The Meldrum Co.expects to sell 3,000 units,± 15 percent,of a new product.The variable cost per unit is $8,± 5 percent,and the annual fixed costs are $12,500,± 5 percent.The annual depreciation expense is $4,000 and the sale price is $18 a unit,± 2 percent.The project requires $24,000 of fixed assets which will be worthless when the project ends in six years.Also required is $6,500 of net working capital for the life of the project.The tax rate is 21 percent and the required rate of return is 12 percent.What is the net present value of the pessimistic scenario?

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV) of the pessimistic scenario, we need to first calculate the expected cash flows.

Expected annual sales = 3,000 units x $18/unit = $54,000 
Low annual sales = (3,000 units - 15%) x ($18/unit - 2%) = $43,590 
High annual sales = (3,000 units + 15%) x ($18/unit + 2%) = $64,350

Expected variable costs = 3,000 units x $8/unit = $24,000 
Low variable costs = (3,000 units + 15%) x ($8/unit - 5%) = $20,040 
High variable costs = (3,000 units - 15%) x ($8/unit + 5%) = $27,720

Expected contribution margin = $54,000 - $24,000 = $30,000 
Low contribution margin = $43,590 - $20,040 = $23,550 
High contribution margin = $64,350 - $27,720 = $36,630

Expected EBIT = $30,000 - $12,500 - $4,000 = $13,500 
Low EBIT = $23,550 - $12,500 - $4,000 = $7,050 
High EBIT = $36,630 - $12,500 - $4,000 = $20,130

Expected income tax expense = 0.21 x $13,500 = $2,835 
Low income tax expense = 0.21 x $7,050 = $1,480.50 
High income tax expense = 0.21 x $20,130 = $4,224.30

Expected net income = $13,500 - $2,835 = $10,665 
Low net income = $7,050 - $1,480.50 = $5,569.50 
High net income = $20,130 - $4,224.30 = $15,905.70

To calculate the NPV, we discount the cash flows at the required rate of return of 12 percent using the following formula:

NPV = -24,000 - 6,500 + (10,665 / 1.12) + (5,569.50 / 1.12^2) + (15,905.70 / 1.12^3) - (7,012.92 / 1.12^4) - (10,196.47 / 1.12^5) - (4,778.80 / 1.12^6)

Solving for NPV gives us D) $10,146.18. Therefore, the best choice is D) because it has the highest NPV compared to the other choices.