Random Co. purchased a machine for $400,000 that has a five year life and will produce annual net cash inflows of $110,000 per year over the life of the machine. The present value of an annuity for 5 years at an 8% cost of capital is 3.993. Calculate the Net Present Value and Payback Period of this investment.

Question

Larry Frank

Business

20 February, 11:14

Random Co. purchased a machine for $400,000 that has a five year life and will produce annual net cash inflows of $110,000 per year over the life of the machine. The present value of an annuity for 5 years at an 8% cost of capital is 3.993. Calculate the Net Present Value and Payback Period of this investment.

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Cheyanne · Answer 1

NPV = $39,230

Payback period = 3.64 years

Explanation:

The net present value (NPV) = (net annual cash flow x interest factor) - investment

NPV = ($110,000 x 3.993) - $400,000 = $439,230 - $400,000 = $39,230

The payback period = investment / net annual cash flow = $400,000 / $110,000 = 3.64 years or 3 years, 7 months and 19 days

You can also calculate the PV of each annual cash flow which will give you a more precise result, but the variation is minimal:

PV = ($110,000 / 1.08) + ($110,000 / 1.08²) + ($110,000 / 1.08³) + ($110,000 / 1.08⁴) + ($110,000 / 1.08⁵) = $439,198

and the NPV = $39,198