Questionl: An engineer is working on the layout of a new research and experiment

Question

Questionl: An engineer is working on the layout of a new research and experimentation facility. Two plant operators will be required. If, however, an. Additional $100,000 of instrumentation and remote controls were added, the plant could be run by a single operator. The total before-tax cost of each plant operator is projected to be S35,000 per year. The instrumentation and controls will be depreciated by means of the modified accelerated cost recovery system (MACRS). If this corporation (34% corporate tax rate) invests in the additional instrumentation and controls, how long will it take for the after-tax benefits to equal the $100,000 cost? In other words, what is the after-tax payback period? (Answer: 3.24 years).

Explanation / Answer

MACRS depreciation rates = 10%, 18%, 14.4%, 11.52%, 9.22%........3.26%

Thus we will first compute the depreciation schedule for the instrumentation and controls:

Now we will compute tax shiled of depreciation. Tax shield = tax rate*depreciation amount

Savings per year = 35,000 (cost of one operator). After tax savings = 35,000*(1-0.34) = 23,100

Thus after tax savings each year would be:

Caclulation of payback:

As we can see that in the 4th year the amount of cumulative savings exceed the amount of $100,000

Thus payback = 3 years + (107,395.6-81,821.25)/107,395.6

= 3+0.24

= 3.24 years

Year Depreciation rate Book value at start of the year Depreciation Book value at end of the year 1 10.00% 100,000.00 10,000.00 90,000.00 2 18.00% 90,000.00 16,200.00 73,800.00 3 14.40% 73,800.00 10,627.20 63,172.80 4 11.52% 63,172.80 7,277.51 55,895.29

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