Automated Manufacturers uses high-tech equipment to produce specialized aluminum

Question

Automated Manufacturers uses high-tech equipment to produce specialized aluminum products for its customers. Each one of these machines costs $1,480,000 to purchase plus an additional $49,000 a year to operate. The machines have a 6-year life after which they can be sold of 10% of the original cost. The equipment is in the 7 year MACRS group. What is the equivalent annual cost of one these machines if the required return is 16 percent and the company’s marginal tax rate is 30%?

What is the shortest way to get the answer (Which is -349,671.58) ?

Thanks!

Explanation / Answer

We need to find NPV of the machine and then compute PMT.

Depreciation = MACRS % x Investment

Cash Flow = Profits + Depreciation + Investment + After-tax salvage value

Book Value at the end of year 6 = Investment x (1 - accumulated depreciation) = 198,172

After-tax salvage value = (148,000 - 198,172) x -30% + 148,000 = 163,051.6

NPV = NPV(16%, 29148...168356) - 1480000 = -1,288,447.43

Annualized Cost = PMT(16%, 6, -1,288,447.43, 0, 0) = 349,671.58

0 1 2 3 4 5 6 MACRS 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 13.39% Investment -1,480,000 198172 Salvage 148000 Expense -49,000 -49,000 -49,000 -49,000 -49,000 -49,000 Depreciation -211492 -362452 -258852 -184852 -132164 -132016 EBT -260,492 -411,452 -307,852 -233,852 -181,164 -181,016 Tax (30%) 78147.6 123435.6 92355.6 70155.6 54349.2 54304.8 Profits -182,344 -288,016 -215,496 -163,696 -126,815 -126,711 Cash Flows -1,480,000 29,148 74,436 43,356 21,156 5,349 168,356 NPV -$1,288,447.43 PMT $349,671.58

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