Question

you are evaluating two different silicon wafer milling machines. The Techron I costs $245,000, has a three- year life and a pretax operating costs of $63,000 per year. The Techron II cosr $420,000, has a five year life, and has pretax operating costs of $35,000 per year. For both milling machines, use straight line depreciation to zero over the project's life and assume a salvage value of $40,000. If your tax rate is 22 percent and your discount rate is 10 percent, compute the EAC for both machines.

Answer 1

The After-tax salvage Value

After-tax salvage value = $31,200 [$40,000 x (1 – 0.22)]

Equivalent Annual Cost (EAC) for Techron I

Operating Cash Flow (OCF)

= Pretax Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= [−$63,000(1 − 0.22)] + [($245,000 / 3 Years) x 0.22]

= −$49,140 + $17,966.67

= -$31,173.33

Net Present Value

Period	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of Cash Flow ($)
1	-31,173.33	0.909091	-28,339.39
2	-31,173.33	0.826446	-25,763.09
3	26.67 [-$31,173.33 + 31,200]	0.751315	20.04
TOTAL		2.486852	-54,082.44

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

= -$54,082.44 - $245,000

= -$2,99,082.44

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 10%, 3 Years]

= -$2,99,082.44 / 2.486852

= -$1,20,265.48 (Negative)

Equivalent Annual Cost (EAC) for Techron II

Operating Cash Flow (OCF)

= Pretax Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= [−$35,000(1 − 0.22)] + [($420,000 / 5 Years) x 0.22]

= −$27,300 + $18,480

= -$8,820

Net Present Value

Period	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of Cash Flow ($)
1	-8,820	0.909091	-8,018.18
2	-8,820	0.826446	-7,289.26
3	-8,820	0.751315	-6,626.60
4	-8,820	0.683013	-6,024.18
5	22,380 [-$8,820 + $31,200]	0.620921	13,896.22
TOTAL		3.790787	-14,061.99

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

= -$14,061.99 - $420,000

= -$4,34,061.99

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 10%, 5 Years]

= -$4,34,061.99 / 3.790787

= -$1,14,504.46 (Negative)

DECISION

We should prefer the “Techron II” since it has the lower Equivalent Annual Cost (EAC) of -$1,14,504.46 as compared with the Equivalent Annual Cost (EAC) of Techron I.

“Equivalent Annual Cost (EAC) for Techron I = -$1,20,265.48 (Negative)”

“Equivalent Annual Cost (EAC) for Techron II = -$1,14,504.46 (Negative)”

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.