Question

An engineer is working on the layout of a new research and experimentation facility. Two plant operation will be required. If, however, an addition $100,000 of instrumentation and remote controls were added, the plant could be run by a single operato. The total before-tax cost of each plant operator is projected to be $35,000 per year. The instrumentation and controls will be depreciated by means of the modified accelerated cost recovery system (MACRS)

If this corporation (34% combined corporate tax rate) invests in additional instrumentation and controls, how long will take for after-tax benefits to equal the $100,000 cost? In other words what is the after-tax payback period?

NOTE: Please Use a net tax rate of 22.98% for the problem (disregard the rate given in the problem)

Answer 1

Working notes:

(1) Instrumentation and remote control equipment used for experimentation has a general class life of 5 years (unless otherwise mentioned) [Ref: Thomson Reuters CS Professional Suite website]

(2) MACRS schedule is as follows.

Year	Depreciation Base ($)	Depreciation Rate (%)	Annual Depreciation ($)
	(A)	(B)	(C) = (A) x (B)
1	1,00,000	20	20,000
2	1,00,000	32	32,000
3	1,00,000	19.2	19,200
4	1,00,000	11.52	11,520
5	1,00,000	11.52	11,520

(3) Before-tax Annual savings = $35,000

(4) Before-tax income = Before-tax Annual savings - Depreciation

(5) After-tax income = Before-tax income x (1 - Tax rate) = Before-tax income x (1 - 0.2298) = Before-tax income x 0.7702

(5) After-tax cash flow (ATCF) = After-tax income + Depreciation

[ATCF in year 0 = -$100,000]

Year	Savings ($)	Depreciation ($)	Before-tax Income ($)	After-tax Income ($)	ATCF ($)
	(D)	(C)	(E)=(D)-(C)	(F)=(E) x 0.7702	(G)=(F)+(C)
0					-1,00,000
1	35,000	20,000	15,000	11,553	31,553
2	35,000	32,000	3,000	2,311	34,311
3	35,000	19,200	15,800	12,169	31,369
4	35,000	11,520	23,480	18,084	29,604
5	35,000	11,520	23,480	18,084	29,604

(6) After-tax payback period (PBP) is the time by when cumulative ATCF equals zero.

Year	ATCF ($)	Cumulative ATCF ($)
0	-1,00,000	-1,00,000
1	31,553	-68,447
2	34,311	-34,136
3	31,369	-2,767
4	29,604	26,837
5	29,604	56,441

PBP lies between years 3 & 4.

PBP = 3 + (Absolute value of cumulative ATCF in year 3 / ATCF in year 4)

= 3 + (2,767 / 29,604) = 3 + 0.09 = 3.09 years