Question

hagar industrial systems company is trying to deciede between two different belt systems.System A costs 212000, has 4 yr life and requires 68000 in pretax annual operating costs.System B costs 300,000 has 6 yr life and requires 62000 in pretax annual operating costs.Both systems are straight line depreciated to zero.HISC always needs a belt and it must be replaced when it wears out. Assume tax rate of 30 percent and discount rate of 9 percent.What is EAC for each project

Answer 1

Equivalent Annual Cost (EAC) – SYSTEM A

The Operating Cash Flow

Operating Cash Flow = Pre-tax Cost(1 – Tax Rate) + (Depreciation x Tax Rate)

= −$68,000(1 − 0.30) + [($212,000 / 4 Years) x 0.30]

= -$47,600 + $15,900

= -$31,700

Net Present Value

Year	Annual Cash flow ($)	Present Value factor at 9%	Present Value of Cash flow ($)
1	-31,700	0.91743	-29,082.57
2	-31,700	0.84168	-26,681.26
3	-31,700	0.77218	-24,478.22
4	-31,700	0.70843	-22,457.08
TOTAL		3.23972	-1,02,699.12

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

= -$1,02,699.12 - $212,000

= -$3,14,699.12 (Negative)

EAC – SYSTEM A

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

= -$3,14,699.12 / 3.23972

= -$97,137.76 (Negative)

Equivalent Annual Cost (EAC) – SYSTEM B

The Operating Cash Flow

Operating Cash Flow = Pre-tax Cost(1 – Tax Rate) + (Depreciation x Tax Rate)

= −$62,000(1 − 0.30) + [($300,000 / 6 Years) x 0.30]

= -$43,400 + $15,000

= -$28,400

Net Present Value

Year	Annual Cash flow ($)	Present Value factor at 9%	Present Value of Cash flow ($)
1	-28,400	0.91743	-26,055.05
2	-28,400	0.84168	-23,903.71
3	-28,400	0.77218	-21,930.01
4	-28,400	0.70843	-20,119.28
5	-28,400	0.64993	-18,458.05
6	-28,400	0.59627	-16,933.99
TOTAL		4.48592	-1,27,400.09

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

= -$1,27,400.09 - $300,000

= -$4,27,400.09 (Negative)

EAC – SYSTEM B

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

= -$4,27,400.09 / 4.48592

= -$95,275.93 (Negative)

EAC – SYSTEM A = -$97,137.76 (Negative)

EAC – SYSTEM B = -$95,275.93 (Negative)

DECISION

Hagar industrial systems company should choose “SYSTEM - B”, since the EAC of the SYSTEM-B is lower than the EAC of SYSTEM-A

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.