Question

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

Answer 1

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