978-1259709685 Chapter 7 Solution Manual Part 1

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CHAPTER 7

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.

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

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

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 afterwards, this ordering will

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

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

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

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

increase, and the amount of timber will almost definitely increase, barring a natural catastrophe or

10. Option analysis should stop 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

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:

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

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

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

NWC, so the NPV is:

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 71,000 units. The OCF at this sales level is:

And the NPV is:

So, the change in NPV for every unit change in sales is:

If sales were to drop by 500 units, then NPV would drop by:

c. To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a

variable cost of $21. 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 $21 is:

So, the change in OCF for a $1 change in variable costs is:

If variable costs decrease by $1 then OCF would increase by $45,500

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:

The best-case NPV is:

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:

3. We can use the accounting breakeven equation:

QA = (FC + D) / (P – v)

to solve for the unknown variable in each case. Doing so, we find:

4. When calculating the financial breakeven point, we express the initial investment as an equivalent

annual cost (EAC). Dividing the initial investment by the five-year annuity factor, discounted at 12

percent, the EAC of the initial investment is:

EAC = Initial Investment / PVIFA12%,5

Note that this calculation solves for the annuity payment with the initial investment as the present

value of the annuity. In other words:

PVA = C({1 – [1/(1 + R)]t } / R)

The annual depreciation is the cost of the equipment divided by the economic life, or:

Now we can calculate the financial breakeven point. The financial breakeven point for this project is:

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

5. If we purchase the machine today, the NPV is the cost plus the present value of the increased cash

flows, so:

NPV0 = –$3,400,000 + $530,000(PVIFA9%,10)

NPV0 = $1,358.58

We should not necessarily purchase the machine today. We would want to purchase the machine when

the NPV is the highest. So, we need to calculate the NPV each year. The NPV each year will be the

Year 1: NPV1 = [–$3,150,000 + $530,000(PVIFA9%,9)] / 1.09

NPV1 = $25,211.79

The company should purchase the machine in Year 2 when the NPV is the highest.

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

marketing first. The NPV of going directly to market now is:

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

Now we can calculate the NPV of test marketing first. Test marketing requires a $1.3 million cash

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.

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

NPV of going directly to market is:

NPV = CSuccess (Prob. of Success)

The NPV of the focus group is:

NPV = C0 + CSuccess (Prob. of Success)

And the NPV of using the consulting firm is:

NPV = C0 + CSuccess (Prob. of Success)

8. The company should analyze both options, and choose the option with the greatest NPV. So, if the

company goes to market immediately, the NPV is:

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

Customer segment research requires a $950,000 cash outlay. Choosing the research 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. So, the NPV of the customer segment research is:

The company should go to market now since it has the largest NPV.

9. a. The accounting breakeven is the aftertax sum of the fixed costs and depreciation charge divided

by the aftertax contribution margin (selling price minus variable cost). So, the accounting

breakeven level of sales is:

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

b. When calculating the financial breakeven point, we express the initial investment as an

equivalent annual cost (EAC). Dividing the initial investment by the seven-year annuity factor,

discounted at 15 percent, the EAC of the initial investment is:

EAC = Initial Investment / PVIFA15%,7

Note that this calculation solves for the annuity payment with the initial investment as the

present value of the annuity. In other words:

Now we can calculate the financial breakeven point. The financial breakeven point for this

project is:

10. When calculating the financial breakeven point, we express the initial investment as an equivalent

annual cost (EAC). Dividing the initial investment by the five-year annuity factor, discounted at 8

percent, the EAC of the initial investment is:

EAC = Initial Investment / PVIFA8%,5

Note that this calculation solves for the annuity payment with the initial investment as the present

value of the annuity. In other words:

The annual depreciation is the cost of the equipment divided by the economic life, or:

Now we can calculate the financial breakeven point. The financial breakeven point for this project is:

Intermediate

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

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,

then the IRR of the project is equal to the required return. It is impossible to state the payback

12. Using the tax shield approach, the OCF at 90,000 units will be:

OCF = [(P – v)Q – FC](1 – tC) + tC(D)

We will calculate the OCF at 91,000 units. The choice of the second level of quantity sold is

arbitrary 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:

The sensitivity of the OCF to changes in the quantity sold is:

OCF will increase by $7.92 for every additional unit sold.

13. a. The base-case, best-case, and worst-case values are shown below. Remember that in the best-

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

increase.

Scenario Unit sales Variable cost Fixed costs

Using the tax shield approach, the OCF and NPV for the base case estimate are:

OCFbase = [($17,200 – 14,300)(420) – $640,000](.65) + .35($760,000 / 4)

The OCF and NPV for the worst case estimate are:

OCFworst = [($17,200 – 15,730)(378) – $704,000](.65) + .35($760,000 / 4)

OCFworst = –$29,921

b. To calculate the sensitivity of the NPV to changes in fixed costs, we choose another level of

fixed costs. We will use fixed costs of $650,000. The OCF using this level of fixed costs and

the other base case values with the tax shield approach is:

And the NPV is:

The sensitivity of NPV to changes in fixed costs is:

c. The accounting breakeven is:

QA = (FC + D) / (P – v)

14. The marketing study and the research and development are both sunk costs and should be ignored.

We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs

and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new

project will be:

Sales

New clubs $850  60,000 = $51,000,000

For the variable costs, we must include the units gained or lost from the existing clubs. Note that the

variable costs of the expensive clubs are an inflow. If we are not producing the sets any more, we

will save these variable costs, which is an inflow. So:

Var. costs

The pro forma income statement will be:

Sales $43,800,000

Variable costs 21,510,000

Fixed costs 9,300,000

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = $5,334,000 + 4,100,000

OCF = $9,434,000

So, the payback period is:

The NPV is: