Suppose you have to decide whether selling an old machine or keeping it with a m

Question

Suppose you have to decide whether selling an old machine or keeping it with a major overhaul: Selling the machine at time zero for $750, 000 with zero book value and paying the tax of 40%. Keeping the machine, which requires a major overhaul cost of $1, 000, 000 at time zero. The overhaul cost is depreciable from time 0 to year 5 (over six years) based on MACRS 5-year life depreciation with the half year convention (table A-1 at IRS). In this case machine can produce and generate equal annual revenue for five years (year 1 to 5) and salvage value of the machine will be $250, 000 with zero book value at the end of year 5. The operating cost of the machine will be $400, 000 per year from year 1 to year 5. Calculate the minimum annual revenue that machine has to generate to break-even the selling with NPV of keeping the machine. Consider 40% income tax rate and after-tax minimum ROR of 10%.

Explanation / Answer

NPV of selling machine = 750000 * (1-0.4) = 450000

let x be the minum annual revenue it has to generate

initial cost = 1000000

cash flow year 1 = (x - 400000 - 100000 * 20%) * (1-0.4) + 100000 * 20%

= 0.6x - 232000

cash flow year 2 = (x - 400000 - 100000 * 32%) * (1-0.4) + 100000 * 32%

= 0.6x - 227200

cash flow year 3 = (x - 400000 - 100000 * 19.2%) * (1-0.4) + 100000 * 19.2%

= 0.6x - 232320

cash flow year 4 = (x - 400000 - 100000 * 11.52%) * (1-0.4) + 100000 * 11.52%

= 0.6x - 235392

cash flow year 5 = (x - 400000 - 100000 * 11.52%) * (1-0.4) + 100000 * 11.52% + 250000 * (1-0.4)

= 0.6x - 85392

NPV = 450000

=>

-100000 + 0.6x * [ 1/1.1 + 1/1.1^2 + 1/1.1^3 + 1/1.1^4 + 1/1.1^5]

- [232000/1.1 + 227200/1.1^2 + 232320/1.1^3 + 235392/1.1^4 + 85392/1.1^5] = 450000

=>

x = 587837.84 (ans)

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