Question

Rocky Mountain Sports Ltd is considering purchasing a new machine that costs $60,000. The machine will generate revenues of $100,000 per year for five years. The cost of materials and labour needed to generate these revenues will total $60,000 per year, and other cash expenses will be $10,000 per year. The machine is expected to sell for $2,500 at the end of its five-year life and will be depreciated on a straight-line basis over five years to zero. Rocky Mountain’s tax rate is 34 percent, and its opportunity cost of capital is 14.40 percent. What is the project's NPV? Should Rocky Mountain accept or reject the project?

Answer 1

Annual Operating cash flow (OCF)

Operating cash flow (OCF) = [(Revenue – Cost of materials – Cash expenses) x (1 – Tax rate)] + [Depreciation x Tax rate]

= [($100,000 - $60,000 - $10,000) x (1 – 0.34)] + [($60,000 / 5 Years) x 0.34]

= [$30,000 x 0.66] + [$12,000 x 0.34]

= $19,800 + $4,080

= $23,880

Cash flow for Year 1-4 = $23,880

Cash flow for Year 5 = Annual cash flow + After-tax salvage value

= $23,880 + [$2,500 x (1 – 0.34)]

= $23,880 + $1,650

= $25,530

Project’s Net Present Value (NPV)

Year	Annual cash flows ($)	Present Value Factor (PVF) at 14.40%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	23,880	0.8741259	20,874.13
2	23,880	0.7640960	18,246.61
3	23,880	0.6679161	15,949.84
4	23,880	0.5838428	13,942.17
5	25,530	0.5103521	13,029.29
TOTAL			82,042.03

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $82,042.03 - $60,000

= $22,042.03

DECISION

YES. Rocky Mountain should accept the Project, since the Net Present Value of the project is Positive $22,042.03.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.