**Basic Valuation Model**

* Basic Valuation Model. *The general principle of valuation also applies to share or stock valuation. The value of a share today is a function of the cash inflows expected by the investors and the risk associated with the cash inflows. The cash inflows expected from an equity share will consist of the dividend expected to be received by the owner while holding the share and the price which he expected to obtain when the share is sold. The price which the owner is expected to receive when the share is sold will include the original investment plus a capital gain. It is normally found that a shareholder does not hold the share in perpetuity. He holds the share for some times, receives the dividends, and finally sells it to obtain capital gains. But when he sells the share, the buyer is also simply purchasing a stream of future dividends and liquidating price when he sells the share. The logic can be extended further.

The ultimate conclusion is that, for shareholders in general, the expected cash inflows consist only of future dividends and, therefore, the value of a common stock is determined by capitalizing the future dividend stream discounted by an appropriate discount rate known as investor’s required rate of return. Basic Valuation Model.

Thus, the value of a share is the present value of its future stream of dividends. The formula for calculating the present value is given as below:

P_{0} = D_{1}/(1 + k) + P_{1}/(1+k)

where,

P_{0} = price per share today,

D_{1}= dividend per share at the end of first year,

P_{1}= price per share at the end of first year,

k = investor’s required rate of return.

It a buyer wishes to hold a share for three years and then sell after purchasing it for P1 at the end of first year, the value of the same to him today will be:

P_{1}/(1+k) = D_{2}/(1 + k)^{2} + D_{3}/(1 + k)^{3} + D_{4}/(1 + k)^{4} + P_{4}/(1 + k)^{4}

The price at the end of the fourth year and all future prices are determined in a similar manner. The general formula for determining the value of the share at the present time can be written as follows:

P_{0} = D_{1}/(1 + k) + D_{2}/(1 + k)^{2} + D_{3}/(1 + k)^{3} + ………. + D_{n}/(1 + k)^{n}

_{n}

= ∑ D_{t}/(1 + k)^{t}

^{ t = 1}

It is obvious from the above equation that the present value of the share is equal to the capitalized value of an infinite stream of dividends. It should be noticed here that D_{t} in the equation are expected dividends. In fact investors estimate the dividends per share likely to be paid by the company in future period if time. These estimates are based on their subjective probability distributions Thus, The D_{t} are expected values or means of these **probability distributions**. Obviously, the present value of future sums would be lower than those future sums.

**Basic Valuation Model**