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		$179,000
Estimated life		8 years		8 years
Salvage value		0		0
Estimated annual cash inflows		$19,900		$40,400
Estimated annual cash outflows		$4,890		$9,940

Click here to view the factor 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		enter a dollar amount rounded to 0 decimal places		enter a dollar amount rounded to 0 decimal places
Profitability index		enter the profitability index rounded to 2 decimal places		enter the profitability index rounded to 2 decimal places

Which machine should be purchased?

select a machine                                                          Machine B/Machine A should be purchased.

Answer 1

Solution

BAK Corp

1. Calculation of net present value of each project:

	Machine A	Machine B
Net Present Value	$6,478	($10,409)

Computations:

Net present value = present value of cash inflows – present value of cash outflows

Machine A

Present value of cash inflows = net annual cash inflows x (P/A, 9%, 8)

Net cash inflows = 19,900 – 4,890 = $15,010

(P/A, 9%, 8) = 5.53482

Present value of cash inflows = 15,010 x 5.53482 = $83,078

Add: present value of salvage value = 0

Present value of cash outflow = ($76,600)

Net present value = 83,078 – 76,600 = $6,478

Machine B

Present value of cash inflows = net annual cash inflows x (P/A, 9%, 8)

Net cash inflows = 40,400 – 9,940 = 30,460

(P/A, 9%, 8) = 5.53482

Present value of cash inflows = 30,460 x 5.53482 = $168,591

Add: present value of salvage value = 0

Less: present value of cash outflows = ($179,000)

Net present value = 168,591 – 179,000 = ($10,409)

Hence, Machine A earns a positive net present value of $6,478, while Machine B earns a negative net present value of $10,409 at the given discount rate of 9% for estimated life of 8 years.

2. Profitability Index:

	Machine A	Machine B
Profitability Index	1.08	0.94

Computations:

Profitability index = present value of cash inflows/present value of cash outflows

Machine A

Present value of cash inflows = $83,078

Present value of cash outflows = $76,600

Profitability index = 83,078/76,600 = 1.08

Machine B

Present value of cash inflows = 168,591

Present value of cash outflows = 179,000

Profitability index = 168,591/179,000 = 0.94

The profitability index of Machine A is more than 1, while the profitability index of Machine B is less than 1.

Machine A should be purchased. Machine B should be rejected.

Explanation:

The net present value and the profitability index of Machine A are positive and more than 1 at the given discount rate of 9%. Hence, it is profitable for the company to invest in Machine A.