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Chapter 10 Project Analysis 321 QUESTIONS AND PROBLEMS Mc 13 Graw Hill 1. Terminology. Match each of the following terms to one of the definitions or descriptions listed below: sensitivity analysis, scenario analysis, break-even analysis, operating leverage, decision tree, real option. (LO10-1 through LO10-5) a. Recalculation of project NPV by making different assumptions about the economic environment. b. Opportunity to modify a project at a future date. c. Analysis of how project NPV changes if different assumptions are made about sales, costs, and other key variables. d. The degree to which fixed costs magnify the effect on profits of a shortfall in sales. e. A graphical technique for displaying possible future events and decisions taken in response to those events. f. Determination of the level of future sales at which project profitability or NPV equals zero. The Capital Budget. True or false? (LO10-1 and LO10-2) a. Approval of the capital budget allows manager to go ahead with any project included in the budget. b. Managers need to ensure that strategic investment proposals exploit the firm’s competitive advantage. c. Project sponsors are likely to be overoptimistic. d. By imposing expenditure limits, management forces project sponsors to set priorities. Project Analysis. True or false? (LO10-3) a. Sensitivity analysis can be used to identify the variables most crucial to a project’s success. b. Sensitivity analysis is used to obtain expected, optimistic, and pessimistic values for total project cash flows. c. Rather than basing one’s estimate of NPV just on expected cash flows, it makes more sense to average the NPVs calculated from the pessimistic and optimistic estimates of cash flow. d. Risk is reduced when a high proportion of costs are fixed. e. The break-even level of sales for a project is higher when break-even is defined in terms of NPV rather than accounting income. Fixed and Variable Costs. In a slow year, Deutsche Burgers will produce 2 million hamburgers at a total cost of $3.5 million. In a good year, it can produce 4 million hamburgers at a total cost of $4.5 million. (LO10-3) What are the fixed costs of hamburger production? What are the variable costs? What is the average cost per burger when the firm produces 1 million hamburgers? . What is the average cost when the firm produces 2 million hamburgers? Why is the average cost lower when more burgers are produced? o pp T Sensitivity Analysis. A project currently generates sales of $10 million, variable costs equal 50% of sales, and fixed costs are $2 million. The firm’s tax rate is 21%. What are the effects of the following changes on cash flow? (LO10-3) a. Sales increase from $10 million to $11 million. b. Variable costs increase to 65% of sales. Sensitivity Analysis. Blooper’s analysts have come up with the following revised estimates for its magnoosium mine (see Section 10.2): Range Pessimistic Optimistic Initial investment +50% —25% Revenues —-15% +20% Variable costs, % of revenues +10% —-10% Fixed costs +50% —30% Working capital, % of expected value +50% -50%

322 Part Two Value Conduct a sensitivity analysis using the revised data. Label your answers as follows: (LO10-3) Project NPV Pessimistic Expected Optimistic Initial investment a. b. c. Revenues d. e f. Variable costs g. h i Fixed costs j. k I Working capital m. n o. 7. Sensitivity Analysis. The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment. The new equipment costs $9 million (the existing equipment has zero salvage value). The attraction of the new machinery is that it is expected to cut manufacturing costs from their current level of $8 a welt to $4. However, as the following table shows, there is some uncertainty about both the future sales and the performance of the new machinery: Pessimistic Expected Optimistic Sales (million welts) 0.4 0.5 0.7 Manufacturing cost ($ per welt) 6 4 3 Life of new machinery (years) 7 10 13 Conduct a sensitivity analysis of the replacement decision assuming a discount rate of 12%. Rustic does not pay taxes. Label your answers as follows: (LOJ 0-3) NPV of Replacement Decision Pessimistic Expected Optimistic Sales (million welts) a. b. C. Manufacturing cost {$ per welt) d. e. Life of new machinery (years) g. h. i 8. Sensitivity Analysis. Emperor’s Clothes Fashions can invest $5 million in a new plant for producing invisible makeup. The plant has an expected life of five years, and expected sales are 6 million jars of makeup a year. Fixed costs are $2 million a year, and variable costs are $1 per jar. The product will be priced at $2 per jar. The plant will be depreciated straight-line over five years to a salvage value of zero. The opportunity cost of capital is 10%, and the tax rate is 40%. (LO10-3) a. What is project NPV under these base-case assumptions? b. What is NPV if variable costs turn out to be $1.20 per jar? c. What is NPV if fixed costs turn out to be $1.5 million per year? d. At what price per jar would project NPV equal zero? 9. Project Risk. The most likely outcomes for a particular project are estimated as follows: Unit price: $50 Variable cost: $30 Fixed cost: $300,000 Expected sales: 30,000 units per year However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 21%, and the required rate of return is 12%. (LO10-3) a. What is project NPV if all variables take on the best possible value? b. What if each variable takes on the worst possible value?

Chapter 10 Project Analysis 323 10. 11. 12. 13. 14. 15. 16. Break-Even Analysis. The following estimates have been prepared for a project: Fixed costs: $20,000 Depreciation: $10,000 Sales price: $2 Accounting break-even: 60,000 units What must be the variable cost per unit? (LO10-3) Break-Even Analysis. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The materials cost for a standard diamond is $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $200,000. The machinery costs $1 million and is depreciated straight-line over 10 years to a salvage value of zero. (LO10-3) a. What is the accounting break-even level of sales in terms of number of diamonds sold? b. What is the NPV break-even level of sales assuming a tax rate of 21%, a 10-year project life, and a discount rate of 12%? Break-Even Analysis. You are evaluating a project that will require an investment of $10 million that will be depreciated over a period of seven years. You are concerned that the corporate tax rate will increase during the life of the project. (LO10-3) a. Would this increase the accounting break-even point? b. Would it increase the NPV break-even point? Break-Even Analysis. Define the cash-flow break-even point as the sales volume (in dollars) at which cash flow equals zero. (LO10-3) a. Is the cash-flow break-even level of sales higher or lower than the zero-profit (accounting) break-even point? b. If a project operates at cash-flow break-even [see part (a)] for all future years, is its NPV positive or negative? NPV Break-Even Analysis. Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $1,000 per year, and variable costs are $60 per unit. The initial investment of $3,000 will be depreciated straight-line over its useful life of five years to a final value of zero, and the discount rate is 10%. (LOI10-3) a. What is the accounting break-even level of sales if the firm pays no taxes? b. What is the NPV break-even level of sales if the firm pays no taxes? c. What is the accounting break-even level of sales if the firm’s tax rate is 40%? d. What is the NPV break-even level of sales if the firm’s tax rate is 40%? NPV Break-Even Analysis. A financial analyst has computed both accounting and NPV break- even sales levels for a project using straight-line depreciation over a six-year period. The project manager wants to know what will happen to these estimates if the firm can make a larger deduction for depreciation in the early years of the project. The firm is in a 21% tax bracket. (L0O10-3) a. Would the accounting break-even level of sales in the first years of the project increase or decrease? b. Would the NPV break-even level of sales in the first years of the project increase or decrease? ¢. If you were advising the analyst, would the answer to part (a) or (b) be important to you? Specifically, would you say that the switch to accelerated depreciation makes the project more or less attractive? NPV Break-Even Analysis. Reconsider Blooper’s mining project. Suppose that by investing an additional $10 million initially, Blooper could reduce variable costs to 35% of sales. (LOI10-3) a. Using the base-case assumptions (Spreadsheet 10.1), find the NPV of this alternative scheme. b. At what level of sales will accounting profits be unchanged if the firm makes the new investment? Assume the equipment receives the same straight-line depreciation treatment as in the original example. (Hint: Focus on the project’s incremental effects on fixed and variable costs.) c. What is the NPV break-even point?

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324 Part Two Value 17. 18. 19. 20. 21. 22. 24. Break-Even Analysis and NPV. If the Blooper project from Problem 16 operates at accounting break-even, will net present value be positive or negative? (LO! 0-3) Operating Leverage. You estimate that your cattle farm will generate $1 million of profits on sales of $4 million under normal economic conditions and that the degree of operating leverage is 8. (LOI10-4) a. What will profits be if sales turn out to be $3.5 million? b. What if they are $4.5 million? Operating Leverage. (LO10-4) a. What is the degree of operating leverage of Modern Artifacts (in Problem 14) when sales are $7,000? b. What is the degree of operating leverage when sales are $12,000?7 c. Why is operating leverage different at these two levels of sales? Operating Leverage. What is the lowest possible value for the degree of operating leverage for a profitable firm? Show with a numerical example that if Modern Artifacts (see Problem 14) has zero fixed costs and zero depreciation, then DOL = | and, in fact, sales and profits are directly proportional, so a 1% change in sales results in a 1% change in profits. (LO10-4) Operating Leverage. A project has fixed costs of $1,000 per year, depreciation charges of $500 a year, annual revenue of $6,000, and variable costs equal to two-thirds of revenues. (LO10-4) a. If sales increase by 10%, what will be the increase in pretax profits? b. What is the degree of operating leverage of this project? Project Options. Section 10.4 describes four types of real options. For each of the following cases, state which type of option is involved: (LO10-5) a. Deutsche Metall postpones a major plant expansion. The expansion has a positive NPV on a discounted cash-flow basis, but before proceeding, management wants to see how product demand grows. b. Western Telecom commits to production of digital switching equipment specially designed for the Buropean market. The project has a negative NPV, but it is justified on strategic grounds by the need for a strong market position in a rapidly growing and potentially very profitable market. ¢. Western Telecom vetoes a fully integrated, automated production line for the new switches. It relies on standard, less expensive equipment. The automated production line is more efficient overall, according to a discounted cash-flow calculation. d. Mount Fuji Airways buys a jumbo jet with special equipment that allows the plane to be switched quickly from freight to passenger use and vice versa. Project Options. Your midrange guess as to the amount of oil in a prospective field is 10 million barrels, but, in fact, there is a 50% chance that the amount of oil is 15 million barrels and a 50% chance of 5 million barrels. If the actual amount of oil is 15 million barrels, the present value of the cash flows from drilling will be $8 million. If the amount is only 5 million barrels, the present value will be only $2 million. It costs $3 million to drill the well. Suppose that a seismic test costing $100,000 can verify the amount of oil under the ground. Is it worth paying for the test? Use a decision tree to justify your answer. (LO10-5) Project Options. A silver mine can yield 10,000 ounces of silver at a variable cost of $32 per ounce. The fixed costs of operating the mine are $40,000 per year. In half the years, silver can be sold for $48 per ounce; in the other years, silver can be sold for only $24 per ounce. Ignore taxes. (LO10-5) a. What is the average cash flow you will receive from the mine if it is always kept in operation and the silver always is sold in the year it is mined? b. Now suppose you can costlessly shut down the mine in years of low silver prices. What happens to the average cash flow from the mine? Project Options. An auto plant that costs $100 million to build can produce a line of flex-fuel cars. The investment will produce cash flows with a present value of $140 million if the line is successful but only $50 million if it is unsuccessful. You believe that the probability of success

Chapter 10 Project Analysis 325 is only about 50%. You will learn whether the line is successful immediately after building the plant. (LO10-5) a. Would you build the plant? b. Suppose that the plant can be sold for $95 million to another automaker if the auto line is not successful. Now would you build the plant? c¢. Ilustrate the option to abandon in part (b) using a decision tree. 26. Project Options. Explain why options to expand or contract production are most valuable when forecasts about future business conditions are most uncertain. (LO10-5) 27. Decision Trees. The Finance in Practice box in Section 10.5 describes Spirit’s option to buy additional Airbus airliners. Draw a decision tree showing the future choices faced by the airline. (LO10-5) 28. Project Analysis. New Energy is evaluating a new biofuel facility. The plant would cost $4.,000 million to build and has the potential to produce up to 40 million barrels of synthetic oil a year. The product is a close substitute for conventional oil and would sell for the same price. The market price of oil currently is fluctuating around $100 per barrel, but there is considerable uncertainty about future prices. Variable costs for the organic inputs to the production process are estimated at $82 per barrel and are expected to be stable. In addition, annual upkeep and maintenance expenses on the facility will be $100 million regardless of the production level. The plant has an expected life of 15 years, and it can be fully depreciated immediately. Salvage value net of cleanup costs is expected to be negligible. Demand for the product is difficult to forecast. Depending on consumer acceptance, sales might range from 25 million to 35 million barrels annually. The discount rate is 12%, and New Energy’s tax bracket is 21%. (LO10-3, LO10-4, and LO10-5) a. Find the project NPV for the following combinations of oil price and sales volume. Which source of uncertainty seems most important to the success of the project? Oil Price Annual Sales $80/Barrel $100/Barrel $120/Barrel 25 million barrels (i) (ii) (iii) 30 million barrels (iv) v) (vi) 35 million barrels (vii) (viii) (ix) b. At an oil price of $100, what level of annual sales, maintained over the life of the plant, is necessary for NPV break-even? (This will require trial and error unless you are familiar with more advanced features of Excel, such as the Goal Seek command.) c. At an oil price of $100, what is the accounting break-even level of sales in each year? Why does it change each year? Does this notion of break-even seem reasonable to you? d. If each of the scenarios in the grid in part (a) is equally likely, what is the NPV of the facility? e. Why might the facility be worth building despite your answer to part (d)? (Hins: What real option may the firm have to avoid losses in low-oil-price scenarios?) WEB EXERCISE 1. Can you guess Hewlett-Packard’s incremental cost for producing one computer? You probably have that amount in your wallet or purse! This gives the company considerable operating leverage. Let’s estimate the degree of operating leverage for HP (ticker symbol HPQ). Go to the annual income statement, which you can find at finance.yahoo.com. Assume that selling, general, administrative, R&D, and depreciation expenses are fixed and cost of goods sold (which Yahoo! calls cost of revenue) is variable. Estimate the degree of operating leverage for HP for the last year (annual).

328 Part Two Value MINICASE Maxine Peru, the CEO of Peru Resources, hardly noticed the plate of savory quenelles de brochet and the glass of Corton Charlemagne '94 on the table before her. She was absorbed by the engineering report handed to her just as she entered the executive dining room. The report described a proposed new mine on the North Ridge of Mt. Zircon. A vein of transcendental zirconium ore had been discovered there on land owned by Ms. Peru’s company. Test borings indicated sufficient reserves to produce 340 tons per year of transcendental zirconium over a seven-year period. The vein probably also contained hydrated zircon gemstones. The amount and quality of these zircons were hard to predict because they tended to occur in “pockets.” The new mine might come across one, two, or dozens of pockets. The mining engineer guessed that 150 pounds per year might be found. The current price for high-quality hydrated zircon gemstones was $3,300 per pound. Peru Resources was a family-owned business with total assets of $45 million, including cash reserves of $4 million. The outlay required for the new mine would be a major commitment. Fortu- nately, Peru Resources was conservatively financed, and Ms. Peru believed that the company could borrow up to $9 million at an interest rate of about 8%. The mine’s operating costs were projected at $900,000 per year, including $400,000 of fixed costs and $500,000 of variable costs. Ms. Peru thought these forecasts were accurate. The big question marks seemed to be the initial cost of the mine and the selling price of transcendental zirconium. Opening the mine, and providing the necessary machinery and ore-crunching facilities, was supposed to cost $10 million, but cost overruns of 10% or 15% were common in the mining business. In addition, new environmental regulations, if enacted, could increase the cost of the mine by $1.5 million. There was a cheaper design for the mine, which would reduce its cost by $1.7 million and eliminate much of the uncertainty about cost overruns. Unfortunately, this design would require much higher fixed operating costs. Fixed costs would increase to $850,000 per year at planned production levels. The current price of transcendental zirconium was $10,000 per ton, but there was no consensus about future prices.'' Some experts were projecting rapid price increases to as much as $14,000 per ton. On the other hand, there were pessimists saying that prices could be as low as $7,500 per ton. Ms. Peru did not have strong views either way: Her best guess was that price would just increase with inflation at about 3.5% per year. (Mine operating costs would also increase with inflation.) Ms. Peru had wide experience in the mining business, and she knew that investors in similar projects usually wanted a forecast nominal rate of return of at least 14%. You have been asked to assist Ms. Peru in evaluating this proj- ect. Lay out the base-case NPV analysis, and undertake sensitivity, scenario, or break-even analyses as appropriate. Assume that Peru Resources pays tax at a 30% rate. For simplicity, also assume that the investment in the mine could be depreciated for tax purposes straight-line over seven years. What forecasts or scenarios should worry Ms. Peru the most? Where would additional information be most helpful? Is there a case for delaying construction of the new mine? 11 There were no traded forward or futures contracts on transcendental zirconium. See Chapter 24,

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