Question

The most likely outcomes for a particular project are estimated as follows: Unit price: $ 80 Variable cost: $ 60 Fixed cost: $ 280,000 Expected sales: 30,000 units per year However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 5% higher or 5% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1.0 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 40% and the required rate of return is 10%.

a. What is project NPV in the best-case scenario, that is, assuming all variables take on the best possible value? (A negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

b. What is project NPV in the worst-case scenario? (A negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

Answer 1

	Most Likely	Best Case	Worst Case
Price	$80	$84	$76
Variable cost	$60	$57	$63
Fixed cost	280,000	266,000	294,000
Sales	30,000	31,500	28,500

Cash flow = [(1?T)×(revenue?cash expenses)] + (T×depreciation)Depreciation expense = $1 million/10 years = $100,000 per year

Best-case CF = 0.60×[31,500×($84?$57)?$266,000] + (0.40×$100,000) = $390,700

Worst-case CF = 0.60×[28,500×($76?$63)?$294,000] + (0.40×$100,000) = $85,900

10%, 10-year annuity factor =[1/0.10 - 1/(0.10*1.10^10] = 6.144567106

Best-case NPV = (6.144567106*$390,700) – $1,000,000 = $1,400,682

Worst-case NPV = (6.144567106*$85,900) – $1,000,000 = –$472,182