We are evaluating a project that costs $1,080,000, has a ten-year life, and has
ID: 2794167 • Letter: W
Question
We are evaluating a project that costs $1,080,000, has a ten-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 52,000 units per year. Price per unit is $50, variable cost per unit is $30, and fixed costs are $730,000 per year. The tax rate is 35 percent, and we require a return of 15 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.
Calculate the best-case and worst-case NPV figures. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.)
Explanation / Answer
The cost of the project is 1,080,000 thus initial outlay = -1080000
the project has no salvage value and will be depreciated over 10 years using SLM
thus depreciation = 1080000/10 = 108000
And as there is no salvage value and no WCinv,
Terminal value = Salvage + WCinv - tax*(savlvage - bookvalue) = 0 (as all variables are 0)
Assuming base case:
Quantity = 52000
Sales = 50*52000 = 2600,000
Variable cost = 30*52000 = 1560,000
Fixed cost = 730,000
Affter tax operating cashflow = (sales-cost-depreciation)*(1-tax) + Depreciation
=(2600,000-1560,000-730000-108000)*(1-0.35)+108000
=239300
Assuming best case: +10%
Quantity = 52000*(1.1) = 57200
Sales = 50*(1.1) * 57200 = 3146,000
Variable cost = 30*(1.1) * 57200 = 1887600
Fixed cost = 730,000*(1.1) = 803,000
Affter tax operating cashflow = (sales-cost-depreciation)*(1-tax) + Depreciation
=(3146000-1887600-803000-108000)*(1-0.35)+108000
=333,810
Assuming worst case: -10%
Quantity = 52000*(0.9) = 46800
Sales = 50*(0.9) * 46800 = 2106,000
Variable cost = 30*(0.9) * 46800 = 1263600
Fixed cost = 730,000*(0.9) = 657,000
Affter tax operating cashflow = (sales-cost-depreciation)*(1-tax) + Depreciation
=(2106000-1263600-657000-108000)*(1-0.35)+108000
=158310
Lets calculate NPV at 15% required return as discount rate:
Year
Worst case cashflows - 10%
Base case cashlows
Best case cashflows +10%
0
-1080000
-1080000
-1080000
1
158310
239300
333810
2
158310
239300
333810
3
158310
239300
333810
4
158310
239300
333810
5
158310
239300
333810
6
158310
239300
333810
7
158310
239300
333810
8
158310
239300
333810
9
158310
239300
333810
10
158310
239300
333810
NPV at 15%
-$248,242.38
$105,209.85
$517,665.35
Thus the best case NPV is $517665.35
Worst case NPV is -248,242.38
Year
Worst case cashflows - 10%
Base case cashlows
Best case cashflows +10%
0
-1080000
-1080000
-1080000
1
158310
239300
333810
2
158310
239300
333810
3
158310
239300
333810
4
158310
239300
333810
5
158310
239300
333810
6
158310
239300
333810
7
158310
239300
333810
8
158310
239300
333810
9
158310
239300
333810
10
158310
239300
333810
NPV at 15%
-$248,242.38
$105,209.85
$517,665.35
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