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 sum of the present values of all future cash flows. The present value of a cash flow is the amount of money that would need to be invested today to generate that cash flow in the future, given a certain rate of return.In this case, the NPV is calculated as follows:```NPV = -Initial cost + Sum of present values of future cash flows```The initial cost is $46,000. The future cash flows are the sales revenue minus the variable costs and fixed costs. The sales revenue is 10,000 units * $22.50 per unit = $225,000. The variable costs are 10,000 units * $14.75 per unit = $147,500. The fixed costs are $56,500. Therefore, the future cash flows are $225,000 - $147,500 - $56,500 = $21,000.The present value of a future cash flow is calculated as follows:```Present value = Future cash flow / (1 + r)^n```where r is the required rate of return and n is the number of years in the future.In this case, the required rate of return is 10% and the number of years in the future is 4. Therefore, the present value of the future cash flows is $21,000 / (1 + 0.10)^4 = $15,372.Therefore, the NPV is $46,000 - $15,372 = $30,628.If the variable cost per unit increases by $1, the future cash flows will decrease by $10,000. The present value of the future cash flows will decrease by $10,000 / (1 + 0.10)^4 = $7,353. Therefore, the NPV will decrease by $7,353.

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