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		$77,700		$181,000
Estimated life		8 years		8 years
Salvage value		0		0
Estimated annual cash inflows		$20,500		$40,400
Estimated annual cash outflows		$5,070		$10,000

Click here to view PV table.

Calculate the net present value and profitability index of each machine. Assume a 9% discount rate.

Answer 1

	Computation	Machine A	Machine B
Purchase cost	a	$             77,700.00	$ 181,000.00
Estimated annual cash inflows	b	$             20,500.00	$             40,400.00
Estimated annual cash outflows	c	$ 5,070.00	$             10,000.00
Estimated annual net cash inflows	d = b - c	$             15,430.00	$             30,400.00
PVAF @ 9% for 8 years	e	5.5348	5.5348
Present value of annual net cash inflows	f = d × e	$             85,401.96	$ 168,257.92
Net present value	f - a	$                7,701.96	$           (12,742.08)
Profitability index	f ÷ a	1.10	0.93

Decision: Since machine B has a negative NPV and a profitability index less than 1, it should be rejected. And machine A should be accepted.

It is assumed that all cash flows are after-tax and also tax shield on depreciation is considered in the cash flows given.

Net present value

• Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over the life of an investment project.
• NPV is used to evaluate investment projects in capital budgeting.
• A project with a positive NPV is accepted. A positive NPV indicates that the project will result in net cash inflows in today's dollars.
• A project with a negative NPV is rejected. A negative NPV indicates that the project will result in net cash outflows in today's dollars.
• The cash flows are discounted at a required rate of return. It may be a weighted average cost of capital, cost of debt, etc.

Profitability index

• The profitability index is a ratio that expresses the relationship between the costs and benefits of a project.
• Profitability index = PV of future cash flows ÷ Initial investment
• Profitability index greater than 1: Project should be accepted (it indicates the present value of anticipated future cash inflows are more than the present value of cash outflows)
• Profitability index less than 1: Project should be rejected. (it indicates the present value of anticipated future cash inflows are less than the present value of cash outflows)
• Profitability index equal to 1: Project is indifferent. (it indicates the present value of anticipated future cash inflows equals the present value of cash outflows)
• In case of mutually exclusive projects, the project with the highest profitability index is accepted.