Question

The most likely outcomes for a particular project are estimated as follows:

Unit price: $ 60 Variable cost: $ 40 Fixed cost: $ 420,000 Expected sales: 47,000 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 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $2.1 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 12%.

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

Best-case scenario: N = 47,000 x (1 + 10%) = 51,700, P = 60 x 1.1 = 66, VC = 40 x (1 - 10%) = 36, FC = 378,000

Annual Cash Flow = (51,700 x (66 - 36) - 378,000 - 210,000) x (1 - 40%) + 210,000 = $787,800

N = 10, I/Y = 12%, PMT = 787,000, FV = 0 => Compute PV = $4,451,246

NPV (best- case scenario) = 4,451,246 - 2,100,000 = $2,351,246

Worst-case scenario: N = 47,000 x (1 - 10%) = 42,300, P = 60 x 0.9 = 54, VC = 44, FC = 462,000

Annual Cash Flow = $60,600

N = 10, I/Y = 12%, PMT = 60,600, FV = 0 => Compute PV = $342,404

NPV (worst case scenario) = 342,404 - 2,100,000 = -$1,757,596