The most likely outcomes for a particular project are estimated as follows: Howe
ID: 1174617 • Letter: T
Question
The most likely outcomes for a particular project are estimated as follows:
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 $2.3 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 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.)
Unit price: $ 50 Variable cost: $ 30 Fixed cost: $ 490,000 Expected sales: 48,000 units per yearExplanation / Answer
a) Best-case Scenario
In the best case scenario, all the variables will be in our favour, i.e., costs will be lower and revenue would be higher.
Unit price = $50 + 10% = $55
Variable cost = $30 - 10% = $27
Fixed costs = $490,000 - 10% = $441,000
Expected sales = 48,000 + 10% = 52,800 units
Now, we compute the cash inflows per year -
NPV = Present value of cash inflows - Initial investment
or, NPV = $795,180 x PVIFA (10%, 10 years) - $2,300,000
or, NPV = $795,180 x 6.14456710558 - $2,300,000 = $2,586,036.87101 or $2,586,037
b) Worst-case Scenario
In this case, every variable will be against us, i.e., costs will be higher and revenue will be lower.
Unit price = $50 - 10% = $45
Variable cost = $30 + 10% = $33
Fixed costs = $490,000 + 10% = $539,000
Units = 48000 - 10% = 43200
NPV = Present value of cash inflows - Initial investment
or, NPV = $54,580 x PVIFA (10%, 10 years) - $2,300,000
or, NPV = $54,580 x 6.14456710558 - $2,300,000 = (-)$1,964,629.52738 or (-)$1,964,630
Sales [ 52,800 x $55 ] $2,904,000 Less: Variable costs [ 52,800 x $27 ] $1,425,600 Less: Fixed costs $441,000 Less: Depreciation [ $2,300,000 / 10 ] $230,000 Earnings before tax $807,400 Less: Tax @30% $242,220 Net income $565,180 Add: Depreciation $230,000 Cash inflows per year $795,180