Question

Average Rate of Return, Cash Payback Period, Net Present Value Method for a Service Company

Spanish Peaks Railroad Inc. is considering acquiring equipment at a cost of $210,000. The equipment has an estimated life of 10 years and no residual value. It is expected to provide yearly net cash flows of $42,000. The company's minimum desired rate of return for net present value analysis is 10%.

Present Value of an Annuity of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	1.833	1.736	1.690	1.626	1.528
3	2.673	2.487	2.402	2.283	2.106
4	3.465	3.170	3.037	2.855	2.589
5	4.212	3.791	3.605	3.353	2.991
6	4.917	4.355	4.111	3.785	3.326
7	5.582	4.868	4.564	4.160	3.605
8	6.210	5.335	4.968	4.487	3.837
9	6.802	5.759	5.328	4.772	4.031
10	7.360	6.145	5.650	5.019	4.192

Compute the following:

a. The average rate of return, giving effect to straight-line depreciation on the investment. If required, round your answer to one decimal place.
%

b. The cash payback period.
years

c. The net present value. Use the above table of the present value of an annuity of $1. Round to the nearest dollar. If required, use a minus sign to indicate negative net present value for current grading purpose.

Present value of annual net cash flows	$
Amount to be invested	$
Net present value	$

Answer 1

Answer a.

Initial Investment = $210,000
Useful Life = 10 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $210,000 / 10
Annual Depreciation = $21,000

Annual Net Income = Annual Net Cash Flows - Annual Depreciation
Annual Net Income = $42,000 - $21,000
Annual Net Income = $21,000

Average Investment = $210,000 / 2
Average Investment = $105,000

Average Rate of Return = Annual Net Income / Average Investment
Average Rate of Return = $21,000 / $105,000
Average Rate of Return = 20%

Answer b.

Payback Period = Initial Investment / Annual Net Cash Flow
Payback Period = $210,000 / $42,000
Payback Period = 5 years

Answer c.

Present Value of Annual Net Cash Flows = $42,000 * PVA of $1 (10%, 10)
Present Value of Annual Net Cash Flows = $42,000 * 6.145
Present Value of Annual Net Cash Flows = $258,090

Net Present Value = Present Value of Annual Net Cash Flows - Amount to be invested
Net Present Value = $258,090 - $210,000
Net Present Value = $48,090