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Break-Even

Reconsider Finefodder`s new superstore. Suppose that by investing an additional $600,000 initially in more efficient checkout equipment, Finefodder could reduce variable costs to 80 percent of sales.

a. Using the base-case assumptions (Table 5.1), find the NPV of this alternative scheme. Hint: Remember to focus on the incremental cash flows from the project.

b. At what level of sales will accounting profits be unchanged if the firm invests in the new equipment? Assume the equipment receives the same 12-year 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?

17. Break-Even and NPV. If the superstore project (see the previous problem) operates at accounting break-even, will net present value be positive or negative?

18. 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 7.5. What will profits be if sales turn out to be $3.5 million? What if they are $4.5 million?

19. Operating Leverage.

a. What is the degree of operating leverage of Modern Artifacts (in problem 14) when sales are $8,000?

b. What is the degree of operating leverage when sales are $10,000?

c. Why is operating leverage different at these two levels of sales?

20. 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 14a) has zero fixed costs, then DOL = 1 and in fact sales and profits are directly proportional so that a 1 percent change in sales results in a 1 percent change in profits.

21. Operating Leverage. A project has fixed costs of $1,000 per year, depreciation charges of $500 a year, revenue of $6,000 a year, and variable costs equal to two-thirds of revenues.

a. If sales increase by 5 percent, what will be the increase in pretax profits?

b. What is the degree of operating leverage of this project?

c. Confirm that the percentage change in profits equals DOL times the percentage change in sales.

22. 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 percent chance that the amount of oil is 15 million barrels, and a 50 percent 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 that costs $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.

23. Project Options. A silver mine can yield 10,000 ounces of copper at a variable cost of $8 per ounce. The fixed costs of operating the mine are $10,000 per year. In half the years, silver can be sold for $12 per ounce; in the other years, silver can be sold for only $6 per ounce. Ignore taxes.

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 shut down the mine in years of low silver prices. What happens to the average cash flow from the mine?

24. Project Options. An auto plant that costs $100 million to build can produce a new line of cars that 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 is only about 50 percent.

a. Would you build the plant?

b. Suppose that the plant can be sold for $90 million to another automaker if the auto line is not successful. Now would you build the plant?

c. Illustrate the option to abandon in (b) using a decision tree.

25. Production Options. Explain why options to expand or contract production are most valuable when forecasts about future business conditions are most uncertain.

26. Abandonment Option. Hit or Miss Sports is introducing a new product this year. If its seeat- night soccer balls are a hit, the firm expects to be able to sell 50,000 units a year at a price of $60 each. If the new product is a bust, only 30,000 units can be sold at a price of $55. The variable cost of each ball is $30, and fixed costs are zero. The cost of the manufacturing equipment is $6 million, and the project life is estimated at 10 years. The firm will use straight-line depreciation over the 10-year life of the project. The firm`s tax rate is 35 percent and the discount rate is 12 percent.

a. If each outcome is equally likely, what is expected NPV? Will the firm accept the project? b. Suppose now that the firm can abandon the project and sell off the manufacturing equipment for $5.4 million if demand for the balls turns out to be weak. The firm will make the decision to continue or abandon after the first year of sales. Does the option to abandon change the firm`s decision to accept the project?

27. Expansion Option. Now suppose that Hit or Miss Sports from the previous problem can expand production if the project is successful. By paying its workers overtime, it can increase production by 20,000 units; the variable cost of each ball will be higher, however, equal to $35 per unit. By how much does this option to expand production increase the NPV of the project?