We are evaluating a project that costs $1,666,000, has a seven-year life, and ha
ID: 2725643 • Letter: W
Question
We are evaluating a project that costs $1,666,000, has a seven-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 88,300 units per year. Price per unit is $34.90, variable cost per unit is $21.15, and fixed costs are $763,000 per year. The tax rate is 30 percent, and we require a return of 12 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.
We are evaluating a project that costs $1,666,000, has a seven-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 88,300 units per year. Price per unit is $34.90, variable cost per unit is $21.15, and fixed costs are $763,000 per year. The tax rate is 30 percent, and we require a return of 12 percent on this project.
Explanation / Answer
For the best case scenario, the price and quantity increase by 10%. The variable costs and fixed costs both decrease by 10%.
For the worst case scenario, the price and quantity decrease by 10%. The variable costs and fixed costs both increase by 10%.
Annual depreciation = Cost of project / Useful life = $1,666,000/7 = $238,000
Present value of annuity factor = {1-(1+r)-n}/r
Present value of annuity factor at 12% for 7 years (PVIFA) = (1-1.12-7)/0.12 = 4.5638
Base
Best case
Worst case
Sales quantity
88,300
88,300 * 1.10
97,130
88,300*0.9
79,470
Selling price
$ 34.90
$34.90*1.10
$ 38.39
$34.90*0.90
$ 31.41
Variable cost
$ 21.15
$21.15*0.90
$ 19.04
$21.15*1.10
$ 23.27
Contribution margin per unit
$ 13.75
$ 19.36
$ 8.15
Contribution margin
$ 1,214,125.00
$ 1,879,951.15
$ 647,283.15
Fixed costs
$ 763,000.00
$763,000*0.9
$ 686,700.00
$763,000*1.10
$ 839,300.00
Depreciation
$ 238,000.00
$ 238,000.00
$ 238,000.00
Income before taxes
$ 213,125.00
$ 955,251.15
-$ 430,016.85
Taxes
$ 63,937.50
$ 286,575.35
-$ 129,005.06
Net income
$ 149,187.50
$ 668,675.81
-$ 301,011.80
Depreciation added back
$ 238,000.00
$ 238,000.00
$ 238,000.00
Free cash flows
$ 387,187.50
$ 906,675.81
-$ 63,011.80
PVIFA
4.5638
4.5638
4.5638
Present value of free cash flows
$ 1,767,046.31
$ 4,137,887.04
-$ 287,573.23
Less: Cost 0f project
-$ 1,666,000.00
-$ 1,666,000.00
-$ 1,666,000.00
Net present value
$ 101,046.31
$ 2,471,887.04
-$ 1,953,573.23
Base
Best case
Worst case
Sales quantity
88,300
88,300 * 1.10
97,130
88,300*0.9
79,470
Selling price
$ 34.90
$34.90*1.10
$ 38.39
$34.90*0.90
$ 31.41
Variable cost
$ 21.15
$21.15*0.90
$ 19.04
$21.15*1.10
$ 23.27
Contribution margin per unit
$ 13.75
$ 19.36
$ 8.15
Contribution margin
$ 1,214,125.00
$ 1,879,951.15
$ 647,283.15
Fixed costs
$ 763,000.00
$763,000*0.9
$ 686,700.00
$763,000*1.10
$ 839,300.00
Depreciation
$ 238,000.00
$ 238,000.00
$ 238,000.00
Income before taxes
$ 213,125.00
$ 955,251.15
-$ 430,016.85
Taxes
$ 63,937.50
$ 286,575.35
-$ 129,005.06
Net income
$ 149,187.50
$ 668,675.81
-$ 301,011.80
Depreciation added back
$ 238,000.00
$ 238,000.00
$ 238,000.00
Free cash flows
$ 387,187.50
$ 906,675.81
-$ 63,011.80
PVIFA
4.5638
4.5638
4.5638
Present value of free cash flows
$ 1,767,046.31
$ 4,137,887.04
-$ 287,573.23
Less: Cost 0f project
-$ 1,666,000.00
-$ 1,666,000.00
-$ 1,666,000.00
Net present value
$ 101,046.31
$ 2,471,887.04
-$ 1,953,573.23
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