We are evaluating a project that costs $1,100,000, has a ten-year life, and has
ID: 2711542 • Letter: W
Question
We are evaluating a project that costs $1,100,000, 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 42,000 units per year. Price per unit is $50, variable cost per unit is $25, and fixed costs are $820,000 per year. The tax rate is 35 percent, and we require a return of 10 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 $1,100,000, 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 42,000 units per year. Price per unit is $50, variable cost per unit is $25, and fixed costs are $820,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.
Explanation / Answer
Annual depreciation = (cost of asset – salvage value)/ Life
= (1,100,000 – 0)/10
= 110,000
Depreciation tax shield = Annual depreciation x tax rate
= 110,000x 35%
= 38,500
Base Case
Best Case
Worst case
Sales
42000
46200
37800
Price
50
55
45
Variable cost
25
22.5
27.5
Fixed cost
820000
738000
902000
Base Case
Best Case
Worst case
Sales revenue
2100000
2541000
1701000
Total variable cost
-1050000
-1039500
-1039500
Fixed cost
-820000
-738000
-902000
EBIT
230000
763500
-240500
Taxes 35%
-80500
-267225
84175
Net Income
149500
496275
-156325
Depreciation tax shield
38500
38500
38500
Operating cash flow
188000
534775
-117825
PV of annuity factor 10%
6.1446
6.1446
6.1446
PV= PV factor x OCF
$1,155,178.62
$3,285,960.87
-$723,983.62
NPV = PV of OCF – initial cash outflow
NPV best case = $1,155,178.62-1,100,000
= $55,178.62
Worst case NPV= -$723,983.62- 1,100,000
= -$1,823,983.62
Base Case
Best Case
Worst case
Sales
42000
46200
37800
Price
50
55
45
Variable cost
25
22.5
27.5
Fixed cost
820000
738000
902000
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