An auto supplier installed new equipment costing $1,050,000. The equipment gener

Question

An auto supplier installed new equipment costing $1,050,000. The equipment generated new income averaging $300,000 per year, and its operating costs averaged $48,000 per year. The equipment was depreciated using the MACRS method, assuming a recovery period of 7 years and no salvage value. However, the equipment was kept in service for a total of 10 years, after which time a scrap dealer bought it for $60,000. The company uses an after-tax MARR rate of 8% per year and is in the 30% tax bracket. Determine the equipment's after-tax net present worth over the 10-year service period.

Explanation / Answer

Working notes:

(1) MACRS Depreciation schedule:

(2) Pre-tax income, years 1-7 = Annual income - Operating cost - Depreciation = $(300,000 - 48,000 - Depreciation)

= $252,000 - Depreciation

(3) Pre-tax income, years 8-9 = Annual income - Operating cost = $252,000

(4) Pre-tax income, year 10 = $252,000 + Salvage value = $252,000 + $60,000

= $312,000

**Assuming salvage value is fully taxable. Relaxation of this assumption will result in a different NPW.

(5) Post-tax income, years 1-7 = Pre-tax income x (1 - Tax rate) = $(252,000 - Depreciation) x 0.7

(6) Post-tax income, years 8-9 = $252,000 x 0.7 = $176,400

(7) Post tax income, year 10 = $312,000 x 0.7 = $218,400

(8) Cash flow after tax (CFAT), year 0 = Equipment cost

(9) CFAT, years 1-10 = Post-tax income + Depreciation (Since depreciation is non-cash expense, it is added back to obtain cash flow).

(10) Net present worth (NPW) is sum of CFAT discounted at MARR.

Year Depreciation Base ($) Depreciation (%) Annual depreciation ($) (A) (B) (C) = (A) x (B) 1 10,50,000 14.29 1,50,045 2 10,50,000 24.49 2,57,145 3 10,50,000 17.49 1,83,645 4 10,50,000 12.49 1,31,145 5 10,50,000 8.93 93,765 6 10,50,000 8.92 93,660 7 10,50,000 8.93 93,765

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