Question

Elemental is considering another project which requires new equipment at a cost of $70,000. The equipment has a 3 year tax life and will be fully depreciated by the straight-line method over 3 years. When the project closes down at the end of the third year, it is expected to sell for $5000 before taxes. The project will require new working capital of $10000, and is expected to be fully recovered at the end of the project's life. Project revenues of $75000 and operating costs of $30000 apart from depreciation ar forecast. No inflation is expected. The firm faces a tax rate of 35% and the project has a discount rate of 10%. what is the NPV of the project?

Answer 1

NPV = Present value of cash inflows - initial investment

Calculation of the free cash inflows :-

Depreciation per year = $ 70,000 / 3 = $ 23,333.333333

Operating vash inflows :-

Particulars	Year 1	year 2	year 3
Revenue	75,000.00	75,000.00	75,000.00
Less-Cost	30,000.00	30,000.00	30,000.00
Less-Depreciation	23,333.33	23,333.33	23,333.33
Profit before tax	21,666.67	21,666.67	21,666.67
Less-Tax@35%	7,583.33	7,583.33	7,583.33
Profit after tax	14,083.33	14,083.33	14,083.33
Add-Depreciation	23,333.33	23,333.33	23,333.33
Operating free cash flows	37,416.67	37,416.67	37,416.67

Terminal cash inflows in year 3 :-

Terminal cash inflows = after tax sale proceeds from machine + recovery of working capital

Here machine is fully depreciation, so any proceeds from sale is gain. so entire amount from proceeds is taxable

Terminal cash flows in year 3 = 5000 * (1 - 0.35) + 10,000 = $ 13,250

Initial investment = Cost of machine + investment in working capital = $ 70,000 + 10,000= $ 80,000

Calculation of the present value of cash inflows :-

Years	Operating free cash flows	Terminal cash inflows	Total CF	PVF@10%	PV of CF
1	37,416.67		37,416.67	0.909091	$    34,015.15
2	37,416.67		37,416.67	0.826446	$    30,922.87
3	37,416.67	13,250	50,666.67	0.751315	$    38,066.62
PV of cash inflows	$ 103,004.63

NPV = Present value of cash inflows - initial investment

= 103,004.63 - 80,000

NPV = $ 23,004.63 (round off upto 2 decimals)

NPV = $ 23,004.63310793890 (without round off)