Question

Your firm is contemplating the purchase of a new $495,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $41,000 at the end of that time. You will be able to reduce working capital by $66,000 at the beginning of the project. Working capital will revert back to normal at the end of the project. The tax rate is 22 percent and the required return on the project is 10 percent. a. If the pretax cost savings are $150,000 per year, what is the NPV of this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. If the pretax cost savings are $115,000 per year, what is the NPV of this project? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. NPV b. NPV c. Cost savings

Answer 1

Solution:

Serial No	Particulars	Amount ( In $ )	Reference
a)	NPV	69,123.06	Working Note a)
b)	NPV	-34,365.42	Working Note b)
c)	Cost saving ( pre tax)	126,644.34	Working Note c)

Working Note a)

Calculation of Present Cash outflows ( In $)

Particulars	Amount ( In $)
a)Purchase of New Computer Based order entry system	495,000
b)Less: Release of Working Capital at the beginning ( Year 0)	66,000
c)Add: Reversion of Working Capital at the end of the period ( Year 5 ) $66,000*0.621	40,980.80
Net Cash Outflow (a-b+c)	469,980.80

b) Calculation of Discounted Cash savings

Years	Pretax Cost Saving ( In $) (a)	Tax Rate (b) (%)	Post Tax Cost saving( $)c= a( 1-b)	Depreciation (In $) d ( Note)	Tax Saving In Depreciation (In $) e= d*b	Net Cash Saving f= c+e	Discounting factor @ 10% (g)	Discounted Value ( In $) h= (f*g)
1	150,000	22	117,000	90,800	19,976	136,976	0.909	124,523.63
2	150,000	22	117,000	90,800	19,976	136,976	0.826	113,203.30
3	150,000	22	117,000	90,800	19,976	136,976	0.751	102,912.09
4	150,000	22	117,000	90,800	19,976	136,976	0.683	93,556.45
5	150,000	22	117,000	90,800	19,976	136,976	0.621	85,051.32
				Net Cash Inflows				519,246.80

Cash flows at the terminal period

Particulars	Amount ( In $)
a)Present Value of Salvage Value at the end ( 41,000*0.621)	25,457.77
b) Less: Tax Expenses @ 22% ( 41,000*0.621* 22%)	5600.71
Net Cash Inflow at the end (a-b)	19,857.06

Total Cash Inflows = $ 519,246.80+$19,857.06= $539,103.86

Net Present Value = Total Cash Inflows - Total Cash outflows = $ 539,103.86-469,980.80= $69,123.06

Note:

Depreciation for Straight Line = $(495,000-$41,000)/5= 90,800

Working Note b)

When pretax cost saving is $ 115,000 per year

Years	Pretax Cost Saving ( In $) (a)	Tax Rate (b) (%)	Post Tax Cost saving( $)c= a( 1-b)	Depreciation (In $) d ( Note)	Tax Saving In Depreciation (In $) e= d*b	Net Cash Saving f= c+e	Discounting factor @ 10% (g)	Discounted Value ( In $) h= (f*g)
1	115,000	22	89,700	90,800	19,976	109,676	0.909	99,705.45
2	115,000	22	89,700	90,800	19,976	109,676	0.826	90,641.32
3	115,000	22	89,700	90,800	19,976	109,676	0.751	82,401.20
4	115,000	22	89,700	90,800	19,976	109,676	0.683	74,910.18
5	115,000	22	89,700	90,800	19,976	109,676	0.621	68,100.16
				Net Cash Inflows				415,758.32

Net Cash Flows at terminal Values

Cash flows at the terminal period

Particulars	Amount ( In $)
a)Present Value of Salvage Value at the end ( 41,000*0.621)	25,457.77
b) Less: Tax Expenses @ 22% ( 41,000*0.621* 22%)	5600.71
Net Cash Inflow at the end (a-b)	19,857.06

Net Cash inflows ( In $) = 415,758.32+19,857.06 = $ 435,615.38

Net Present Values = $ 435,615.38 - $ 469,980.80 (as earlier computed in working note a)= -34,365.42

Working Note c)

Let the pretax cost saving be x

For Indifferent point,

Net Cash inflows = Net Cash outflows

Therefore Net Cash Inflows = Present Value of Post tax savings + Present Value of Tax shield on Depreciation + Terminal Cash Inflows.

Calculation of post tax savings = x(1-0.22) = 0.78x

Present Value of annuity factor ( 10% , 5 years) = 3.790786

Present Value of Post tax savings = 0.78x*3.790786

Present Value of Tax shield on Depreciation = 90,800*22%*3.790786= $75,724.74

Terminal Cash Inflow = 19,857.06

Net Cash Outflows= $469,980.80

Indifference Point

0.78x*3.790786+75724.74+19,857.06= 469,980.80

$\equiv$ 2.9568x+75724.74+19,857.06= 469,980.80

$\equiv$2.9568x+95,518.80= 469,980.80

$\equiv$2.9568x= 469,980.80-95,518.80

$\equiv$x= (469,980.80-95,518.80)/2.9568

$\equiv$x= 374,462/2.9568

$\equiv$x = 126,644.34

Therfore , Pre tax saving would be Indifferent at $ 126,644.34

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