. Explain your finding.

> 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?

> 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

> 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 C1 = $2 million in the first year. You estimate that you could earn an expected return of r = 12% from investing

> 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