Question

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

Bi-Coastal Railroad Inc. is considering acquiring equipment at a cost of $144,000. The equipment has an estimated life of 10 years and no residual value. It is expected to provide yearly net cash flows of $72,000. 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, 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

Solution:

Calculation of Annual Earnings
Annual Net Cash Flows	$72,000
Less: Depreciation Expense (Refer Note 1)	-$14,400
Annual Earnings	$57,600

Part a – Average Rate of Return

Accounting/Average rate of return is the percentage of annual return on initial or average investment. This method uses Net Income after depreciation and tax in calculation.

ARR is calculated by using (i) Initial Invested Amount or (ii) Average Invested Amount

Average Rate of Return (ARR) = Annual earnings / Average Investment x 100

Average Investment = Cost of Assets / 2 = $144,000 / 2 = $72,000

Average Rate of Return (based on average investment) = $57,600 / $72,000 x 100 = 80%

Average Rate of Return (based on Initial Investment) = $57,600 / $144,000 x 100 = 40%

Part b – Cash Payback Period

Payback period is the length of time within which initial invested amount is returned back to the company.

Cash Payback Period = Initial Invested Amount $144,000 / Annual Cash Flow given in the question $72,000

= 2 Years

Part c – Net Present Value

A	Annual Cash Flow	$72,000
B	PV Annuity factor at 12% for 10 periods (from the given table)	5.65
C=A*B	Present Value of Cash Flow ($72,000*5.65)	$406,800
D	Less: Present Value of Cash Outflow (i.e. Cost of Equipment)	-$144,000
E = C - D	Net Present Value	$262,800

Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you