1. Investment Analysis Lecture: 14 Course Code: MBF702

2. Outline RECAP DIVIDEND VALUATION MODEL - CONTINUE COST OF EQUITY COST OF PREFERENCE SHARES

3. Objectives - RECAP To develop a model for the valuation of shares and bonds. To use this model to estimate the cost of equity and the cost of debt. To consider further practical influences on the valuation of securities.

4. Elements of cost of capital - RECAP

5. DIVIDEND VALUATION MODEL The theoretical model - RECAP The model then becomes: If the dividend is assumed to be constant this is a perpetuity that simplifies to:

6. DIVIDEND VALUATION MODEL The theoretical model This model can then be used to determine the ex-div market value of a share with a constant dividend each year given the assumptions upon which the model is based. With growth If dividends are forecast to grow at a constant rate in perpetuity, where g = growth rate

7. DIVIDEND VALUATION MODEL The theoretical model Assumptions behind the dividend valuation model rational investors all investors have the same expectations and therefore the same required rate of return perfect capital market assumptions, for example − no transactions costs − no individual can affect the share price − all investors have all available information dividends are paid just once a year and one year apart dividends are either constant or are growing at a constant rate. Using the dividend valuation model The model in its most simple form (with constant dividends) can be used to estimate the theoretical fair values of shares.

8. DIVIDEND VALUATION MODEL The theoretical model ILLUSTRATION Suppose that a share has a current ex-div market value of 80 pence and investors expect a dividend of 10 pence per share to be paid each year as has been the case for the past few years. Using the dividend valuation model the required return of the investors for this share can be determined:

9. DIVIDEND VALUATION MODEL The theoretical model ILLUSTRATION Investors will all require this return from this share as they all have the same information about the risk of this share and they are all rational. If investors think that the dividend is due to increase to 15 pence each year then at a price of 80 pence the share is giving a higher return than 12.5%. Investors will therefore buy the share and the price will increase until, according to the model, the value will be:

10. DIVIDEND VALUATION MODEL The theoretical model ILLUSTRATION Alternatively suppose that the investors perception is that the dividend will remain at 10 pence per share but that the risk of the share has increased thereby requiring a return of 15%. If the share only gives a return of 12.5% (on an 80 pence share price) then investors will sell and the price will fall. The fair value of the share according to the model will be:

11. DIVIDEND VALUATION MODEL It is to be noted that it is the only model for the determination of market value of equity. It should also be noted that if the company does not pay dividend in any period, the shareholders would recover the same return through capital gain, since the company would invest the same retained amount in some profitable venture which would automatically affect the share market price of the company. As a result the shareholder would benefit with the extra capital gain earned. In a question where the examiner requires the market value of Equity, preference should be given to this model. However, as mentioned above, not only dividends but capital gains also contribute to the share value and therefore, needs to be considered. In addition, cash profits may also be used for the purpose.

12. Cost of Equity The cost of equity should be higher for riskier investments and lower for safer investments While risk is usually defined in terms of the variance of actual returns around an expected return, risk and return models in finance assume that the risk that should be rewarded (and thus built into the discount rate) in valuation should be the risk perceived by the marginal investor in the investment Most risk and return models in finance also assume that the marginal investor is well diversified, and that the only risk that he or she perceives in an investment is risk that cannot be diversified away (I.e, market or non-diversifiable risk)

13. Cost of equity Shareholders required rate of return The basic dividend valuation model is: This can be rearranged to find r:

14. Cost of equity If r is the return required by the shareholders in order for the share value to remain constant then r is also the return that the company must pay its shareholders. Therefore r also equates to the cost of equity of the company, denoted as Ke. Therefore the cost of equity for a company can be estimated using the dividend valuation model with a constant annual dividend as:

15. Cost of equity The ex-div market value is the market value of the share assuming that the current dividend has just been paid. A cum-div market value is one which includes the value of the dividend just about to be paid. If a cum-div market value is given then this must be adjusted to an ex div market value by taking out the current dividend.

16. Example A company's shares have a market value of £2.20 each. The company is just about to pay a dividend of 20p per share as it has every year for the last ten years. What is the company's cost of equity?

17. Example solution MV (cum div) = £2.20 MV (ex div) = £2.00 Ke = Dividend / MV ex di = ( 20 / 200) × 100% = 10%

18. Cost of equity Dividend with constant growth The model can also deal with a dividend that is growing at a constant annual rate of g. This is still a perpetuity. Now the required formula is as follows.

19. Cost of equity Dividend with constant growth Rearranged this becomes

20. Cost of equity Dividend with constant growth Illustration

21. Cost of equity Dividend with constant growth This constant growth rate of dividends can be estimated using either of two methods.

22. Cost of equity Growth from past dividends Look at historical growth and use this to predict future growth. If you have specific information about future growth, use that. If dividends have grown at 5% in each of the last 20 years, predicted future growth = 5%. Uneven but steady growth – take an average overall growth rate. Discontinuity in growth rate – take the most recent evidence. New company with very high growth rates – take care! It is unlikely to retain such high growth in perpetuity. No pattern – do not use this method (i.e. dividends up one year, down the next).

23. Example A company has paid the following dividends over the last five years. Pence per share 19X0 100 19X1 110 19X2 125 19X3 136 19X4 145 Estimate the growth rate and the cost of equity if the current ex div market value is £10.50 per share.

24. Solution

25. Cost of equity Gordon’s growth model Gordon’s growth model: growth is achieved by retention and reinvestment of funds. These figures can be obtained from the balance sheet and profit and loss account.