The sale of equity shares
Companies issue equity shares on the primary market in order to raise capital. They record the cash received on the liabilities side of their balance sheet as equity. After this first step, the shares are traded on the secondary market, for example on stock exchanges such as the NYSE, Nasdaq or Deutsche Börse. However, trading there does not affect the company's balance sheet equity.
Introduction to equity
The book value of equity, also known as the book value is calculated from the subscribed capital, the retained earnings and capital reserves and the net profit for the year. The market value of equity or market capitalization is calculated from the current share price multiplied by the number of shares issued. Part of the company's profit can be distributed to shareholders as a dividend - a decision that is made at the Annual General Meeting and is subject to tax.
Valuation of shares using the DCF method
Shares can also be valued using the discounted cash flow (DCF) method by calculating the present value of the cash flows expected by the shareholders. These cash flows include dividends and potential price gains in the event of a sale. If a share is only held for a certain period of time, for example, the formula applies:
Pv0= DIVv1+Pv1/(1+r).
Here r corresponds to the opportunity costs of a comparable investment. In order to calculate the fair price, assumptions must therefore be made about future dividends and the sale value of the share. In the example of the Allianz share ($ALV), we adjust the expected return based on a similar company and thus calculate the purchase price in order to achieve an equivalent return.
As an example, we use the $ALV (-0.14%) . We take the r from the$MUV2 (-0.6%) (not similar but comparable) and adjust it for what (too complicated to explain here). The result is a one-year r of 27% with div included. We now put the values into the share formula: 11.40+241.85/(1+0.27)=€199.41 should have been the purchase price in Pv0 in order not to be worse off. If you had bought higher, you would be worse off than with the MR.
Cost of equity and expected return
The expected return on equity (r) must be high enough to convince shareholders to invest in the company - in other words, it corresponds to the opportunity costs of comparable alternatives on the capital market. It is calculated using the formula: r= DIVv1+Pv1-Pv0/Pv0 = DIVv1/Pv0 + Pv1-Pv0/Pv0 . Here is an example: What is the expected return on Fledgling Electronics if the share costs €100 today, you can sell it for €110 in a year's time and you assume that the company will pay a dividend of €5 in a year's time? r= 5+110-100/100=0.15=15%
Extended DCF valuation for longer holding periods
For a longer holding period of several years, the present value of all future dividends must be taken into account. The corresponding formula is
Pv0= DIVv1/(1+r) + DIVv2+Pv2/(1+r)^2
A longer investment horizon H means that the sale value lies in an increasingly distant future and therefore has less and less influence on the current cash value. The longer you hold a share, the greater the influence of dividend payments compared to the sale value.
Dividend growth and the dividend discount model (DDM)
If dividends grow at a constant rate (g), the valuation of a share is determined by the formula
Pv0= DIVv1/r-g or r= DIVv1/Pv0 +g
The cost of equity (r) is made up of the expected dividend and the growth rate. It is often difficult to determine this growth rate. To do this, analysts' estimates are used or the future dividends from investment projects and the company's retention strategies are evaluated.
Share valuation using the multiples method
Another valuation method is the comparison using multiples. These include the price/earnings ratio (P/E ratio) or the market-to-book value ratio. The selection of comparable companies has a major influence on the result, which is why average values are used. Nevertheless, market distortions - such as an over- or undervaluation of the entire sector - can lead to inaccurate valuations.
Quiz
Which statement is true?
a) The value of a share corresponds to the present value of the future dividend.
b) In a stable capital market, all shares in a risk class have the same price.
c) The value of a share corresponds to the present value of the expected profits of the issuer.
d) If the capital market functions well, all shares are priced in such a way that they have the same expected return.
Company X will pay a dividend of USD 5 per share at the end of the year. After the dividend payment, the share can be sold at USD 110. What would be the current market price of the share if an investment with a similar risk yielded a return of 8 %?
a) USD 106.48
b) USD 102.86
c) USD 108.00
d) 105.00 USD
summary
Share valuations are based on the present value of future dividend flows. The discount rate corresponds to the cost of equity and can be measured against the return on comparable investments. The higher the growth of the company, the higher its value. In addition to the DCF method, the multiples method is also used to estimate the fair share price.
Source: Brealey, R., S. Myers, F. Allen, A. Edmans (2022): Principles of Corporate Finance14th edition, McGraw Hill
