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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
$725 45,000 = $32,625,000
Exp. clubs
$1,200 (–11,000) = –13,200,000
Cheap clubs
$390 10,000 = 3,900,000
$23,325,000
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
New clubs
–$315 45,000 = –$14,175,000
Exp. clubs
–$640 (–11,000) = 7,040,000
Cheap clubs
–$175 10,000 = –1,750,000
–$8,885,000
The pro forma income statement will be:
Sales
$23,325,000
Variable costs
8,885,000
Costs
5,900,000
Depreciation
1,850,000
EBT
6,690,000
Taxes
2,676,000
Net income
$ 4,014,000
Using the bottom up OCF calculation, we get:
IRR = 35.27%
15. The best-case and worst-case for the variables are:
Base Case Best Case Worst Case
Unit sales (new) 45,000 49,500 40,500
Price (new) $725 $798 $653
VC (new) $315 $284 $347
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
$798 49,500 = $39,476,250
Exp. clubs
$1,200 (–9,900) = – 11,880,000
Cheap clubs
$390 11,000 = 4,290,000
$31,886,250
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
New clubs
–$284 49,500 = –$14,033,250
Exp. clubs
–$640 (–9,900) = 6,336,000
Cheap clubs
–$175 11,000 = – 1,925,000
–$9,622,250
The pro forma income statement will be:
Sales
$31,886,250
Variable costs
9,622,250
Costs
5,310,000
Depreciation
1,850,000
EBT
$15,104,000
Taxes
6,041,600
Net income
$9,062,400
Using the bottom up OCF calculation, we get:
NPV = –$12,950,000 – 1,900,000 + $10,912,400(PVIFA14%,7) + 1,900,000/1.147
NPV = $32,705,008.64
Worst-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
$653 40,500 = $26,426,250
Exp. clubs
$1,200 (– 12,100) = – 14,520,000
Cheap clubs
$390 9,000 = 3,510,000
$15,416,250
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
New clubs
–$347 40,500 = –$14,033,250
Exp. clubs
–$640 (–12,100) = 7,744,000
Cheap clubs
–$175 9,000 = –1,575,000
–$7,864,250
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
To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we need to
will be the same no matter what quantity 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:
NPV/Q = $1,054.92
17. a. The base-case NPV is:
NPV = –$3,650,000 + $693,000(PVIFA11%,10)
NPV = $431,237.78
$1,550,000 = ($63)Q(PVIFA11%,9)
Q = $1,550,000/[$63(5.5370)]
Q = 4,443.37
Abandon the project if Q < 4,443, because the NPV of abandoning the project is greater than the
NPV of the future cash flows.
18. a. If the project is a success, the present value of the future cash flows will be:
one year, the expected value of the project in one year is the average of the success and failure
cash flows, plus the cash flow in one year, so:
Expected value of project at year 1 = [($5,930,177.91 + $1,550,000)/2] + $693,000
The NPV is the present value of the expected value in one year plus the cost of the equipment,
so:
NPV = –$3,650,000 + ($4,433,088.95)/1.11
value of the option to abandon today is:
Option value = (.50)($363,964.42)/1.11
19. If the project is a success, the present value of the future cash flows will be:
PV future CFs = $63(22,000)(PVIFA11%,9)
PV future CFs = $7,674,347.88
If the sales are only 3,400 units, from Problem 17, we know we will abandon the project, with a value
value of the project in one year is the average of the success and failure cash flows, plus the cash flow
in one year, so:
Expected value of project at year 1 = [($7,674,347.88 + $1,550,000)/2] + $693,000
find the value of the option to expand today, so:
Option value = (.50)($5,930,177.91)/1.11
Option value = $2,671,251.31
20. a. The accounting breakeven is the aftertax sum of the fixed costs and depreciation charge divided
QA = [(FC + Depreciation)(1 – tC)]/[(P – VC)(1 – tC)]
QA = [($0 + 8,300) (1 – .30)]/[($13 – 4.45)(1 – .30)]
QA = 970.76
b. When calculating the financial breakeven point, we express the initial investment as an equivalent
annual cost (EAC). The initial investment is the $20,000 in licensing fees. Dividing the initial
PVA = C({1 – [1/(1 + R)t]}/R)
$20,000 = C{[1 – (1/1.12)3 ]/.12}
C = $8,326.98
QF = [EAC + FC(1 – tC) – Depreciation(tC)]/[(P – VC)(1 – tC)]
QF = ($8,326.98 + 0 – 0)/[($13 – 4.45)(.70)]
QF = 1,391.31
21. The payoff from taking the lump sum is $50,000, so we need to compare this to the expected payoff
from taking one percent of the profit. The decision tree for the movie project is:
Big audience
30%
$105,000,000
Movie is
good
15%
Make
movie
Script is
good
Movie is
bad
Read
script
70%
Small
audience
Script is
bad
No profit
85%
Don't make
movie
No profit
good, and the audience is big, so the expected value of this outcome is:
Value = $105,000,000 × .30
The expected value that the movie is good, and has a big audience, assuming the script is good is:
Value = $31,500,000 × .15
Value = $4,725,000
The screenwriter should take the cash offered today.
