Question

A company is considering a new project requiring an upfront fixed-asset investment of $1,000,000 with an economic life of five years. Depreciation is taken on a straight-line basis, with no expected salvage value. Net working capital required immediately is expected to be $100,000 and will be recovered in full upon the project's completion in five years. In the expected-scenario forecast, the annual sales volume is 53,700 units, while the sale price is $145 per unit with a variable cost of $95 per unit. Annual fixed costs are estimated to $1,255,000. If the appropriate discount rate is 13.25% and the tax rate 30%, what is the project's NPV?

	$2,596,240
	$2,662,811
	$2,729,381
	$2,795,951
	$2,862,521

Answer 1

Initial cash outlay = Initial investment + increase in NWC

Initial cash outlay = 1,000,000 + 100,000

Initial cash outlay = 1,100,000

Annual depreciation = 1,000,000 / 5

Annual depreciation = 200,000

Revenue = 53,700 * 145 = 7,786,500

Variable cost = 53,700 * 95 = 5,101,500

Operating cash flow from year 1 to year 5 = (Revenue - variable costs - fixed costs - depreciation)(1 - tax) + depreciation

Operating cash flow from year 1 to year 5 = (7,786,500 - 5,101,500 - 1,255,000 - 200,000)(1 - 0.3) + 200,000

Operating cash flow from year 1 to year 5 = 861,000 + 200,000

Operating cash flow from year 1 to year 5 = 1,061,000

NWC will be recovered at the end

NPV = Present value of cash inflows - present value of cash outflows

NPV = Annuity * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n - Initial investment

NPV = 1,061,000 * [1 - 1 / (1 + 0.1325)^5] / 0.1325 + 100,000 / (1 + 0.1325)^5 - 1,100,000

NPV = 1,061,000 * [1 - 0.536796] / 0.1325 + 53,679.5599 - 1,100,000

NPV = 1,061,000 * 3.495882 + 53,679.5599 - 1,100,000

NPV = $2,662,810.65