3. A machine with a useful life of 3 years is purchased for $100,000. It is know

Question

3. A machine with a useful life of 3 years is purchased for $100,000. It is known that the market value of the machine decreases by 10% each year. The book value can be calculated by assuming straight-line depreciation over a 4-year depreciable life t $20,000. The machine generates a gross income of $50,000 annually. The operating and maintenance costs are $30,000 in year 1, increasing by $5,000 each year. Determine the after-tax marginal costs if the tax rate is 40% and i = 10%. If the minimum EUAC of a challenger is $56,000 when should the machine be replaced? (40 marks) o a salvage value of

Explanation / Answer

Annual depreciation = (100,000 - 20,000)/4 = 80,000/4 = 20,000

Tax = 40%, r = 10%

Gross Income = Revenue - COGS = 50,000

Tax on income = 50,000*0.4 = 20,000; if we consider it, cost will increase by 20,000

Above income could be same in both cases; hence, it can be ignored in calculation.

Steps:

1. You have MV and BV

2. After-tax MV = MV – (MV – BV) * Tax

3. Capital recovery = (MVk-1 – MVk) + r*MVk-1

4. Depreciation: D = BVk-1 - BVk

5. You have O&M

6. Taxable Income: TI = -O&M – Depreciation

7. Tax = TI*0.40

8. MC = Capital recovery + O&M + Tax + 20,000

9. Convert it into EUAC: PMT (r%, k, NPV(r%, 1 to kth MC), 0) for kth year

Table depicted that based on useful life, machine be replaced at the end of 3rd year and additionally, if we do further, we have to definitely replace at the end of 4th year.

If we consider tax on given income, the annual cost will increase by tax 50,000*0.4 = 20,000; and hence EUAC will increase by 20,000

Year BV MV After-tax MV Capital recovery D O&M Cost TI Tax MC EUAC 0 100,000 100,000 100,000 1 80,000 90,000 86,000 24,000 20,000 30,000 -50,000 -20,000 54,000 54,000 2 60,000 81,000 72,600 22,000 20,000 35,000 -55,000 -22,000 55,000 54,476 3 40,000 72,900 59,740 20,120 20,000 40,000 -60,000 -24,000 56,120 54,973 4 20,000 65,610 47,366 18,348 20,000 45,000 -65,000 -26,000 57,348 55,485 5 0 59,049 35,429 16,673 20,000 50,000 -70,000 -28,000 58,673 56,007

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