Question

Average Rate of Return, Cash Payback Period, Net Present Value Method

Bi-Coastal Railroad Inc. is considering acquiring equipment at a cost of $248,000. The equipment has an estimated life of 10 years and no residual value. It is expected to provide yearly net cash flows of $62,000. 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, assuming the annual earnings are equal to the net cash flows less the annual depreciation expense on the equipment. 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	$
Less amount to be invested	$
Net present value	$

Answer 1

Cost of Machine = $248,000
Estimated Life = 10 years

Annual Depreciation = Cost of Machine / Estimated Life
Annual Depreciation = $248,000 / 10
Annual Depreciation = $24,800

Answer a.

Net Cash Flow = $62,000
Annual Depreciation = $24,800

Annual Income = Net Cash Flow - Annual Depreciation
Annual Income = $62,000 - $24,800
Annual Income = $37,200

Average Investment = $248,000 / 2
Average Investment = $124,000

Annual Rate of Return = Annual Income / Average Investment
Annual Rate of Return = $37,200 / $124,000
Annual Rate of Return = 30.0%

Answer b.

Cash Payback Period = Investment / Net Cash Flow
Cash Payback Period = $248,000 / $62,000
Cash Payback Period = 4 years

Answer c.

Present Value of Annual Net Cash Flows = Net Cash Flow * PV of Annuity of $1 (10%, 10)
Present Value of Annual Net Cash Flows = $62,000 * 6.145
Present Value of Annual Net Cash Flows = $380,990

Net Present Value = Present Value of Annual Net Cash Flows - Amount to be invested
Net Present Value = $380,990 - $248,000
Net Present Value = $132,990