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. This is just one of many projects for the firm, so any losses can be used to offset gains on other firm projects. What is the project's expected NPV?
A) $15,925
B) $16,764
C) $17,646
D) $18,528
E) $19,455

Question

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. This is just one of many projects for the firm, so any losses can be used to offset gains on other firm projects. What is the project's expected NPV? 
A) $15,925 
B) $16,764 
C) $17,646 
D) $18,528 
E) $19,455

Quizplus · Accepted Answer

To calculate the expected NPV, we need to first calculate the expected cash flows for each year. We start by calculating the expected sales revenue for each year, which is equal to unit sales multiplied by the sales price adjusted for inflation. The sales price for year 1 is $10 x (1+3%) = $10.30, for year 2 it is $10.30 x (1+4%) = $10.72, and for year 3 it is $10.72 x (1+5%) = $11.26. Therefore, the expected sales revenue for each year is:

Year 1: 10,000 x $10.30 = $103,000
Year 2: 10,000 x $10.72 = $107,200
Year 3: 10,000 x $11.26 = $112,600

Next, we need to calculate the expected variable costs for each year, which are equal to unit variable cost multiplied by the variable cost adjusted for inflation. The variable cost for year 1 is $5 x (1+6%) = $5.30, for year 2 it is $5.30 x (1+7%) = $5.69, and for year 3 it is $5.69 x (1+8%) = $6.14. Therefore, the expected variable cost for each year is:

Year 1: 10,000 x $5.30 = $53,000
Year 2: 10,000 x $5.69 = $56,900
Year 3: 10,000 x $6.14 = $61,400

Finally, we can calculate the expected operating cash flow for each year by subtracting the expected fixed costs and variable costs from the expected sales revenue. The fixed cost for each year is $35,000. Therefore, the expected operating cash flow for each year is:

Year 1: $103,000 - $35,000 - $53,000 = $15,000
Year 2: $107,200 - $35,000 - $56,900 = $15,300
Year 3: $112,600 - $35,000 - $61,400 = $16,200

We can now calculate the expected NPV using the following formula:

Expected NPV = (Expected CF1 / (1 + r)^1) + (Expected CF2 / (1 + r)^2) + (Expected CF3 / (1 + r)^3) - Initial Investment

The initial investment is $100,000 and the discount rate is 10%. Plugging in the expected cash flows, we get:

Expected NPV = ($15,000 / 1.1^1) + ($15,300 / 1.1^2) + ($16,200 / 1.1^3) - $100,000 = $17,645.69

Therefore, the expected NPV is $17,646, which is closest to choice C.

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