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 $456,000. The equipment has an estimated life of 10 years and no residual value. It is expected to provide yearly net cash flows of $57,000. 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	$

Check My Work

Answer 1

a. Depreciation as per straight line method = ( Cost - Estimated residual value ) / Estimated useful life = ( $456,000 - $0 ) / 10 years = $45,600

Annual net income = Annual cash flow - Annual depreciation = $57,000 - $45,600 = $11,400

As annual net income is same every year, Annual net income = Average net income

Average investment = [ Value in the beginning + Value at the end of useful life ] / 2 = [ $456,000 + $0 ] / 2 = $228,000

Average rate of return = [ Average net income / Average investment ] * 100 = [ $11,400 / $228,000 ] * 100 = 5%

b. As the net cash inflows are same every year, we can use the following formula for calculating cash payback period :

Cash payback period = Initial investment / Annual net cash inflows = $456,000 / $57,000 = 8 years

c.

Present value of annual net cash flows [ Annual net cash inflow * Present value annuity factor at 10% of 10th year = $57,000 * 6.145 ]	$350,265
Amount to be invested	( $456,000 )
Net present value	( $105,735 )