The shareholders buy shares with the expectations of receiving dividends and increase in the value of the shares. A conscious investor buys shares when they are undervalued and sell them when they are overvalued. Under valuation means the shares’ true value is more than their market value and overvaluation means their true value is less than the market value. The true value of a share is the present value of all future dividends over an indefinite time period. As the future dividends keep on growing therefore it’s become imperative to compute the value of the share with respect to expected growth pattern of future dividends. According to growth theory the valuation models can be categorized into three broad categories.

• Zero Growth Model
• Constant Growth Model
• Variable Growth Model

### Zero Growth Model

If a firm pays constant dividend every year the value of the share is calculated under the zero growth model. This model assumes no growth in dividend and value of share would equal the present value of perpetuity of dividends discounted at the required rate of return. Symbolically,

P = D1 / Ke

Where,

P   = Price of the share
D1 = Constant dividend per share
Ke = required rate of return for investors

Example

A firm pays dividend of \$10 constantly over an indefinite time horizons. Required rate of return for investors is 16%. Compute the value of the share.

Solution

P = \$10 / 0.16 = \$62.5

### Constant Growth Model

When dividends grow at a constant rate every year the value of the share is determined through constant growth model. This model also called Gordon Model. The value of the share is given by the following equation.

P = D1 / Ke – G

Where,

P    = Price/value of the share
Ke  = Required return
G    = Growth rate in dividend

Example

A firm paid the dividends over the six years at constant growth rate of 7%. Required rate of return is 16% and in year 7 DPS expected is \$3. Compute the value of the share.

Solution

P = \$3 / 0.16 – 0.07 = \$33.3%

### Variable Growth Model

Most of the firms pay dividends over the years with some growth rate and after that the growth rate is changed. In this case computations of value of the share become more complex because it incorporates the changes in the dividend payment over the years. In this model the share value is determined through following steps:

1. Compute the present values of the expected cash dividends for the initial growth years and compute the sum total.

2. Find out the value of the share at the end of year from which dividend growth is expected to change.

3. Determine the present value of the value of the share computed in step 2.

4.Add the values calculated in step 1 and 3, which is the value of the share.

The above-mentioned steps can be more precisely understood through the use of this example.

Example

A firm pays \$3 dividend per share in the currently, which is expected to grow at 10% for the next three years after which growth rate will decrease to 5% forever. Assuming 15% required rate of return compute the value of the share.

Solution

Step 1

Present value of dividends for first three years.

 Year end DPS after growh 10% (\$) PVIF 15%,1to3 PV (\$) 1 3.3 0.87 2.87 2 3.63 0.756 2.75 3 4 0.0658 2.63 8.25

Step 2

Dividend expected in year 4 after the growth of 5% = \$4.2

Price at the end of year 3 = P = \$4.2 / 0.15 – 0.05 = \$42

Step 3

Present Value = P3 x PVIF 15%, 3 = \$42 x 0.658 = \$27.64

Step 4

Value of the share = P = \$8.25 + \$27.64 = \$35.89

### Other Approaches to The Valuation of Shares

In addition to above there are other valuation techniques for common shares. These approaches are:

• Book value approach
• Liquidation value
• Price / Earning multiples

### Book Value Approach

Under book value approach the value of the share is book worth divided by number of equity shares. Book worth is the equity capital plus reserves and surpluses. The above statement can be described, as that book value per share is the amount per share on the sale of the assets of the firm at their exact book value minus all liabilities including preference shares.

### Liquidation Value

Liquidation value per share is based on the concept that if all assets are sold, liabilities including preference shares are paid, and any remaining amount is divided among common stock holders.

### P/E Ratio

This is a technique to compute value of the shares multiplying expected return per share by the average price / earning ratio for the industry.