Net Present Value If offered an investment that costs $5,000 today and promises to pay

Net Present Value If offered an investment that costs $5,000 today and promises to pay

you $7,000 two years from today and if your opportunity cost for projects of similar risk is 10%, would you make this investment? You need to compare your $5,000 investment with the $7,000 cash flow you expect in two years. Because you feel that a discount rate of 10% reflects the degree of uncertainty associated with the $7,000 expected in two years, today it is worth:

Present value of $7,000 to be received in two years

$7,000 = ----------------------------- = $5,785.12

By investing $5,000 today, you are getting in return a promise of a cash flow in the future that is worth $5,785.12 today. You increase your wealth by $785.12 when you make this investment.

Another way of stating this is that the present value of the $7,000 cash inflow is $5,785.12, which is more than the $5,000, today’s cash outflow to make the investment. When we subtract the $5,000 from the present value of the cash inflow from the investment, the difference is the increase or decrease in our wealth referred to as the net present value.

The net present value (NPV) is the present value of all expected cash flows.

Net Present Value = Present value of all expected cash flows

Capital Budgeting Techniques

or, in terms of the incremental operating and investment cash flows, Net present value = Present value of the change in operating cash flows

+ Present value of the investment cash flows The term “net” is used because we want to determine the difference

between the change in the operating cash flows and the investment cash flows. Often the change in operating cash flows are inflows and the investment cash flows are outflows. Therefore we tend to refer to the net present value as the difference between the present value of the cash inflows and the present value of the cash outflows.

We can represent the net present value using summation notation, where t indicates any particular period, CF t represents the cash flow at the end of period t, r represents the cost of capital, and N the number of periods comprising the economic life of the investment:

CF

NPV =

∑ (13-1)

------------------ t

Cash inflows are positive values of CF t and cash outflows are negative values of CF t . For any given period t, we collect all the cash flows (posi- tive and negative) and net them together. To make things a bit easier to track, let’s just refer to cash flows as inflows or outflows, and not specif- ically identify them as operating or investment cash flows.

Let’s take another look at Investments A and B. Using a 10% cost of capital, the present values of inflows are:

Investment A Investment B End of Year

End of Year Value at the Year

Value at the

Cash Flow

End of 2000

Cash Flow End of 2000

1,000,000 620,921 Present value of the cash inflows

$1,552,620 The present value of the cash outflows is the outlay of $1,000,000. The

net present value of A is $516,315:

LONG-TERM INVESTMENT DECISIONS

NPV of A = $1,516,315 − $1,000,000 = $516,315

and the Net Present Value of B is $552,620:

NPV of B = $1,552,620 − $1,000,000 = $552,620

These NPVs tell us if we invest in A, we expect to increase the value of the firm by $516,315. If we invest in B, we expect to increase the value of the firm by $552,620.