A 6-year project has expected sales of 2,000 units, ±4 percent. The expected variable cost per...

A 6-year project has expected sales of 2,000 units, ±4 percent. The expected variable cost per unit is $8, and the expected fixed costs are $9,800. The fixed and variable cost estimates are considered accurate within a range of ±2 percent. The sales price is estimated at $22 a unit, ±3 percent. The project requires an initial investment of $42,000 for equipment that will be depreciated straight-line to zero over the project's life. The equipment has a pretax salvage value of $5,000 at the end of the project. The project requires $2,600 in net working capital during its life. The discount rate is 9 percent, and tax rate is 30 percent. What is the net present value for the optimistic scenario?

O $22,295.33

O $31,490.07

O $34,008.12

O $28,008.46

O $35,096.52

Expert Solution

In the optimistic scenario, the unit sales and sales price would increase and the costs would reduce.

Unit sales = 2000 + 4% = 2080 units

Sales price per unit = $22 + 3% = $22.66, Variable cost per unit = $8 - 2% = $7.84

Fixed costs = $9800 - 2% = $9604

Inital investment = Cost of equipment + working capital required = $42000 + $2600 = $44600

Cash Inflows
Particulars	Years 1 - 5	Year 6
Sales (2080 x $22.66)	$47,132.80	$47,132.80
Less: Variable cost (2080 x $7.84)	$16,307.20	$16,307.20
Less: Fixed cost	$9,604	$9,604
Less: Depreciation ($42000 / 6)	$7,000	$7,000
Income before tax	$14,221.60	$14,221.60
Less: Tax@30%	$4,266.48	$4,266.48
Net income	$9,955.12	$9,955.12
Add: Depreciation	$7,000	$7,000
Add: working capital recovered		$2,600
Add: Salvage value net of tax [$5000 x (1 - 0.30)]		$3,500
Cash inflows	$16,955.12	$23,055.12
PVIF@9%	3.8896512633	0.59626732686
Present value of cash Inflows	$65,949.50	$13,747.02

NPV = Total present value of cash inflows - initial investment = $79,696.52 - $44,600 = $35,096.52

jeff jeffy answered 2 years ago

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