Question

You are considering a new product launch. The project will cost $2,125,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 240 units per year; price per unit will be $18,900, variable cost per unit will be $12,650, and fixed costs will be $630,000 per year. The required return on the project is 9 percent, and the relevant tax rate is 22 percent. a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.)

Answer 1

Initial Investment = $2,125,000
Useful Life = 4 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $2,125,000 / 4
Annual Depreciation = $531,250

Selling Price Variable Cost Fixed Cost Sales Quantity Worst Case $ 17,010 $ 13,915 $ 693,000 216 $ $ $ Base Case 18,900 12,650 630,000 240 $ $ $ Best Case 20,790 11,385 567,000 264

Base Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($18,900 - $12,650) * 240 - $630,000] * (1 - 0.22) + 0.22 * $531,250
Annual OCF = $870,000 * 0.78 + 0.22 * $531,250
Annual OCF = $795,475

NPV = -$2,125,000 + $795,475 * PVA of $1 (9%, 4)
NPV = -$2,125,000 + $795,475 * 3.23972
NPV = $452,116.27

Worst Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($17,010 - $13,915) * 216 - $693,000] * (1 - 0.22) + 0.22 * $531,250
Annual OCF = -$24,480 * 0.78 + 0.22 * $531,250
Annual OCF = $97,780.60

NPV = -$2,125,000 + $97,780.60 * PVA of $1 (9%, 4)
NPV = -$2,125,000 + $97,780.60 * 3.23972
NPV = -$1,808,218.23

Best Case:

Annual OCF = [(Price per unit - Variable Cost per unit) * Sales Quantity - Fixed Cost] * (1 - Tax Rate) + Tax Rate * Depreciation
Annual OCF = [($20,790 - $11,385) * 264 - $567,000] * (1 - 0.22) + 0.22 * $531,250
Annual OCF = $1,915,920 * 0.78 + 0.22 * $531,250
Annual OCF = $1,611,292.60

NPV = -$2,125,000 + $1,611,292.60 * PVA of $1 (9%, 4)
NPV = -$2,125,000 + $1,611,292.60 * 3.23972
NPV = $3,095,136.86