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CHAPTER 9

RISK ANALYSIS, REAL OPTIONS, AND CAPITAL BUDGETING

Answers to Concepts Review and Critical Thinking Questions

1. Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows.

The danger is greatest with a new product because the cash flows are probably harder to predict.

2. With a sensitivity analysis, one variable is examined over a broad range of values. With a scenario

analysis, all variables are examined for a limited range of values.

3. It is true that if average revenue is less than average cost, the firm is losing money. This much of the

statement is therefore correct. At the margin, however, accepting a project with marginal revenue in excess of its marginal cost clearly acts to increase operating cash flow.

4. From the shareholder perspective, the financial break-even point is the most important. A project can

exceed the accounting and cash break-even points but still be below the financial break-even point. This causes a reduction in shareholder (your) wealth.

5. The project will reach the cash break-even first, the accounting break-even next and finally the

financial break-even. For a project with an initial investment and sales after, this ordering will always apply. The cash break-even is achieved first since it excludes depreciation. The accounting break-even is next since it includes depreciation. Finally, the financial break-even, which includes the time value of money, is achieved.

6. Traditional NPV analysis is often too conservative because it ignores profitable options such as the

ability to expand the project if it is profitable, or abandon the project if it is unprofitable. The option to alter a project when it has already been accepted has a value, which increases the NPV of the project.

7. The type of option most likely to affect the decision is the option to expand. If the country just

liberalized its markets, there is likely the potential for growth. First entry into a market, whether an entirely new market, or with a new product, can give a company name recognition and market share. This may make it more difficult for competitors entering the market.

8. Sensitivity analysis can determine how the financial break-even point changes when some factors

(such as fixed costs, variable costs, or revenue) change.

9. There are two sources of value with this decision to wait. Potentially, the price of the timber can

potentially increase, and the amount of timber will almost definitely increase, barring a natural catastrophe or forest fire. The option to wait for a logging company is quite valuable, and companies in the industry have models to estimate the future growth of a forest depending on its age.

10. When the additional analysis has a negative NPV. Since the additional analysis is likely to occur

almost immediately, this means when the benefits of the additional analysis outweigh the costs. The benefits of the additional analysis are the reduction in the possibility of making a bad decision. Of course, the additional benefits are often difficult, if not impossible, to measure, so much of this decision is based on experience.

Solutions to Questions and Problems

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic

1. a. To calculate the accounting breakeven, we first need to find the depreciation for each year. The

depreciation is:

Depreciation = $896,000/8 Depreciation = $112,000 per year And the accounting breakeven is: QA = ($900,000 + 112,000)/($38 ¨C 25) QA = 77,846 units b. We will use the tax shield approach to calculate the OCF. The OCF is: OCFbase = [(P ¨C v)Q ¨C FC](1 ¨C tc) + tcD

OCFbase = [($38 ¨C 25)(100,000) ¨C $900,000](0.65) + 0.35($112,000) OCFbase = $299,200 Now we can calculate the NPV using our base-case projections. There is no salvage value or

NWC, so the NPV is:

NPVbase = ¨C$896,000 + $299,200(PVIFA15%,8) NPVbase = $446,606.60 To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the

NPV at a different quantity. We will use sales of 105,000 units. The NPV at this sales level is:

OCFnew = [($38 ¨C 25)(105,000) ¨C $900,000](0.65) + 0.35($112,000) OCFnew = $341,450 And the NPV is: NPVnew = ¨C$896,000 + $341,450(PVIFA15%,8) NPVnew = $636,195.93

c.

So, the change in NPV for every unit change in sales is: ?NPV/?S = ($636,195.93 ¨C 446,606.60)/(105,000 ¨C 100,000) ?NPV/?S = +$37.918

If sales were to drop by 100 units, then NPV would drop by: NPV drop = $37.918(100) = $3,791.80

You may wonder why we chose 105,000 units. Because it doesn¡¯t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same. To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $24. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $24 is: OCFnew = [($38 ¨C 24)(100,000) ¨C 900,000](0.65) + 0.35($112,000) OCFnew = $364,200

So, the change in OCF for a $1 change in variable costs is: ?OCF/?v = ($299,200 ¨C 364,200)/($25 ¨C 24) ?OCF/?v = ¨C$65,000

If variable costs decrease by $5 then, OCF would increase by OCF increase = $65,000*5 = $325,000

2.

We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. For the best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get: OCFbest = {[($38)(1.1) ¨C ($25)(0.9)](100K)(1.1) ¨C $900K(0.9)}(0.65) + 0.35($112K) OCFbest = $892,650 The best-case NPV is:

NPVbest = ¨C$896,000 + $892,650(PVIFA15%,8) NPVbest = $3,109,607.54

For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get: OCFworst = {[($38)(0.9) ¨C ($25)(1.1)](100K)(0.9) ¨C $900K(1.1)}(0.65) + 0.35($112K) OCFworst = ¨C212,350