Question

Scholastic Co. is evaluating different equipment. Machine A costs $85,000 has a four-year life, and costs $45,000 per year to operate. The machine will be depreciated using straight-line and the relevant discount rate is 8%. The machine will have a salvage value of $20,000 at the end of the project's life. The firm has a tax rate of 21%. Calculate the EAC for the project. (Enter a positive value and round to 2 decimals)

Answer 1

Equivalent Annual Cost (EAC) for the Project

Annual Operating cash flow (OCF)

Annual Operating cash flow (OCF) = [Annual costs x (1 – Tax rate)] + [Depreciation x Tax rate]

= [-$45,000 x (1 – 0.21)] + [($85,000/4 Years) x 0.21]

= [-$45,000 x 0.79] + [$21,250 x 0.21]

= -$35,550 + $4,462.50

= -$31,087.50 (Negative OCF)

After-tax salvage value

After-tax salvage value = Salvage value x (1 – Tax rate)

= $20,000 x (1 – 0.21)

= $20,000 x 0.79

= $15,800

Net Present Value

Year	Annual cash flows ($)	Present Value Factor (PVF) at 8.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	(31,087.50)	0.9259259	(28,784.72)
2	(31,087.50)	0.8573388	(26,652.52)
3	(31,087.50)	0.7938322	(24,678.26)
4	(15,287.50) [-$31,087.50 + $15,800]	0.7350299	(11,236.77)
TOTAL	3.3121268	(91,352.27)

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

= -$91,352.77 - $85,000

= -$176,352.27 (Negative NPV)

Equivalent Annual Cost (EAC) for the Project

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 8.00%, 4 Years]

= -$176,352.27 / 3.3121268

= -$53,244.42 (Negative EAC)

Therefore, the Equivalent Annual Cost (EAC) for the Project will be $53,244.42 (Negative EAC)

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.