Question

Barry Boswell is a financial analyst for Dossman Metal​ Works, Inc. and he is analyzing two alternative configurations for the​ firm's new plasma cutter shop.
(Related to Checkpoint 11.2) (Calculating EAC) Barry Boswell is a financial analyst for Dossman Metal Works, Inc. and he is analyzing two alternative configurations for the firm's new plasma cutter shop. The two alternatives, denoted A and B below, will perform the same task, but alternative A will cost $75,000 to purchase, while alternative B will cost only $65,000. Moreover, the two alternatives will have very different cash flows and useful lives. The after-tax costs for the two projects are as follows: a. Calculate each project's EAC, given a discount rate of 9 percent. b. Which of the alternatives do you think Barry should select? Why?

Answer 1

Equivalent Annual Cost (EAC) for Alternative-A

Period	Annual Cash Flow ($)	Present Value factor at 9.00%	Present Value of Cash Flow ($)
1	-17,000	0.917431	-15,596.33
2	-17,000	0.841680	-14,308.56
3	-17,000	0.772183	-13,127.12
4	-17,000	0.708425	-12,043.23
5	-17,000	0.649931	-11,048.83
6	-17,000	0.596267	-10,136.54
7	-17,000	0.547034	-9,299.58
TOTAL		5.032953	-85,560.20

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$85,560.20 - $75,000

= -$160,560.20 (Negative)

Therefore, the Equivalent Annual Cost (EAC) for Alternative-A = Net Present Value / [PVIFA 9.00%, 7 Years]

= -$160,560.20 / 5.032953

= -$31,901.79 (Negative)

Equivalent Annual Cost (EAC) for Alternative-B

Period	Annual Cash Flow ($)	Present Value factor at 9.00%	Present Value of Cash Flow ($)
1	-8,000	0.917431	-7,339.45
2	-8,000	0.841680	-6,733.44
3	-8,000	0.772183	-6,177.47
TOTAL		2.531295	-20,250.36

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$20,250.36 - $65,000

= -$85,250.36 (Negative)

Therefore, the Equivalent Annual Cost (EAC) for Alternative-B = Net Present Value / [PVIFA 9.00%, 3 Years]

= -$85,250.36 / 2.531295

= -$33,678.56 (Negative)

DICISION

Barry should select “Alternative-A”, since it has the lower Equivalent Annual Cost of $31,901.79.

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.