# Discounted Cash Flow Formula

The value of most investments is generally equal to the present value of its future cash flows. So 1 method of estimating the value of an asset or a business is by calculating the discounted cash flow that the asset will earn. The price of a bond, for instance, is equal to the cash flows of each interest payment plus the principal repayment, discounted by the bond yield. In short, the present value of an asset is the value of its cash flows, discounted by the investor's required rate of return, calculated thus:

PV | = | n ∑ k=1 | CF_{k}(1+r) ^{k} |

PV = Present Value of Cash Flows Discounted by rate of return r CF _{k} = cash flow at time kr = rate of return per time period n = number of cash flows |

This is nothing more than calculating the present value of an annuity, where the cash flows are equal to the annuity payments.

## Calculating a Business Value Using Discounted Cash Flow

An investor in a business receives cash flows in the form of income earned while holding the interest and capital gains when the business interest is sold. For a shareholder of a corporation, income is received as dividends and capital gains is received when the shares are sold (if the investment was profitable). So the value of the investment can be calculated by discounting the cash flows of the dividend payments plus the expected capital gain.

From the constant-growth dividend discount model, we can infer the market capitalization rate, k, or the required rate of return, demanded by investors. Note that:

Capitalization Rate = Dividend Yield + Capital Gains Yield

If a stock is held for 1 year, and is bought and sold for its intrinsic value, then the following **discounted cash flow formula** calculates the **market capitalization rate**:

Capitalization Rate (k) | = | Dividend Yield | + | Capital Gains Yield |

= | D_{1}P _{0} | + | P_{1} - P_{0}P _{0} | |

= | D_{1}P _{0} | + | P_{0}(1+g) - P_{0}P _{0} | |

= | D_{1}P _{0} | + | g | |

g = Dividend Growth Rate |

Often, this is how rates are determined for public utilities by the agencies responsible for setting public rates. Public utilities are generally allowed to charge rates that cover their costs plus a fair market return, with the fair market return being the market capitalization rate.

## Example—Calculating the Market Capitalization Rate

If a stock, with an average risk, has a current market price of $40, pays a $1 quarterly dividend, and is growing 6% annually, then the market capitalization rate based on this information would be:

**Market Capitalization Rate** = $1 × 4 / $40 + 0.06 = 0.16 = **16%**

Hence, we can infer that the market is demanding a required rate of return of 16% for compensating them for the risk of owning stock.