Question

A firm is considering the following investment project:

Year	Before Tax Cash Flow (thousands)
0	-1,000
1	500
2	340
3	244
4	100
5	100 125 Salvage Value

The project has a 5 year useful life with a $125,000 salvage value as shown. Double declining balance depreciation will be used. The combined income tax rate is 24% (21% federal, and 3% state). If the firm requires a 10% after tax rate of return, should this project be undertaken?

Answer 1

First we estimate depreciation allowed for each year.

We have converted cash flows from thousand dollar to dollars for better accuracy

Initial Cost=-$1000000

Useful life=n=5

DDB depreciation rate=200%/5=40%

Salvage value=$125000

Year	Initial BV	Depreciation @40%	Depreciation allowed	Year End BV
0	1000000	0	0	1000000
1	1000000	400000	400000	600000
2	600000	240000	240000	360000
3	360000	144000	144000	216000
4	216000	86400	86400	129600
5	129600	51840	4600	125000

(If 5th year depreciation allowed is calculated such a way that Closing BV = Salvage value)

(Depreciation allowed in 5th year=129600-125000=$4600)

Now we estimate Interest factors (PVFn) needed for calculating PW of cash flows

n	PVFn=(P/F,10%,n)
0	1/(1+10%)0=	1.000000
1	1/(1+10%)1=	0.909091
2	1/(1+10%)2=	0.826446
3	1/(1+10%)3=	0.751315
4	1/(1+10%)4=	0.683013
5	1/(1+10%)5=	0.620921

Now, we estimate NPW of project

Year , n	BTCF	Deprectaion allowed, D	Tax= (BTCF-D)*24%	ATCF=BTCF+Tax	Interest factor, PVFn	PW of cash Flow= ATCF*PVFn
0	-1000000	0	0	-1000000	1.000000	-1000000.00
1	500000	400000	-24000	476000	0.909091	432727.27
2	340000	240000	-24000	316000	0.826446	261157.02
3	244000	144000	-24000	220000	0.751315	165289.26
4	100000	86400	-3264	96736	0.683013	66071.99
5	100000	4600	-22896	77104	0.620921	47875.52
5	125000	0	0	125000	0.620921	77615.17
NPW						50736.23

NPW of project=Sum of PW of individual PW of cash flows=$50736,23 or $50.74 thousand

NPW of project is positive at 10% after tax return. It should be undertaken.