# Discounted cash flow

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In finance, discounted cash flow (DCF) analysis is a method of valuing a project, company, or asset using the concepts of the time value of money. All future cash flows are estimated and discounted to give their present values (PVs) – the sum of all future cash flows, both incoming and outgoing, is the net present value (NPV), which is taken as the value or price of the cash flows in question.

Using DCF analysis to compute the NPV takes as input cash flows and a discount rate and gives as output a price; the opposite process – taking cash flows and a price and inferring a discount rate, is called the yield.

Discounted cash flow analysis is widely used in investment finance, real estate development, and corporate financial management.

## Contents

### Discount rate

The most widely used method of discounting is exponential discounting, which values future cash flows as "how much money would have to be invested currently, at a given rate of return, to yield the cash flow in future". Other methods of discounting, such as hyperbolic discounting, are studied in academia and said to reflect intuitive decision-making, but are not generally used in industry.

The discount rate used is generally the appropriate Weighted average cost of capital (WACC), that reflects the risk of the cashflows. The discount rate reflects two things:

An alternative to including the risk in the discount rate is to use the risk free rate, but multiply the future cash flows by the estimated probability that they will occur (the success rate). This method, widely used in drug development, is referred to as rNPV (risk-adjusted NPV), and similar methods are used to incorporate credit risk in the probability model of CDS valuation.

### History

Discounted cash flow calculations have been used in some form since money was first lent at interest in ancient times. As a method of asset valuation it has often been opposed to accounting book value, which is based on the amount paid for the asset. Following the stock market crash of 1929, discounted cash flow analysis gained popularity as a valuation method for stocks. Irving Fisher in his 1930 book "The Theory of Interest" and John Burr Williams's 1938 text 'The Theory of Investment Value' first formally expressed the DCF method in modern economic terms.