We discount the cash flow in the first period (CF1) for one period, discount the cash flow received in the second period (CF2) for two periods, and so forth until we have discounted all of the cash flows. The present value is the sum of the discounted cash flows. We can shorten this formula using the summation symbol(pronounced sigma) to represent the sum of a series.

PV = CFt[ 1/ (1 + R) ]

These two equations are equal; they both represent the sum of a series of discounted cash flows. In the shortened version, the T at the top of the means that we end with the T (last) cash flow, and the t = 1 at the bottom means that we start the summation with the first cash flow.

Net Present Value of Cash Flows

The calculation for the present value of a series of cash flows may be used to find out how much an investor will be willing to pay for an investment. Because the investor has a specific required rate of return, it is unlikely that a rational investor will pay more than the present value for an investment.

Present value minus initial investment

The term net present value refers to an investor's position after making an investment. To calculate the net present value of an investment, we modify the present value formula by subtracting the initial investment from the present value calculation.

NPV = CFt[1/ (1 + R)]t ­ CF

Where:
NPV = Net present value of the project or investment
T = Number of cash flows generated by the project
CFt = Cash flow in period t
CF0 = Initial cash investment
R = Discount rate (required rate of return)

The original capital investment is often called the cash flow at time 0 (or present time) and is represented by the symbol CF0 The net present value (NPV) is equal to the sum of all the discounted cash flows minus the original payment made in order to receive the cash flows.

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