Question

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BAK Corp. is considering purchasing one of two new diagnostic machines. Either machine would make it possible for the company to bid on jobs that it currently isn’t equipped to do. Estimates regarding each machine are provided below.

		Machine A		Machine B
Original cost		$74,500		$183,000
Estimated life		8 years		8 years
Salvage value		0		0
Estimated annual cash inflows		$20,300		$40,200
Estimated annual cash outflows		$5,100		$9,810

Click here to view PV table.

Calculate the net present value and profitability index of each machine. Assume a 9% discount rate. (If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round answer for present value to 0 decimal places, e.g. 125 and profitability index to 2 decimal places, e.g. 10.50. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

		Machine A		Machine B
Net present value
Profitability index

Which machine should be purchased?

Machine BMachine A should be purchased.

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Answer 1

Net present value is difference between present value of cash inflow and cash outflow

Higher the NPV better the machine

Machine A

year	Cash flow	PV factor	present value of cash flow
0	-$74,500	1	-$74,500
1-8	$15,200	5.53482 [P/A,9%,8YEARS]	$84129	net cash flow= inflow-outflow =20300-5100 =$15,200
		Net Present Value	$9,629	[$84,129-$74,500]

we will use PV factor annuity as there is continuous cash flow for eight years

[1/1.09]¹+[1/1.09]²+[1/1.09]³+[1/1.09]⁴+[1/1.09]⁵+[1/1.09]⁶+[1/1.09]⁷+[1/1.09]⁸+[1/1.09]⁹

^=5.5348

^{MACHINE B}

year	Cash flow	PV factor	present value of cash flow
0	-$183,000	1	-$183,000
1-8	$30,390	5.53482 [P/A,9%,8YEARS]	$168203 [30390*5.53482]	net cash flow= inflow-outflow =40,200-9,810 =$30,390
		Net Present Value	-$14,797	[168203-183000]

machine B NPV is negative as present value of cash inflow is lower than cash outflow.

profitability index

= present value of cash inflow/ cash outflow

profitability index higher than 1 is recommended for acceptance of machine/project

MACHINE A =84129/74500

=1.13

MACHINE B = 168203/183000

=0.92

Analysis

MAchine A should be purchased as it have higher NPV and better profitability index than Machine B