BASIC INFORMATION: A three-year project will cost $60,000 to construct. This will be depreciated straight-line to zero over the three-year life. The price per unit sold is $20 and the variable cost per unit sold is $10. Fixed costs are $30,000 per year.

In addition to the BASIC INFORMATION, you expect the number of units sold to be 7,000 with an upper bound of 8,000 and a lower bound of 6,000, and you expect the variable cost per unit to be $10 per unit with an upper bound of $12.50 and a lower bound of $7.50. Assuming a tax rate of 30%, compute the IRR for the BEST case. Note that salvage is $0, and NWC is $0.
A) 5%
B) 12%
C) 17%
D) 34%
E) 74%

Question

BASIC INFORMATION: A three-year project will cost $60,000 to construct. This will be depreciated straight-line to zero over the three-year life. The price per unit sold is $20 and the variable cost per unit sold is $10. Fixed costs are $30,000 per year.

In addition to the BASIC INFORMATION, you expect the number of units sold to be 7,000 with an upper bound of 8,000 and a lower bound of 6,000, and you expect the variable cost per unit to be $10 per unit with an upper bound of $12.50 and a lower bound of $7.50. Assuming a tax rate of 30%, compute the IRR for the BEST case. Note that salvage is $0, and NWC is $0.
A) 5%
B) 12%
C) 17%
D) 34%
E) 74%

Quizplus · Accepted Answer

In the best case scenario, the highest number of units sold would be 8,000 at the highest price per unit ($20) and the lowest variable cost per unit ($7.50). The fixed costs remain at $30,000, and the project cost of $60,000 is depreciated straight-line over three years, resulting in an annual depreciation of $20,000. The best case annual revenue is 8,000 units * $20/unit = $160,000. The total variable cost is 8,000 units * $7.50/unit = $60,000. Thus, the annual profit before fixed costs and depreciation is $160,000 - $60,000 = $100,000. After subtracting fixed costs ($30,000) and depreciation ($20,000), the profit before tax is $50,000. After a 30% tax, the net profit is $35,000 annually. The initial investment is $60,000, and with no salvage value or NWC changes, the cash flow is purely from operations. The IRR that equates the NPV to zero with these cash flows is exceptionally high, reflecting the significant return relative to the investment, which in this case is calculated or approximated to be 74%.

BASIC INFORMATION: a Three-Year Project Will Cost $60,000 to Construct