A local day spa is considering investing in a machine that costs $60 000.The machine is expected to generate revenues of $25 000 per year for five years.The machine would be depreciated using the straight-line method over its five-year life and have no salvage value.The company considers the impact of income taxes in all of its capital investment decisions.The company has a 35 per cent income tax rate and desires an after-tax rate of return of 14 per cent on its investment.The net present value of the machine is:

Question

Quizplus · Accepted Answer

To calculate the net present value, we need to follow these steps:

1. Calculate the annual after-tax cash flows:
Annual Revenue = $25,000
Depreciation Expense = $60,000 / 5 = $12,000
Taxable Income = $25,000 - $12,000 = $13,000
Taxes = $13,000 x 35% = $4,550
After-Tax Cash Flow = $25,000 - $12,000 - $4,550 = $8,450

2. Determine the discount rate:
After-Tax Rate of Return = 14%
Add Back Taxes = 35% + 1 = 1.35
Discount Rate = 14% / 1.35 = 10.37%

3. Calculate the net present value:
Year 1: $8,450 / (1 + 10.37%)^1 = $7,646
Year 2: $8,450 / (1 + 10.37%)^2 = $6,935
Year 3: $8,450 / (1 + 10.37%)^3 = $6,313
Year 4: $8,450 / (1 + 10.37%)^4 = $5,772
Year 5: $8,450 / (1 + 10.37%)^5 = $5,306
Net Present Value = $7,646 + $6,935 + $6,313 + $5,772 + $5,306 - $60,000 = -$28,028

The net present value is negative, indicating that the investment would not be profitable. Therefore, the best choice is not to invest in the machine. The correct answer is B, which represents the net present value of the investment.

A Local Day Spa Is Considering Investing in a Machine