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Fixed and Variable Costs

In a slow year, Wimpy`s Burgers will produce 1 million hamburgers at a total cost of $1.75 million. In a good year, it can produce 2 million hamburgers at a total cost of $2.25 million. What are the fixed and variable costs of hamburger production?

2. Average Cost. Reconsider Wimpy`s Burgers from problem 1.

a. What is the average cost per burger when the firm produces 1 million hamburgers?

b. What is average cost when the firm produces 2 million hamburgers?

c. Why is average cost lower when more burgers are produced?

3. Sensitivity Analysis. A project currently generates sales of $10 million, variable costs equal to 50 percent of sales, and fixed costs of $2 million. The firm`s tax rate is 35 percent. What are the effects of the following changes on after-tax profits and cash flow?

a. Sales increase from $10 million to $11 million.

b. Variable costs increase to 60 percent of sales.

4. Sensitivity Analysis. The project in the preceding problem will last for 10 years. The discount rate is 12 percent.

a. What is the effect on project NPV of each of the changes considered in the problem?

b. If project NPV under the base-case scenario is $2 million, how much can fixed costs increase before NPV turns negative?

c. How much can fixed costs increase before accounting profits turn negative?

5. 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 5 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 5 years to a salvage value of zero. The opportunity cost of capital is 12 percent, and the tax rate is 40 percent.

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?

6. Scenario Analysis. 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 percent higher or 10 percent 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 35 percent and the required rate of return is 14 percent. What is project NPV in the ¬best-case scenario, ­ that is, assuming all variables take on the best possible value? What about the worst-case scenario?

7. Scenario Analysis. Reconsider the best- and worst-case scenarios in the previous problem. Do the best- and worst-case outcomes when each variable is treated independently seem to be reasonable scenarios in terms of the combinations of variables? For example, if price is higher than predicted, is it more or less likely that cost is higher than predicted? What other relationships may exist among the variables?

8. Break-Even. The following estimates have been prepared for a project under consideration:

Fixed costs: $20,000

Depreciation: $10,000

Price: $2

Accounting break-even: 60,000 units

What must be the variable cost per unit?

9. Break-Even. 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 $30. 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.

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 35 percent, a 10-year project life, and a discount rate of 12 percent?

10. Break-Even. Turn back to problem 9.

a. Would the accounting break-even point in the first year of operation increase or decrease if the machinery were depreciated over a 5-year period?

b. Would the NPV break-even point increase or decrease if the machinery were depreciated over a 5-year period?

11. Break-Even. You are evaluating a project that will require an investment of $10 million that will be depreciated over a period of 7 years. You are concerned that the corporate tax rate will increase during the life of the project. Would such an increase affect the accounting break-even point? Would it affect the NPV break-even point?

12. Break-Even. Define the cash-flow break-even point as the sales volume (in dollars) at which cash flow equals zero. Is the cash-flow break-even level of sales higher or lower than the zero-profit break-even point?

13. Break-Even and NPV. If a project operates at cash-flow break-even (see problem 12) for its entire life, what must be true of the project`s NPV?

14. Break-Even. Modern Artifacts can produce keepsakes that will be sold for $80 each. Non depreciation fixed costs are $1,000 per year and variable costs are $60 per unit.

a. If the project requires an initial investment of $3,000 and is expected to last for 5 years and the firm pays no taxes, what are the accounting and NPV break-even levels of sales?

The initial investment will be depreciated straight-line over 5 years to a final value of zero, and the discount rate is 10 percent.

b. How do your answers change if the firm`s tax rate is 40 percent?

15. Break-Even. A financial analyst has computed both accounting and NPV break-even sales levels for a project under consideration using straight-line depreciation over a 6-year period. The project manager wants to know what will happen to these estimates if the firm uses MACRS depreciation instead. The capital investment will be in a 5-year recovery period class under MACRS rules (see Table 7.4). The firm is in a 35 percent tax bracket.

a. What (qualitatively) will happen to the accounting break-even level of sales in the first years of the project?

b. What (qualitatively) will happen to NPV break-even level of sales?

c. If you were advising the analyst, would the answer to (a) or (b) be important to you?

Specifically, would you say that the switch to MACRS makes the project more or less attractive?