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

Question

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

Unit price: $50

Variablecost: $30

Fixed cost: $500,000

Expected sales: 49,000 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 $2.2 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 30% 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.) NPV $

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.) NPV

Explanation / Answer

a. Best case scenario :

Unit price = $ 50 + 10% = $ 55

Variable cost = $ 30 - 10% = $ 27

Fixed cost = $ 500,000 - 10% = $ 450,000

Expected sales = 49,000 + 10% = 53,900 units per year

NPV at 12% discount rate = Annual cash inflows x PVIFA 12%,10 years - Initial investment = 807,440 x 5.6502 - 2,200,000 = $ 2,362,197

b. Worst case scenario

Unit price = $ 45

Variable cost = $ 33

Fixed cost = $ 550,000

Expected sales = 49,000 - 10% = 44,100

NPV = $ 51,440 x 5.6502 - 2,200,000 = $ (1,909,354)

$ Sales ( 53,900 x $ 55) 2,964,500 Variable cost ( 53,900 x $ 27) (1,455,300) Fixed cost (450,000) Depreciation expense (220,000) Earnings before tax 8,39,200 Tax @ 30% 2,51,760 Net income 587,440 Add depreciation expense 220,000 Annual cash inflows 807,440

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