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

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 $

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Solutions

Expert Solution

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 )

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