Question

Letang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $295,000, has a four-year life, and requires $97,000 in pretax annual operating costs. System B costs $375,000, has a six-year life, and requires $91,000 in pretax annual operating costs. Suppose the company always needs a conveyor belt system; when one wears out, it must be replaced. Assume the tax rate is 21 percent and the discount rate is 9 percent.

Calculate the EAC for both conveyor belt systems. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) System A? System B?

Answer 1

Equivalent Annual Cost (EAC) – SYSTEM A

The Operating Cash Flow

Operating Cash Flow = −$97,000(1 − 0.21) + [($295,000 / 4 Years) x 0.21]

= -$76,630 + $15,487.50

= -$61,142.50

Net Present Value

Net Present Value = Present Value of annual cash inflows – Initial Investment

= -$61,142.50[PVIFA 9%, 4 Years] – $295,000

= [-$61,142.50 x 3.2397199] - $295,000

= -$1,98,084.57 - $295,000

= -$4,93,084.57

EAC – SYSTEM A

EAC = Net Present Value / [PVIFA 9%, 4 Years]

= -$4,93,084.57 / 3.2397199

= -$152,199.76 (Negative)

Equivalent Annual Cost (EAC) – SYSTEM B

The Operating Cash Flow

Operating Cash Flow = −$91,000(1 − 0.21) + [($375,000 / 6 Years) x 0.21]

= -$71,890 + $13,125

= -$58,765

Net Present Value

Net Present Value = Present Value of annual cash inflows – Initial Investment

= -$58,765[PVIFA 9%, 6 Years] – $375,000

= [-$58,765 x 4.4859186] - $375,000

= -$263615.01 - $375,000

= -$638,615.01

EAC – SYSTEM B

EAC = Net Present Value / [PVIFA 9%, 6 Years]

= -$638,615.01 / 4.4859186

= -$1,42,359.92 (Negative)

EAC – SYSTEM A = -$152,199.76 (Negative)

EAC – SYSTEM B = -$1,42,359.92 (Negative)

DECISION

The firm should choose “SYSTEM - B” Conveyor Belt System, since the EAC of the SYSTEM-B is lower than the EAC of SYSTEM-A

NOTE

The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Discount Rate and “n” is the number of periods.