## What is DCF Formula (Discounted Cash Flow)?

Discounted Cash Flow (DCF) formula is an Income-based valuation approach and helps in determining the fair value of a business or security by discounting the future expected cash flows. Under this method, the expected future cash flows are projected up to the life of the business or asset in question, and the said cash flows are discounted by a rate called the Discount Rate to arrive at the Present Value.

The basic formula of DCF is as follows:

**DCF Formula =CF**

_{t}/( 1 +r)^{t}Where,

- CFt = cash flow in period t
- R = appropriate discount rate given the riskiness of the cash flows
- t = life of the asset, which is valued.

It is not possible to forecast cash flow till the whole life of a business, and as such, usually, cash flows are forecasted for a period of 5-7 years only and supplemented by incorporating a Terminal Value for the period thereafter. Terminal Value is basically the Estimated Value of business beyond the period for which cash flows are forecasted. It is a very important part of the Discounted Cash flow formula and accounts for as much as 60%-70% of the Firm’s value and thus warrants due attention.

The terminal value of a business is calculated using the Perpetual growth rate method or Exit Multiple Method.

Under the Perpetual Growth Rate Method, the terminal value is calculated as

**TV**

_{n}= CFn (1+g)/( WACC-g)Where,

- TV
_{n }Terminal Value at the end of the specified period - CF
_{n }represents the cash flow of the last specified period - g is the growth rate
- WACC is the Weighted Average Cost of Capital.

Under the Exit Multiple methods, the terminal value is calculated using multiple of EV/EBITDA, EV/Sales, etc., and giving a multiplier to it. For instance, using Exit multiple ones can value the Terminal with ‘x’ times the EV/EBITDA sale of the business with the cash flow of Terminal Year.

### FCFF and FCFE used in DCF Formula Calculation

The discounted Cashflow (DCF) formula can be used to value the FCFF or Free Cash flow to Equity.

Let’s understand both and then try to find the relation between the two with an example:

#### #1 – Free Cashflow to Firm (FCFF)

Under this DCF calculation approach, the entire value of the business, which includes besides equities, the other claim holders in the firm as well (debt holders, etc.). The cash flows for the projected period under FCFF are computed as under

**FCFF=Net income after tax+ Interest * (1-tax rate) + Non cash expenses (including depreciation & provisions) – Increase in working capital – Capital expenditure**

These Cash flows calculated above are discounted by the Weighted Average Cost of Capital (WACC), which is the cost of the different components of financing used by the firm, weighted by their market value proportions.

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**WACC=Ke*(1-DR) + Kd*DR**

where

- Ke represents the cost of equity
- Kd represents the cost of debt
- DR is the debt proportion in the company.

Cost of Equity (Ke) is computed by using the CAPM as under:

**Ke=Rf + β * (Rm-Rf)**

where,

- Rf represents the risk-free rate
- Rm represents the market rate of return
- β – Beta represents a systematic risk.

Finally, all the numbers are added to arrive at the enterprise value as under:

**Enterprise Value Formula ** = PV of the (CF1,CF2…..CFn) + PV of the TVn

#### #2 – Free Cashflow to Equity (FCFE)

Under this DCF Calculation method, the value of the equity stake of the business is calculated. It is obtained by discounting the expected cash flows to equity, i.e., residual cash flows after meeting all expenses, tax obligations, and interest and principal payments. The cash flows for the projected period under FCFE are calculated as under:

**FCFE=FCFF-Interest * (1-tax rate)-Net repayments of debt**

The above cash flows for the specified period are discounted at the cost of equity (Ke), which was discussed above, and then the Terminal Value is added (discussed above) to arrive at the Equity Value.

### Example of DCF Formula (with Excel Template)

**Let’s understand how Enterprise/Firm Value and Equity Value is calculated using a Discounted Cash Flow Formula with the help of an example:**

The following data is used for the calculation of Value of Firm and Value of Equity using the DCF Formula.

Also, assume that cash at hand is $100.

#### Valuation using FCFF Approach

First, we have calculated the Value of the Firm using the DCF Formula as follows.

**Cost of Debt**

Cost of Debt is 5%

**WACC**

- WACC = 13.625% ($1073/$1873)+5%( $800/$1873)
- = 9.94%

Calculation of Value of Firm using DCF Formula

Value of Firm= PV of the (CF1, CF2…CFn) + PV of the TVn

- Enterprise Value = ($90/1.0094) + ($100/1.0094^2) + ($108/1.0094^3) + ($116.2/1.0094^4) + ({$123.49+$2363}/1.0094^5)

**Value of Firm using DCF Formula**

Thus Value of the Firm using a Discounted Cash flow formula is $1873.

- Value of Equity = Value of the Firm – Outstanding Debt + Cash
- Value of Equity = $1873 – $800+ $100
- Value of Equity = $1,173

#### Valuation using FCFE Approach

Let us now apply DCF Formula to calculate the value of equity using the FCFE approach

Value of Equity= PV of the (CF1, CF2…CFn) + PV of the TVn

Here Free Cash flow to Equity (FCFE) is discounted using the Cost of Equity.

- Value of Equity= ($50/1.13625) + ($60/1.13625^2) + ($68/1.13625^3) + ($76.2/1.13625^4) + ({$83.49+$1603}/1.13625^5)

**Value of Equity using DCF Formula**

Thus Value of Equity using a Discounted Cash flow (DCF) formula is $1073.

Total Value of Equity = Value of Equity using DCF Formula + Cash

- $1073 + $100 = $1,173

### Conclusion

The discounted Cash flow (DCF) formula is a very important business valuation tool which finds its utility and application in the valuation of an entire business for mergers acquisition purpose. It is equally important in the valuation of Greenfield Investments. It is also an important tool in the valuation of securities such as Equity or a Bond or any other income generating asset whose cash flows can be estimated or modeled.

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