Question

Le Pew cosmetics is evaluating a new fragrance mixing machine. The machine requires an initial investment of $360,000 and will generate after tax cash flows of $62,650 per year for 8 years. For each of the capital listed, 1) calculate net present value (NPV) 2) indicate whether to accept or reject the machine and why.

a)cost of capital is 6%

b)cost of capital is 8%

c)cost of capital is 10%

Answer 1

Answer a.

Initial Investment = $360,000
Annual After-tax Cash Flow = $62,650
Life of Project = 8 years
Cost of Capital = 6%

Net Present Value = -$360,000 + $62,650 * PVA of $1 (6%, 8)
Net Present Value = -$360,000 + $62,650 * (1 - (1/1.06)^8) / 0.06
Net Present Value = -$360,000 + $62,650 * 6.209794
Net Present Value = $29,043.59

NPV of the project is positive. Therefore, the company should accept the machine.

Answer b.

Initial Investment = $360,000
Annual After-tax Cash Flow = $62,650
Life of Project = 8 years
Cost of Capital = 8%

Net Present Value = -$360,000 + $62,650 * PVA of $1 (8%, 8)
Net Present Value = -$360,000 + $62,650 * (1 - (1/1.08)^8) / 0.08
Net Present Value = -$360,000 + $62,650 * 5.746639
Net Present Value = $26.93

NPV of the project is positive. Therefore, the company should accept the machine.

Answer c.

Initial Investment = $360,000
Annual After-tax Cash Flow = $62,650
Life of Project = 8 years
Cost of Capital = 10%

Net Present Value = -$360,000 + $62,650 * PVA of $1 (10%, 8)
Net Present Value = -$360,000 + $62,650 * (1 - (1/1.10)^8) / 0.10
Net Present Value = -$360,000 + $62,650 * 5.334926
Net Present Value = -$25,766.89

NPV of the project is negative. Therefore, the company should reject the machine.