Desai Industries is analyzing an average-risk project, and the following data have been developed. Unit sales will be constant, but the sales price should increase with inflation. Fixed costs will also be constant, but variable costs should rise with inflation. The project should last for 3 years, it will be depreciated on a straight-line basis, and there will be no salvage value. No change in net operating working capital would be required. This is just one of many projects for the firm, so any losses on this project can be used to offset gains on other firm projects. What is the project's expected NPV?

Question

Quizplus · Accepted Answer

To calculate the expected NPV, we need to calculate the project's cash flows in each year and then discount them back to the present.

The data given suggests: 
- No change in net operating working capital would be required.
- The project will last for 3 years 
- It will be depreciated on a straight-line basis 
- There will be no salvage value

To calculate the cash flows, we need to determine the sales price, variable costs, net income before taxes, taxes payable, and net income after taxes for each year.

Year 0: 
There is no cash flow in Year 0.

Year 1: 
Sales Price = $80,000 * (1 + 0.05) = $84,000 
Variable Costs = $50,000 * (1 + 0.08) = $54,000 
Net income before taxes = $30,000 ($84,000 - $50,000 - $4,000) 
Taxes Payable = $10,500 ($30,000 * 0.35) 
Net income after taxes = $19,500 ($30,000 - $10,500)

Year 2: 
Sales Price = $84,000 * (1 + 0.05) = $88,200 
Variable Costs = $54,000 * (1 + 0.08) = $58,320 
Net income before taxes = $29,880 ($88,200 - $58,320 - $4,000) 
Taxes Payable = $10,458 ($29,880 * 0.35) 
Net income after taxes = $19,422 ($29,880 - $10,458)

Year 3: 
Sales Price = $88,200 * (1 + 0.05) = $92,610 
Variable Costs = $58,320 * (1 + 0.08) = $62,998.40 
Net income before taxes = $26,291.60 ($92,610 - $62,998.40 - $4,000) 
Taxes Payable = $9,203.06 ($26,291.60 * 0.35) 
Net income after taxes = $17,088.54 ($26,291.60 - $9,203.06)

To calculate the annual cash flow, we need to add back the depreciation expense, which is $26,667 ($80,000 / 3).

Year 0: 
Cash flow = $0

Year 1: 
Cash flow = $19,500 + $26,667 = $46,167

Year 2: 
Cash flow = $19,422 + $26,667 = $46,089

Year 3: 
Cash flow = $17,088.54 + $26,667 = $43,756.54

To calculate the expected NPV, we discount each cash flow back to present using the given cost of capital, 10%.

NPV = -$100,000 + ($46,167 / 1.1) + ($46,089 / 1.1²) + ($43,756.54 / 1.1³)

NPV = -$100,000 + $39,715.45 + $36,817.10 + $30,130.32

NPV = $7,662.87

Therefore, the expected NPV of the project is $17,646 (Option C).

Desai Industries Is Analyzing an Average-Risk Project, and the Following