# Stock Valuation

Stock valuation is the process of determining the intrinsic value of a share of common stock of a company. There are two approaches to value a share of common stock: (a) absolute valuation i.e. the discounted cashflow method and (b) relative valuation (also called the comparables approach).

The purpose of stock valuation is to find the value of a common share which is justified by the company earnings and growth potential, identify undervalued and overvalued stocks, overweight or underweight them in an investment portfolio and generate alpha i.e. excess return.

## Methods

There are two types of stock valuation methods namely:

- Discounted Cash Flow Methods
- Relative Valuation

### Discounted Cash Flow Methods

The absolute valuation approach attempts to find intrinsic value of a stock by discounting future cash flows at an discount rate which reflects the risk inherent in the stock. Hence, it is also called discounted cash flow approach. Common discounted cash flow valuations model includes single-stage dividend discount model (also called Gordon Growth Model), multi-stage dividend discount model and free cash flow valuation.

#### Constant Growth DDM

The constant growth dividend discount model (also called single-stage dividend discount model or Gordon Growth Model) is appropriate for valuation of a minority stake in mature dividend-paying companies. Stock value under the DDM equals the discounted present value of dividends per share expected to grow at a constant rate.

$$ Stock\ Value\ (DDM)=\frac{D_0\times(1+g)}{r-g} $$

Where **D _{0}** is current dividend per share per annum,

**r**is the required return on equity (i.e. cost of equity) and

**g**is the growth rate of dividends. g is the sustainable growth rate which equals the product of retention ratio (1 – dividend payout ratio) and return on equity (ROE):

$$ g=(1\ -\ dividend\ payout\ ratio)\times ROE $$

#### Multi-stage DDM

The multi-stage dividend discount model can be used to value minority stake in companies which are expected to have abnormal growth rate for some initial period, say 5 years, and the growth rate is expected to stabilize in the long-run. Dividend per share per annum are forecasted based on actual growth rate in initial years, the value of stock at the end of initial high-growth period (called terminal value) is determined using the single-stage dividend growth model or using some price multiple such as P/E ratio and the dividends and the terminal value are discounted at the required return on equity (i.e. cost of equity).

$$ Stock\ Value\ =\ \frac{D_1}{{(1+r)}^1}+\frac{D_2}{{(1+r)}^2}+...+\frac{D_n}{{(1+r)}^n}+\frac{V_n}{{(1+r)}^n} $$

Where D_{1}, D_{2} and D_{n} are the dividend per share at the end of Year 1, Year 2 and Year n and V_{n} is the terminal value.

#### Free Cash Flow Models

The free cash flow valuation models can be used to value a majority i.e. controlling ownership based on free cash flows of the company which equals the cash flows from operating activities less any expected changes in working capital less any expected capital expenditure.

The single-stage free cash flow model discounts the expected free cash flows at the end of Year 1 at the weighted average cost of capital.

$$ Stock\ Value\ =\frac{{\rm FCF}_1}{w-g} $$

Where **FCF _{1}** is the free cash flow at the end of Year 1,

**w**is the weighted average cost of capital and

**g**is the growth rate of free cash flows.

Stock value under the multi-stage free cash flow valuation model can be determined as follows:

$$ Stock\ Value\ =\ \frac{{\rm FCF}_1}{{(1+w)}^1}+\frac{{\rm FCF}_2}{{(1+w)}^2}+...+\frac{{\rm FCF}_n}{{(1+w)}^n}+\frac{V_n}{{(1+w)}^n} $$

The value determined using the free cash flow models is the total firm value and the market value of debt must be subtracted to arrive at the equity value.

There are two other free cash flow models which discount free cash flow to equity (FCFE) (instead of the free cash flow to firm) using the required return on equity (instead of the weighted average cost of capital). The value determined using free cash flow to equity (FCFE) models is the equity value.

### Relative Valuation

In relative valuation, value of a stock is determined with reference to market value of comparable stocks. Price multiples of comparable companies such as price to earnings (P/E) ratio, price to book ratio, price to sales ratios are calculated and the average is multiplied with earnings per share, book value per share or sales per share of the company respectively to arrive at the stock’s relative value.