Question
A project requires an initial investment of $10,000, straight-line depreciable to zero over four years. The...
A project requires an initial investment of $10,000, straight-line depreciable to zero over four years. The discount rate is 10%. Your tax bracket is 34% and you receive a tax credit for negative earnings in the year in which the loss occurs. Additional information for variables with forecast error are shown below.
| Base Case | Lower Bound | Upper Bound | |
| Unit Sales | 3,000 | 2,750 | 3,250 |
| Price/unit | $14 | $13 | $16 |
| Variable cost/unit | $9 | $8 | $10 |
| Fixed costs | $9,000 | $8,500 | $10,000 |
Suppose you are interested in the project's sensitivity to unit price. What is the NPV at a price of $13 per unit?
A. -$10,967
B. -$1,029
C. $105
D. $1,868
E. $2,056
The answer is B, please show all the steps, thanks
Answers
NPV = PV of After tax OCF + PV of Annual depreciation tax shield –Initial cost
OCF = Qty(S.P-V.C)-F.C
3000*(13-9)-9000 = $3000
After tax OCF = 3000*(1-0.66) = $1980
PV of After tax OCF = $1980 * PVAF, 10%,4 = $1980*3.1698 = $6,276.204
Annual depreciation tax shield = Depreciation*tax
10000/4 * 0.34 = $850
PV of Annual depreciation tax shield = $850*3.1698 = $2694.33
NPV = $6,276.204+$2694.33-$10000 = -$1029
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