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 $108,000. The equipment has an estimated life of 10 years and no residual value. It is expected to provide yearly net cash flows of $54,000. The company's minimum desired rate of return for net present value analysis is 12%.

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.
2 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)Average rate of return = [(Annual cash inflows - Annual Depreciation) / Average investment] × 100

Annual cash inflows = $54,000

Annual Depreciation = (Cost of Equipment - Residual value) / Useful life of Asset

Annual Depreciation = ( $108,000 - $0) / 10 years

Annual Depreciation = $10,800

Average Investment = (Cost of Equipment - Residual value) / 2

Average Investment = ($108,000 - $0) / 2

Average Investment = $54,000

Average Rate of Return = [ ($54,000 - $10,800) / $54,000] × 100

Average Rate of Return = 80%

b) Cash payback period = Initial investment / Annual cash inflows

Initial Investment = $108,000

Annual cash inflows = $54,000

Cash payback period = $108,000 / $54,000

Cash payback period = 2 years

c)The net present value are as follows :-

Particular	Amount
Present value of Annual cash flows (Note 1)	$305,100
Amount to be invested (Initial Investment)	($108,000)
Net present value	$197,100

Note 1 :-

Present value of Annual cash inflow = Annual cash inflows × Present value of an annuity ( i = 12% , n = 10 years)

Annual Cash inflows = $54,000

Present value of an annuity (i = 12% , n = 10 years) = 5.650

Present value of Annual cash inflows = $54,000 × 5.650

Present value of Annual cash inflows = $305,100