Share valuation
Shares and share trading
Equity shares (stocks, shares) are sold (issued) by companies on the primary market. This enables companies to raise cash and show (new) equity on the liabilities side of the balance sheet. The shares are then traded on the secondary market. This trading on the stock exchange does not affect the (book value of the company's) equity.
In the USA, the NYSE and Nasdaq are the largest trading centers; in Germany, it is Deutsche Börse.
Equity capital
Book value of equity capital: This is the balance sheet value of equity capital and is made up of subscribed capital, retained earnings and capital reserves and the net profit for the year; it is also possible to have a negative book value.
The market value of equity = market capitalization: This is calculated as the share price - number of outstanding (circulating) shares (cannot be negative and usually deviates significantly from the book value).
The dividend is a distribution of (part of) the profit and is determined at the Annual General Meeting based on a proposal by the Executive Board. However, there is no obligation to pay a dividend and it is subject to final withholding tax in Germany.
Share valuation: DCF method
Share prices can also be calculated using the DCF formula, i.e. as the present value of the cash flows received by the shareholders. Cash flows for shareholders are dividends over the holding period and the price gain (or loss) on sale.
If, for example, a share is only held for one period and then sold, Pv0= DIVv1+Pv1/1+r , where r - as always - is determined as the interest rate of a comparable investment (opportunity cost). In order to calculate today's share price, you have to form expectations about the future share price and the future dividend.
As an example, we use the $ALV . We take the r from the$MUV2 (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.
Addition:Return on equity
r is the (expected) return on equity for the company's shareholders. This means that it must also be the return that another company in the same sector with comparable risk would have to offer the equity providers so that they are prepared to invest their assets in the company instead of choosing an alternative financial investment. Thus, r again results from an opportunity cost consideration, i.e. as the return on an alternative investment with the same risk. All investments with the same degree of risk should therefore have the same expected return on the capital market ((why is this not always the case?). From the company's point of view, it corresponds to the cost of equity.
If you know the current and expected future share price and the dividend, you can calculate the expected return with 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%
Share valuation DCF continuation
Earlier we again assumed only one payment. Now we are looking at several payments. The question then arises: How is the share price determined if the investment period is two years? It looks like this, Pv0= DIVv1/(1+r) + DIVv2+Pv2/(1+r)^2. If we look at the calculation, the question arises: Is the price of a share with a holding period of two years different from that with one? No, because if the person who buys the share from me after one year wants to hold it for one year, they would pay the following price Pv1=DIVv2+Pv2/1+r. In other words, the second person does not pay your dividend but only his and his selling price. If you now put everything you have learned together, you get the formulas:Pv0= DIVv1+Pv1/1+r = DIVV1/(1+r) + Pv1/(1+r) = DIVv1/(1+r) + DIVv2+Pv2/(1+r)^2 . Since Pv2 and all other prices can also be determined using this formula, the result for an investor with an investment horizon H is Pv0=DIVv1/(1+r) + DIVv2/(1+r)^2 + .... + DIVvH+PvH/(1+r)^H = (summation sign formula is omitted here)
As the investment horizon increases, the sales proceeds move further and further into the future, causing their present value to fall. However, the share price is independent of the investment horizon and therefore H only determines what proportion of the total cash value (= share price) the sales proceeds account for
Share valuation: Investment horizon
What effect does the investment horizon H have? As H increases, the purchase price Pv1 becomes less and less important. At around 20 years after purchase, the purchase price accounts for only 50% of the PV in the model. This means that future dividends and the future selling price are much more important. In slightly more theoretical terms, this means that the share price remains constant, only the composition of PV (future dividends) and PV (future share price) changes. With an infinite investment horizon, this means that the value of a share is determined as the present value of all future dividends that the company will pay out
→ Dividend discount model (dividend discount model)
Share valuation: investment horizon and dividend growth
Often it is not so much the fair (i.e. market equilibrium) share price that is of interest, but the cost of equity, r. So far we have seen that r=DIVv1+Pv1-Pv0/Pv0 , but if we assume a constantly growing dividend (with growth rate g), then the present value from this infinite, growing annuity is: Pv0= DIVv1/r-g or r= DIVv1/Pv0 +g .
Example: Northwest Natural Gas currently has a share price of €49.43. A dividend of €2.00 is expected for the coming year. Analysts expect Northwest's dividend to grow at a constant rate of 7.7%. What is the company's cost of equity? r= 2/49,43 + 0,077= 0,118 =11,8%
However, determining the growth rate g is usually the most difficult part. In most cases, one simply uses the estimate of the security analysts. Alternatively, the growth rate can be determined from the company's investment and dividend policy. The question is asked: What money can the company retain (reinvest, i.e. not distribute as dividends) in order to invest it? How profitable are the company's investment projects? This combination determines the growth rate of profits and therefore the future dividend value.
But growth is not always constant, how do you regulate this? For example, initially high but possibly fluctuating dividends could be paid and only from time H does the company switch to a stable but lower growth path.
The valuation formula would be: PV= DIV/(1+r) + DIV/(1+r)^2 +....+ DIVvH/(1+r)^H + PvH/(1+r)^H with PvH= DIVvH+1/r-g
Example: Phoenix AG pays dividends of EUR 0, EUR 0.31 and EUR 0.65 in three consecutive years. The dividend in the fourth year is estimated at EUR 0.67 and is expected to grow by 4% from then on. What is the share price of Phoenix at a discount rate/cost of equity of 10%? PV= 0/(1+0.1) + 0.31/(1+0.1)^2 + 0.65/(1+0.1)^3 + [1/(1+0.1^3 - 0.67/(0.10-0.04)]
Share valuation: Multiples method
Multiples method: An attempt to derive the value of a company from the observable market prices of comparable companies (comparables). For this purpose, the share price of a comparable company is related to a value from its balance sheet or income statement → multiple
Typical multiples:
Price/earnings ratio (P(rice)/E(earnings) ratio)
Market-to-book ratio (market-to-book ratio)
The multiples are then multiplied by the corresponding balance sheet or income statement value of the company to be analyzed. Dividing by the number
of shares in circulation, an estimate of the share price is obtained.
Problems
Care must be taken when selecting companies, as the choice of peer companies influences the result. Typically, average multiple values are therefore used to balance out the extreme values.
The multiples method assumes that the market value of the equity of the peer companies is correctly priced, but if an entire industry is over/undervalued, the multiples method does not provide a meaningful estimate... .
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 issuer's expected profits.
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
The most important points from the text
The share price can be determined as the present value of the series of payments associated with the share investment, which results from discounting a (potentially infinite) stream of future dividends.
The discount rate is the cost of equity
The cost of equity can be calculated as the return on an investment with identical risk on the capital market
The higher the company growth (with r > g), the higher the value of the company In addition to the DCF method, multiples are also used to value equity
SourceBrealey, R., S. Myers, F. Allen, A. Edmans (2022): Principles of Corporate Finance, 14th edition, McGraw Hill, ISBN 1260013901 and lecture slides
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