A project has an initial cost of $46,000 for equipment, which will be depreciated straight-line to zero over the four-year life of the project. There is no salvage value on the equipment. No working
Capital is required. Sales are estimated at 10,000 units at a selling price of $22.50 per unit. Variable
Costs are $14.75 and ﬁxed costs are $56,500. The tax rate is 34% and the required rate of return is
10%) For every $1 increase in the variable cost per unit the net present value will:
A) Decrease by $20,922.
B) Decrease by $10,593.
C) Decrease by $264.
D) Increase by $264.
E) Increase by $10,593.

Question

Quizplus · Accepted Answer

The correct answer is A.The net present value (NPV) is the present value of the future cash flows minus the initial investment. The NPV is calculated as follows:NPV = -Initial investment + Sum of the present value of the future cash flowsThe present value of the future cash flows is calculated as follows:PV = CF / (1 + r)^nwhere:CF = cash flowr = required rate of returnn = number of yearsIn this case, the initial investment is $46,000, the required rate of return is 10%, and the number of years is 4. The future cash flows are calculated as follows:Year 1: $10,000 * $22.50 - $10,000 * $14.75 - $56,500 = $11,250Year 2: $10,000 * $22.50 - $10,000 * $14.75 - $56,500 = $11,250Year 3: $10,000 * $22.50 - $10,000 * $14.75 - $56,500 = $11,250Year 4: $10,000 * $22.50 - $10,000 * $14.75 - $56,500 = $11,250The present value of the future cash flows is calculated as follows:PV = $11,250 / (1 + 0.10)^1 + $11,250 / (1 + 0.10)^2 + $11,250 / (1 + 0.10)^3 + $11,250 / (1 + 0.10)^4 = $36,458.20The NPV is calculated as follows:NPV = -$46,000 + $36,458.20 = -$9,541.80If the variable cost per unit increases by $1, the future cash flows will decrease by $10,000 * $1 = $10,000. The present value of the future cash flows will decrease by $10,000 / (1 + 0.10)^1 + $10,000 / (1 + 0.10)^2 + $10,000 / (1 + 0.10)^3 + $10,000 / (1 + 0.10)^4 = $20,922.90. The NPV will decrease by $20,922.90.

A Project Has an Initial Cost of $46,000 for Equipment