Final answer:
To determine the Equivalent Annual Cost (EAC) for Machine A, we account for depreciation, tax-adjusted operating costs, after-tax salvage value, and calculate the present value of these costs at a discount rate of 10%. After computing these values, the EAC for Machine A is approximately $137,991.45.
Step-by-step explanation:
To calculate the Equivalent Annual Cost (EAC) of Machine A, we need to consider the initial cost, operating costs, salvage value, the tax rate, and the discount rate. Using the formula for EAC, we first calculate the annual depreciation by subtracting the salvage value from the initial cost, then divide the result by the life of the machine. Depreciation for Machine A is ($256,654 - $44,596) / 3 = $70,686 per year. Since there is a tax saving from depreciation, we must adjust the operating costs for taxes and add the tax-adjusted depreciation.
The tax-adjusted operating costs are the operating costs less the tax shield on depreciation: $67,338 - ($70,686 × 34%) = $43,540.98. Next, we calculate the after-tax salvage value which is the salvage value less the taxes on the gain from salvage, assuming the book value is zero: $44,596 × (1 - 34%) = $29,433.16. We treat this as a cash inflow at the end of year three. Now, we can calculate the present values (PV) of the operating costs and salvage value and use them to determine the EAC. The formula for EAC is: EAC = PV of costs / Annuity factor, where the Annuity factor is calculated using the formula [1 - (1 + r)^-n]/r. In this case (r = 10%, n = 3), it is $1 = [(1 - (1 + 0.10)^-3) / 0.10] = 2.48685.
Using these calculations, EAC for Machine A becomes:
EAC = {[(Operating costs × Annuity factor) - PV of after-tax salvage value] / Annuity Factor},
EAC = {[$43,540.98 × 2.48685] - $29,433.16} / 2.48685,
EAC = $137,991.45.