April 3, 2019

CHAPTER 11 B-211

19. a. The base-case, best-case, and worst-case values are shown below. Remember that in the best-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 190 $11,200 $410,000

Best 209 $10,080 $369,000

Worst 171 $12,320 $451,000

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

OCFbase = [($18,000 – 11,200)(190) – $410,000](0.65) + 0.35($1,700,000/4)

OCFbase = $722,050

NPVbase = –$1,700,000 + $722,050(PVIFA12%,4)

NPVbase = $493,118.10

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 $420,000. The OCF using this level of fixed costs and the other

base case values with the tax shield approach, we get:

OCF = [($18,000 – 11,200)(190) – $410,000](0.65) + 0.35($1,700,000/4)

OCF = $715,550

And the NPV is:

B-212 SOLUTIONS

c. The cash breakeven is:

Q

C = FC/(P – v)

Q

d. The accounting breakeven is:

Q

A = (FC + D)/(P – v)

Q

20. 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 $750 51,000 = $38,250,000

Exp. clubs $1,200 (–11,000) = –13,200,000

Cheap clubs $420 9,500 = 3,990,000

$29,040,000

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 anymore, we will

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

Var. costs

New clubs –$330 51,000 = –$16,830,000

Exp. clubs –$650 (–11,000) = 7,150,000

Cheap clubs –$190 9,500 = –1,805,000

–$11,485,000

The pro forma income statement will be:

Sales $29,040,000

Variable costs 11,485,000

Costs 8,100,000

21. The best case and worst cases for the variables are:

Base Case Best Case Worst Case

Unit sales (new) 51,000 56,100 45,900

Price (new) $750 $825 $675

VC (new) $330 $297 $363

Fixed costs $8,100,000 $7,290,000 $8,910,000

Sales lost (expensive) 11,000 9,900 12,100

Sales gained (cheap) 9,500 10,450 8,550

Best-case

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 $750 56,100 = $46,282,500

Exp. clubs $1,200 (–9,900) = – 11,880,000

Cheap clubs $420 10,450 = 4,389,000

$38,791,500

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 anymore, we will

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

Var. costs

New clubs –$297 56,100 = –$16,661,700

Exp. clubs –$650 (–9,900) = 6,435,000

Cheap clubs –$190 10,450 = – 1,985,500

–$12,212,200

B-214 SOLUTIONS

The pro forma income statement will be:

Sales $38,791,500

Variable costs 12,212,200

Costs 7,290,000

Depreciation 3,200,000

EBT 16,089,300

Taxes 6,435,720

Net income $9,653,580

Using the bottom up OCF calculation, we get:

OCF = Net income + Depreciation = $9,653,580 + 3,200,000

OCF = $12,853,580

And the best-case NPV is:

NPV = –$22,400,000 – 1,250,000 + $12,853,580(PVIFA10%,7) + 1,250,000/1.107

NPV = $39,568,058.39

Worst-case

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

22. To calculate the sensitivity of the NPV to changes in the price of the new club, we simply need to

change the price of the new club. We will choose $800, but the choice is irrelevant as the sensitivity will

be the same no matter what price we choose.

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 $800 51,000 = $40,800,000

Exp. clubs $1,200 (–11,000) = –13,200,000

Cheap clubs $420 9,500 = 3,990,000

$31,590,000

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 anymore, we will

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

Var. costs

New clubs –$330 51,000 = –$16,830,000

Exp. clubs –$650 (–11,000) = 7,150,000

Cheap clubs –$190 9,500 = –1,805,000

–$11,485,000

The pro forma income statement will be:

Sales $31,590,000

Variable costs 11,485,000

Costs 8,100,000

Depreciation 3,200,000

EBT 8,805,000

Taxes 3,522,000

Net income $ 5,283,000

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = $5,283,000 + 3,200,000

OCF = $8,483,000

B-216 SOLUTIONS

And the NPV is:

NPV = –$22,400,000 – 1,250,000 + $8,483,000(PVIFA10%,7) + 1,250,000/1.107

NPV = $18,290,244.48

So, the sensitivity of the NPV to changes in the price of the new club is:

NPV/P = ($10,841,563.69 – 18,290,244.48)/($750 – 800)

NPV/P = $148,973.62

For every dollar increase (decrease) in the price of the clubs, the NPV increases (decreases) by

$148,973.62.

To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we simply need

23. a. First we need to determine the total additional cost of the hybrid. The hybrid costs more to

purchase and more each year, so the total additional cost is:

Total additional cost = $5,450 + 6($400)

Total additional cost = $7,850

Next, we need to determine the cost per mile for each vehicle. The cost per mile is the cost per

gallon of gasoline divided by the miles per gallon, or:

Cost per mile for traditional = $3.60/23

Cost per mile for traditional = $0.156522

Cost per mile for hybrid = $3.60/25