Question

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		$76,600		$187,000
Estimated life		8 years		8 years
Salvage value		0		0
Estimated annual cash inflows		$20,400		$40,400
Estimated annual cash outflows		$5,190		$10,130

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				-19461.03
Profitability index		1.099		.91

Answer 1

	Machine A	Machine B
Net Present Value	7585	(19461)
Profitability Index	1.10 or 1.09	0.89 or 0.90

Explanation and calculation

Net Present value is the Present value cash inflows less Present value of cash outflow at the given discounted rate.

Net Present value = - Initial Investment + Present Value of Cash Flow + PV of Salvage

As in the given question annual Cash inflow and outflow are same over the year . So instead of calculating Present value annually we can directly take Annuity factor for 8 year

Check present value anuuity table for 9% for 8th year and if Only Present value table is provided that add all factory upto 8 year.

Calculation of Net Present value

	Machine A	Machine B
Annual CASH Inflows	20400	40400
Annual CASH outflows	5190	10130
Net Annual Cash flow ( a-b ) (C)	15210	30270
Present value annuity factor @9 % , for 8 year ( See Table of Present value of Annuity	5.53482	5.53482
Present value of Cashflows ( C × PVAF )	84185	167539
Initial Investment	76600	187000
Net Present Value ( NPV ) ( PV of Inflows - Initial outflow)	7585	(19461)

ii) Profitability index, also known as profit investment ratio and value investment ratio, is the ratio of payoff to investment of a proposed project.

Profitability index = Present value of future cash flows ÷ Initial Investment

	Machine A	Machine B
PI	84185÷76600	167539÷187000
	1.09 or 1.10	0.89 or 0.90