Question

A firm is examining some alternatives to invest their money. All the alternatives have the same useful life, 10 years. The interest rate is 7% and the firm has a flat tax rate of 31%. The options are summarized in the following table. Alternatives First Cost Annual Costs Annual Benefits Dep. Method A $17,000 $900 $4,500 SL $25,000 $1,050 $3,250 SOYD $22,000 $1,125 $5,125 MACRS (7-yr) B С What is the after-tax benefit-cost ratio for project C?

Answer 1

Alternative C		Cost of Asset	22,000
Year	Initial Cost	Net Annual Benefits	Depreciation	Before tax income	Tax @ 31%	After tax cash flow	PVF @ 7%	PV of Cost	PV of Benefits		Year	Rate	Depreciation
N	A	B	C	D=B-C	E=D*31%	F=D-E+C	G=1/1.07^N	H=A*G	I=F*G		Year 1	14.29%	3,144
-	22,000						1.000	22,000	-		Year 2	24.49%	5,388
1		4,000	3,144	856	265	3,735	0.935		3,490		Year 3	17.49%	3,848
2		4,000	5,388	-1,388	-430	4,430	0.873		3,870		Year 4	12.49%	2,748
3		4,000	3,848	152	47	3,953	0.816		3,227		Year 5	8.93%	1,965
4		4,000	2,748	1,252	388	3,612	0.763		2,755		Year 6	8.92%	1,962
5		4,000	1,965	2,035	631	3,369	0.713		2,402		Year 7	8.93%	1,965
6		4,000	1,962	2,038	632	3,368	0.666		2,244		Year 8	4.46%	981
7		4,000	1,965	2,035	631	3,369	0.623		2,098
8		4,000	981	3,019	936	3,064	0.582		1,783
9		4,000	-	4,000	1,240	2,760	0.544		1,501
10		4,000	-	4,000	1,240	2,760	0.508		1,403
							Total	22,000	24,774
							Benefit Cost ratio		1.13	(24,774/22,000)

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