Question

AMT, Inc., is considering the purchase of a digital camera for maintenance of design specifications by feeding digital pictures directly into an engineering workstation where computer-aided design files can be superimposed over the digital pictures. Differences between the two images can be noted, and corrections, as appropriate, can then be made by design engineers. (7.12)

a. You have been asked by management to determine the PW of the EVA of this equipment, assuming the following estimates: capital investment = $345,000; market value at end of year six = $120,000; annual revenues = $120,000; annual expenses = $8,000; equipment life = 6 years; effective income tax rate = 50%; and after-tax MARR = 10% per year. MACRS depreciation will be used with a five-year recovery
period.

b. Compute the PW of the equipment’s ATCFs. Is your answer in Part (a) the same as your answer
in Part (b)

Answer 1

5-MACRS depreciation schedule:

Year (n)	Cost (C)	Depreciation rate (r)	Depreciation (C*r)	Book value (BV)
0	345,000
1		20%	69,000	276,000
2		32%	110,400	165,600
3		19.20%	66,240	99,360
4		11.52%	39,744	59,616
5		11.52%	39,744	19,872
6		5.76%	19,872	0

a). EVA = NOPAT in Year n - (after-tax MARR * Book value at the beginning of Year n)

NOPAT = Taxable income - Income tax

Formula	Year end (n)	0	1	2	3	4	5	6	6
Capital outflow & inflow; Revenue - expense	Before-tax Cash Flow (BTCF)	-	112,000	112,000	112,000	112,000	112,000	112,000	120,000
From depreciation schedule	Depreciation (D)		69,000	110,400	66,240	39,744	39,744	19,872
BTCF - D	Taxable income (TI)		43,000	1,600	45,760	72,256	72,256	92,128	120,000
-50%*TI	Income tax (IT)		(21,500)	(800)	(22,880)	(36,128)	(36,128)	(46,064)	(60,000)
TI - IT	NOPAT		21,500	800	22,880	36,128	36,128	46,064	60,000
From depreciation schedule: BVn-1 - Dn	Book value (BV)	345,000	276,000	165,600	99,360	59,616	19,872	-
NOPATn - MARR*BVn-1	Annual EVA		(13,000)	(26,800)	6,320	26,192	30,166	44,077	60,000
1/(1+after-tax MARR)^n	Discount factor @ 10%		0.909	0.826	0.751	0.683	0.621	0.564	0.564
Discount factor*Annual EVA	Present Value (PV) of annual EVA		(11,818.18)	(22,148.76)	4,748.31	17,889.49	18,730.96	24,880.20	33,868.44
Sum of all PVs	PW of EVA	66,150.46

PW of EVA = 66.150.46

b). PW of the equipment's ATCFs:

Formula	Year end (n)	0	1	2	3	4	5	6	6
Capital outflow & inflow; Revenue - expense	Before-tax Cash Flow (BTCF)	(345,000)	112,000	112,000	112,000	112,000	112,000	112,000	120,000
From depreciation schedule	Depreciation (D)		69,000	110,400	66,240	39,744	39,744	19,872
BTCF - D	Taxable income (TI)		43,000	1,600	45,760	72,256	72,256	92,128	120,000
-50%*TI	Income tax (IT)		(21,500)	(800)	(22,880)	(36,128)	(36,128)	(46,064)	(60,000)
BTCF - IT	After-tax Cash Flow (ATCF)	(345,000)	90,500	111,200	89,120	75,872	75,872	65,936	60,000
1/(1+after-tax MARR)^n	Discount factor @ 10%	1.000	0.909	0.826	0.751	0.683	0.621	0.564	0.564
Discount factor*ATCF	Present Value (PVs) of ATCF	(345,000)	82,273	91,901	66,957	51,822	47,111	37,219	33,868
Sum of all PVs	PW of ATCF	66,150.46

PW of ATCFs = 66,150.46

Yes, the PW of EVA is equal to the PW of ATCFs.