Models for the Valuation of Shares

Topics: Time value of money, Stock, Stock market Pages: 7 (1393 words) Published: January 12, 2014
2.1 The concept of a cost of equity
The cost of equity is the cost to the company of providing equity holders with the return they require on their investment. The primary financial objective is to maximize the return to equity shareholders. This return is as the future dividend yield and capital growth.

Until new shareholders become members of the company, the objective above is concerned with existing shareholders. Company management will need to offer new shareholders the minimum acceptable future return on the funds they put into the company, thereby retaining as much benefit as possible for existing shareholders. In practice, this return will be such as to provide new shareholders with the same future returns as existing shareholders expect to obtain on their investment at market values.

For example if the future return on ABC plc's shares is 15% and future return on new issue is 20% if this is viewed quite simplistically, investors would sell their existing shares and take up the new offer. The price of existing shares would fall, and as a result the percentage return would increase, until it matched the 20% of new shares. This would mean existing shareholders would suffer a capital loss as the price of their shares declined. Thus, the object of management must be to offer the shares so as to provide a return identical to that of existing shares (in this case 15%). They could not offer less than 15% as it might then be difficult to find investors for the new issue. Note: in all cases the relevant return is the future return anticipated by shareholders. Thus, the problem of determining the cost of new equity becomes the problem of establishing the anticipated market return on existing equity.

The cost of equity ,equals the rate of return which investors expect to achieve on their equity holdings.

2.2 Anticipated rate of return on existing equity
The anticipated rate of return on a share acquired in the market consists of two components:

Component I - Dividends paid until share sold
Component 2 - Price when sold
In this sense, the returns are directly analogous to those on a debenture, with dividends replacing interest and sale price replacing redemption price.
Applying the concept of compound interest, in making a purchase decision it is assumed that the investor discounts future receipts at a personal discount rate (or personal rate of time preference). For the illustration below I will define this rate as 'i'.

In order to make a purchase decision, the shareholder must believe the price is below the value of the receipts, i.e, Current price, Po < Dividends to sale + Sale price Discounted at rate i
Algebraically, if the share is held for n years then sold at a price Pn and annual dividends to year n are D1, D2, D3, ...Dn Then:

Po < D1/(1+i)¹ + D2/(1+i)² + D3/(1+i)³ + (Dn + Pn)/(1+i)Ķ By similar logic, the seller of the share must believe that
Po > D1/(1+i)¹ + D2/(1+i)² + D3/(1+i)³ + (Dn + Pn)/(1+i)Ķ These different views will occur for two reasons.
(a) Different forecasts for D1, D2 etc and for Pn by the different investors. (b) Different discount rates being applied by different investors. However, since the price of shares is normally in equilibrium, for the majority of investors who are not actively trading in that security:

Po = D1/(1+i)¹ + D2/(1+i)² + D3/(1+i)³ + (Dn + Pn)/(1+i)Ķ

2.3 Limitations of the above valuation model
It is important to appreciate that there are a number of problems and specific assumptions in this model. (a) Anticipated values for dividends and prices - all of the dividends and prices used in the model are the investor's estimates of the future.

(b) Assumption of investor rationality - the model assumes investors act rationally and make their decisions about share transactions on the basis of financial evaluation.
(c) Application of discounting - it assumes that the conventional compound interest approach equates cash...
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