# Discounted Cash Flow

Discounted cash flow (DCF) is a method used to determine intrinsic value of stocks, bonds, real estate or any other investments by discounting their future expected net cash flows to time 0 using a discount rate appropriate for the risk inherent in those cash flows.

Investors must identify undervalued/overvalued investments and buy/sell them to earn money. Whether an investment is undervalued or overvalued depends on whether it is priced correctly. The price is available from recent transactions in market, but value is a subjective measure. A rational investor will assign value to any asset based on its future earnings potential after considering the risk involved. Discounted cash flow is such an approach to find present value of expected cash flows.

DCF approach has multiple applications including (a) net present value, a method that discounts present values of project cash flows and subtracts initial investment to identify feasible projects, (b) dividend discount model used to value a share of common stock representing a minority stake in a company, (c) free cash flow valuation to find equity value or enterprise value (i.e. total firm value of a business), (d) bond pricing based on coupon payments and redemption value, and (e) real estate valuation based on net operating income.

## Formula

The mechanics of DCF valuation are the same as that of time value of money. Value at time 0 of cash flows received from investments in future is determined using a discount rate.

Value of a dividend-paying stock using DCF analysis (Gordon Growth Model is worked out using the following equation:

$$\text{Stock Price}=\frac{\text{D} _ \text{1}}{\text{r}-\text{g}}$$

Where D1 is dividend (a cash flow) at the end of first year, r is the required return on equity (i.e. the cost of equity) and g is the growth rate of dividends. An advanced version of this model is the multi-stage dividend discount model which estimates near-future dividends (say for 5 years) individually and then finds a terminal value using the present value of perpetuity equation.

Enterprise value (i.e. value of whole firm inclusive of debt) can be estimated using the free cash flow model.

The simplest version assumes that the cash flows will stay constant forever.

$$\text{Enterprise Value}=\frac{\text{Free Cash Flow}}{\text{WACC}}$$

Where free cash flow (FCF) equals operating cash flow minus changes in working capital minus changes in capital expenditures and WACC is the firm-wide blended cost of capital. A more sophisticated version identifies actual incremental cash flow for say initial 5-10 years and then adds a terminal value:

$$\text{Enterprise Value}=\frac{\text{FCF1}}{{(\text{1}+\text{WACC})}^\text{1}}+\frac{\text{FCF2}}{{(\text{1}+\text{WACC})}^\text{2}}\\+\frac{\text{FCF3}}{{(\text{1}+\text{WACC})}^\text{3}}+\text{...}+\frac{\text{FCFn}}{{(\text{1}+\text{WACC})}^\text{n}}\\+\frac{\text{1}}{{(\text{1}+\text{WACC})}^\text{n}}\times\frac{\text{Terminal Cash Flow}}{{(\text{1}+\text{WACC})}^\text{n}}$$

The discount rate depends on the valuation purpose and the risk of the cash flows. We must match the cash flows with the discount rate, nominal (i.e. inflation adjusted cash flows) must be discounted using a nominal discount rate and real cash flows must be discounted with real rates. Further, cash flows representing equity position must be discounted using required return on equity and cash flows to firm (i.e. inclusive of interest) must be discounted using weighted average cost of capital.

## Example

Let’s illustrate application of DCF approach to a value a 5% stake in a company that pays dividends. The company paid dividend of $1.5 last year and its dividend per share is expected to be$1.75, $1.80,$1.90, $2.20 and$2.30 for next 5 years. Afterwards, dividends are expected to grow at a stable rate of 5% per annum. The company’s required return on equity is 12% and the weighted average cost of capital is 9%. We need to find the present value of cash flow received on each share of common stock. We have exact cash flows for first 5 years which we can discount individually using the present value factor. After the fifth year, the company’s growth will stabilize, and we can use the single stage dividend growth model to find terminal value which must be discounted 5 years to time 0.

The appropriate discount rate is the cost of equity because we are valuing a minority equity position. Please follow the equation below to identify DCF mechanics:

$$\text{Stock Value}=\frac{\text{\1.75}}{{(\text{1}+\text{12%})}^\text{1}}+\frac{\text{\1.80}}{{(\text{1}+\text{12%})}^\text{2}}\\+\frac{\text{\1.90}}{{(\text{1}+\text{12%})}^\text{3}}+\frac{\text{\2.20}}{{(\text{1}+\text{12%})}^\text{4}}+\frac{\text{\2.30}}{{(\text{1}+\text{12%})}^\text{5}}\\+\frac{\text{1}}{{(\text{1}+\text{12%})}^\text{5}}\times\frac{\text{\2.30}\times(\text{1}+\text{5%})}{\text{12%}-\text{5%}}\\=\text{\26.63}$$

We discounted the dividend per share in first 5 years to time 0 individually, determined the terminal value (i.e. value of dividends after 5th year) at the end of 5th year using the single-stage dividend discount model (same as the present value of perpetuity with growth) and then discounted that terminal value to time 0. If the current price is $22, we know that the investment is undervalued and is a good buy. If the current market price is$30, we know it is not a good investment.