978-1259289903 Chapter 9 Solution Manual Part 1

CHAPTER 9

RISK ANALYSIS, REAL OPTIONS, AND

CAPITAL BUDGETING

Answers to Concept Questions

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

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

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

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

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

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

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.

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

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

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

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 = $780,000/8

Depreciation = $97,500 per year

b. We will use the tax shield approach to calculate the OCF. The OCF is:

OCFbase = [(P – v)Q – FC](1 – tc) + tcD

OCFbase = [($37 – 23)(92,000) – $875,000](.65) + .35($97,500)

Now we can calculate the NPV using our base-case projections. There is no salvage value or

NWC, so the NPV is:

NPVbase = –$780,000 + $302,575(PVIFA15%,8)

NPVbase = $577,751.31

NPVnew = –$780,000 + $375,375(PVIFA15%,8)

NPVnew = $904,428.31

NPV/S = +$40.83

NPV change = $40.83(–500)

NPV change = –$20,417.31

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 = [($43 – 24)(92,000) – 875,000](.65) + .35($97,500)

OCFnew = $242,775

OCF/v = ($302,575 – 242,775)/($23 – 24)

OCF/v = –$59,800

numbers by 1.10, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so

we will multiply the base case numbers by .90, a 10 percent decrease. Doing so, we get:

OCFbest = {[($37)(1.10) – ($23)(.90)](93,000)(1.10) – $875,000(.90)}(.65) + .35($97,500)

OCFbest = $837,850

NPVbest = –$780,000 + $837,850(PVIFA15%,8)

NPVbest = $2,979,702.33

NPVworst = –$780,000 – $160,940(PVIFA15%,8)

NPVworst = –$1,502,189.52

QA = (FC + D)/(P – v)

annual cost (EAC). Dividing the initial investment by the five-year annuity factor, discounted at 10

percent, the EAC of the initial investment is:

EAC = Initial Investment/PVIFA10%,5

EAC = $483,000/PVIFA10%,5

EAC = $127,414.18

PVA = C({1 – [1/(1 + R)]t }/R)

$483,000 = C{[1 – (1/1.10)5 ]/.10}

C = $127,414.18

Annual depreciation = $483,000/5

Annual depreciation = $96,600

QF = [EAC + FC(1 – tC) – Depreciation(tC)]/[(P – VC)(1 – tC)]

QF = [$127,414.18 + $365,000(1 – .35) – $96,600(.35)]/[($34 – 9)(1 – .35)]

QF = 20,360.26 or about 20,360 units

NPV0 = –$2,300,000 + $435,000(PVIFA12%,10)

NPV0 = $157,847.02

We should not purchase the machine today since the NPV is negative, but the NPV could be positive

Year 1: NPV1 = [–$2,130,000 + $435,000(PVIFA12%,9)]/1.12

NPV1 = $167,668.45

6. We need to calculate the NPV of the two options, go directly to market now, or utilize test marketing

NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure)

NPV = $29,000,000(.50) + $8,500,000(.50)

NPV = $19,775,000

outlay. Choosing the test marketing option will also delay the launch of the product by one year. Thus,

the expected payoff is delayed by one year and must be discounted back to Year 0.

NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]}/(1 + R)t

7. We need to calculate the NPV of each option, and choose the option with the highest NPV. So, the

NPV = CSuccess (Prob. of Success)

NPV = $1,550,000(.40)

NPV = C0 + CSuccess (Prob. of Success)

NPV = –$75,000 + $1,550,000(.60)

NPV = C0 + CSuccess (Prob. of Success)

NPV = –$345,000 + $1,550,000(.85)

NPV = $972,500

NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure)

NPV = $26,000,000(.60) + $4,200,000(.40)

must be discounted back to Year 0. So, the NPV of the customer segment research is:

NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]}/(1 + R)t

NPV = –$550,000 + {[$26,000,000(.75)] + [$4,200,000(.25)]}/1.12

QA = [($625,000 + $58,000)(1 – .35)]/[($47.50 – 13.14) (1 – .35)]

QA = 19,877.76

Research

Success

$26 million at t = 1

at 13 percent, the EAC of the initial investment is:

value of the annuity. In other words:

PVA = C({1 – [1/(1 + R)]t}/R)

$406,000 = C{[1 – (1/1.13)7 ]/.13}

C = $91,800.99

is:

QF = [EAC + FC(1 – tC) – Depreciation(tC)]/[(P – VC)(1 – tC)]

QF = [$91,800.99 + $625,000(.65) – $58,000(.35)]/[($47.50 – 13.14)(.65)]

QF = 21,391.20

percent, the EAC of the initial investment is:

EAC = Initial Investment/PVIFA12%,6

EAC = $609,000/PVIFA12%,6

EAC = $148,124.46

PVA = C({1 – [1/(1 + R)]t }/R)

$609,000 = C{[1 – (1/1.12)6 ]/.12}

C = $148,124.46

Annual depreciation = $609,000/6

Annual depreciation = $101,500

QF = [$148,124.46 + $360,000(1 – .34) – $101,500(.34)]/[($51 – 18)(1 – .34)]

QF = 16,125.55

11. a. At the accounting breakeven, the IRR is zero percent since the project recovers the initial

investment. The payback period is N years, the length of the project since the initial investment

is exactly recovered over the project life. The NPV at the accounting breakeven is:

b. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and the

c. The definition of the financial breakeven is where the NPV of the project is zero. If this is true,

period, except to say that the payback period must be less than the length of the project. Since

the discounted cash flows are equal to the initial investment, the undiscounted cash flows are

greater than the initial investment, so the payback must be less than the project life.

OCF = [(P – v)Q – FC](1 – tC) + tC(D)

OCF = [($27 – 19)(76,000) – 345,000](.66) + .34($496,000/4)

OCF = $215,740

and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So,

the OCF at this level of sales is:

Sensitivity = OCF/Q = ($215,740 – 221,020)/(76,000 – 77,000)

OCF/Q = +$5.28

case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease,

and costs increase.

Scenario Unit sales Variable cost Fixed costs

Base 200 $12,600 $315,000

OCFbest = [($17,100 – 11,340)(220) – $283,500](.65) + .35($790,000/4)

OCFbest = $708,530

NPV = –$790,000 + $442,875(PVIFA15%,4)

NPV = $474,398.54

NPV/FC = ($492,955.90 – 474,398.54)/($315,000 – 325,000)

NPV/FC = –$1.86

QA = (FC + D)/(P – v)

QA = [$315,000 + ($790,000/4)]/($17,100 – 12,600)