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Miller Corporation is considering replacing a machine. The replacement will reduce operating expenses (thatis, increase earnings before depreciation, interest, and taxes) by $16,000 per year foreach of the 5 years the new machine is expected to last. Although the old machinehas zero book value, it can be used for 5 more years. The depreciable value of thenew machine is $48,000. The firm will depreciate the machine under MACRS usinga 5-year recovery period (see Table 4.2 on page 117 for the applicable depreciationpercentages) and is subject to a 40% tax rate. Estimate the incremental operatingcash inflows generated by the replacement. (Note: Be sure to consider the depreciation in year 6.)

Question

Miller Corporation is considering replacing a machine. The replacement will reduce operating expenses (thatis, increase earnings before depreciation, interest, and taxes) by 16,000peryearforeachofthe5yearsthenewmachineisexpectedtolast.Althoughtheoldmachinehaszerobookvalue,itcanbeusedfor5moreyears.Thedepreciablevalueofthenewmachineis16,000 per year foreach of the 5 years the new machine is expected to last. Although the old machinehas zero book value, it can be used for 5 more years. The depreciable value of thenew machine is 48,000. The firm will depreciate the machine under MACRS usinga 5-year recovery period (see Table 4.2 on page 117 for the applicable depreciationpercentages) and is subject to a 40% tax rate. Estimate the incremental operatingcash inflows generated by the replacement. (Note: Be sure to consider the depreciation in year 6.)

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Solution

To calculate the incremental operating cash inflows generated by the replacement, we need to consider the annual savings, the tax savings from depreciation, and the depreciation in year 6.

  1. Annual Savings: The new machine will reduce operating expenses by 16,000peryearfor5years.Thisgivesusatotalsavingsof16,000 per year for 5 years. This gives us a total savings of 16,000 * 5 = $80,000.

  2. Tax Savings from Depreciation: The depreciable value of the new machine is $48,000. According to the MACRS 5-year recovery period, the depreciation percentages are 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76% for each year respectively.

    Year 1: 48,000∗2048,000 * 20% = 9,600 Year 2: 48,000∗3248,000 * 32% = 15,360 Year 3: 48,000∗19.248,000 * 19.2% = 9,216 Year 4: 48,000∗11.5248,000 * 11.52% = 5,530 Year 5: 48,000∗11.5248,000 * 11.52% = 5,530 Year 6: 48,000∗5.7648,000 * 5.76% = 2,765

    The total depreciation is 9,600+9,600 + 15,360 + 9,216+9,216 + 5,530 + 5,530+5,530 + 2,765 = $48,001.

    The tax savings from depreciation is the total depreciation * tax rate = 48,001∗4048,001 * 40% = 19,200.4

  3. Depreciation in Year 6: The depreciation in year 6 is 2,765.Thetaxsavingsfromthisdepreciationis2,765. The tax savings from this depreciation is 2,765 * 40% = $1,106.

Adding all these together, the incremental operating cash inflows generated by the replacement is 80,000(annualsavings)+80,000 (annual savings) + 19,200.4 (tax savings from depreciation) + 1,106(taxsavingsfromdepreciationinyear6)=1,106 (tax savings from depreciation in year 6) = 100,306.4.

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