Question

The PARC Co. Inc. asked you to determine some of the after-tax cash flows (ATCF) for equipment used for research and development that is being considered. PARC expects the equipment to require the purchase of $190,000 worth of capital equipment (first cost) and to operate for five years. The capital equipment will have a resale value of $55,000 at the end of the 5^th year. PARC plans to use the sum-of-years’-digits depreciation method for income tax calculations. The income tax rate is 35%, and PARC uses an after-tax MARR of 10%. The equipment results in PARC's before-tax income of $40,000 each year. Answer the following questions.

(a) Show before-tax cash flows (BTCF) from n=0 to n=5.

(b) Calculate depreciation charges.

(c) Determine taxable incomes.

(d) Compute income taxes.

(e) Show after-tax cash flows (ATCF).

(f) Determine both the after-tax NPW and after-tax rate of return for this investment.

(g) Indicate if it is worth investing on this equipment.

Answer 1

Working notes:

(i) SOYD depreciation:

Sum-of-years-digit (SOYD) = 1 + 2 + 3 + 4 + 5 = 15

Annual depreciation in year N = (Cost - Salvage value) x (Number of years remaining at beginning of year N / SOYD)

= $(190,000 - 55,000) x (Number of years remaining at beginning of year N / 15)

= $135,000 x (Number of years remaining at beginning of year N / 15)

SOYD Depreciation schedule as follows.

SOYD
Year	Net Cost ($)	Depreciation Rate	Annual Depreciation ($)	Accumulated Depreciation ($)	End-of-Year Book Value ($)
1	1,35,000	5/15	45,000	45,000	90,000
2	1,35,000	4/15	36,000	81,000	54,000
3	1,35,000	3/15	27,000	1,08,000	27,000
4	1,35,000	2/15	18,000	1,26,000	9,000
5	1,35,000	1/15	9,000	1,35,000	0
TOTAL			1,35,000

(ii) Since BTCF = Taxable income (TI) - Depreciation, we have

TI = BTCF + Depreciation

(iii) Income tax (T) = TI x Tax rate = TI x 0.35

(iv) ATCF = TI - T + Depreciation

Therefore, Parts (a) - (e) are as follows.

Year	BTCF ($)	Depreciation ($)	TI ($)	Tax ($)	ATCF ($)
0	-1,90,000				-1,90,000
1	40,000	45,000	85,000	29,750	1,00,250
2	40,000	36,000	76,000	26,600	85,400
3	40,000	27,000	67,000	23,450	70,550
4	40,000	18,000	58,000	20,300	55,700
5	95,000	9,000	1,04,000	36,400	76,600

(f) After tax NPW & IRR are computed as follows. Note that PV factor in year N = (1.10)^-N. IRR is computed using Excel IRR function.

Year	BTCF ($)	Depreciation ($)	TI ($)	Tax ($)	ATCF ($)	PV Factor @10%	Discounted ATCF ($)
0	-1,90,000				-1,90,000	1.0000	-1,90,000
1	40,000	45,000	85,000	29,750	1,00,250	0.9091	91,136
2	40,000	36,000	76,000	26,600	85,400	0.8264	70,579
3	40,000	27,000	67,000	23,450	70,550	0.7513	53,005
4	40,000	18,000	58,000	20,300	55,700	0.6830	38,044
5	95,000	9,000	1,04,000	36,400	76,600	0.6209	47,563
				IRR of ATCF =	0	NPW ($) =	1,10,327

(g) Since IRR < MARR, project is not acceptable. But NPW > 0, so as per the Conflict Decision Rule, project is accepted since it generates positive discounted net cash low.