# Net Present Value

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A Net Present Value is a microeconomic measure of the profitability of an undertaking that is calculated by subtracting the present values (PV) of cash outflows (including initial cost) from the present values of cash inflows over a period of time.

## References

### 2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/net_present_value Retrieved:2016-9-23.
• In finance, the net present value (NPV) or net present worth (NPW)[1] is a measurement of the profitability of an undertaking that is calculated by subtracting the present values (PV) of cash outflows (including initial cost) from the present values of cash inflows over a period of time. Incoming and outgoing cash flows can also be described as benefit and cost cash flows, respectively.[2] Time value of money dictates that time affects the value of cash flows. In other words, a lender may give you 99 cents for the promise of receiving \$1.00 a month from now, but the promise to receive that same dollar 20 years in the future would be worth much less today to that same person (lender), even if the payback in both cases was equally certain. This decrease in the current value of future cash flows is based on the market dictated rate of return. More technically, cash flows of nominal equal value over a time series result in different effective value cash flows that make future cash flows less valuable over time. If for example there exists a time series of identical cash flows, the cash flow in the present is the most valuable, with each future cash flow becoming less valuable than the previous cash flow. A cash flow today is more valuable than an identical cash flow in the future[3] because a present flow can be invested immediately and begin earning returns, while a future flow cannot. Net present value (NPV) is determined by calculating the costs (negative cash flows) and benefits (positive cash flows) for each period of an investment. The period is typically one year, but could be measured in quarter-years, half-years or months. After the cash flow for each period is calculated, the present value (PV) of each one is achieved by discounting its future value (see Formula) at a periodic rate of return (the rate of return dictated by the market). NPV is the sum of all the discounted future cash flows. Because of its simplicity, NPV is a useful tool to determine whether a project or investment will result in a net profit or a loss. A positive NPV results in profit, while a negative NPV results in a loss. The NPV measures the excess or shortfall of cash flows, in present value terms, above the cost of funds. [4] In a theoretical situation of unlimited capital budgeting a company should pursue every investment with a positive NPV. However, in practical terms a company's capital constraints limit investments to projects with the highest NPV whose cost cash flows, or initial cash investment, do not exceed the company's capital. NPV is a central tool in discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. It is widely used throughout economics, finance, and accounting.

In the case when all future cash flows are positive, or incoming (such as the principal and coupon payment of a bond) the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV can be described as the “difference amount” between the sums of discounted cash inflows and cash outflows. It compares the present value of money today to the present value of money in the future, taking inflation and returns into account.

The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputs a price. The converse process in DCF analysis — taking a sequence of cash flows and a price as input and inferring as output a discount rate (the discount rate which would yield the given price as NPV) — is called the yield and is more widely used in bond trading.

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3. Berk, DeMarzo, and Stangeland, p. 94.
4. erk, DeMarzo, and Stangeland, p. 64.