Question

Farmers are deciding the purchase of harvesting-related processing equipment which both have the same output. Processor A has a first cost of $32,000, its operating cost will be $5500 per year, and its salvage after 3 years will be $7000. Processor B has a first cost of $37,000, an operating cost of $7250, and a resale value of $12,000 after 4 years. Use an interest rate of 8%. What is the net EUAC of each processor and which one should be chosen?

Answers: EUAC_A = __________, EUAC_B = __________, Select? __________<12 pts>

Work:

Answer 1

Equivalent Uniform Annual Cost for Processor-A (EUACA)

Net Present Value (NPV)

Year	Annual cash flows ($)	Present Value Factor (PVF) at 8.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	-5,500	0.9259259	-5,092.59
2	-5,500	0.8573388	-4,715.36
3	1,500 [-5,500 + 7,000]	0.7938322	1,190.75
TOTAL	2.5770970	-8,617.21

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

= -$8,617.21 - $32,000

= -$40,617.21

Equivalent Uniform Annual Cost for Processor-A (EUACA)

Equivalent Uniform Annual Cost for Processor-A (EUACA) = Net Present Value / [PVIFA 8.00%, 3 Years]

= -$40,617.21 / 2.5770970

= -$15,760.84 (Negative)

Equivalent Uniform Annual Cost for Processor-B (EUACB)

Net Present Value (NPV)

Year	Annual cash flows ($)	Present Value Factor (PVF) at 8.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	-7,250	0.9259259	-6,712.96
2	-7,250	0.8573388	-6,215.71
3	-7,250	0.7938322	-5,755.28
4	4,750 [-7,250 + 12,000]	0.7350299	3,491.39
TOTAL	3.3121268	-15,192.56

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

= -$15,192.56 - $37,000

= -$52,192.56

Equivalent Uniform Annual Cost for Processor-B (EUACB)

Equivalent Uniform Annual Cost for Processor-B (EUACB) = Net Present Value / [PVIFA 8.00%, 4 Years]

= -$52,192.56 / 3.3121268

= -$15,758.02 (Negative)

DECISION

The Farmers should choose “PROCESSIOR-B”, Since it has the lower Equivalent Uniform Annual Cost.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)n], Where “r” is the Discount/Interest Rate and “n” is the number of years.