Lecture 4 Valuation of Stocks (a)

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Hubert Elliott
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1 Lecture 4 Valuation of Stocks (a) After examining the characteristics of bonds and their valuation, we now turn our attention towards the more common financial asset we all know as share or stock

2 Equity A Source of Financing Referring back to our very first lecture where we deliberated upon the decisions that a financial manager has to take. Amongst them, one was to identify the sources of financing. During the last two lectures, we focused on debt or leverage financing; now we will turn our attention towards equity. Firms when in need to raise capital or raise money sometimes opt for equity financing. In such a case, they either issue shares of common stock or issue preferred shares. Regardless of the case, the need of capital is fulfilled by resorting to this source of capital.

3 Equity Common Terminologies Used Primary Market These are the markets in which shares or securities are issued for the very first time by corporations. Secondary Market These are the markets in which the subsequent trading of already issued securities take place. Initial Public Offering (IPO) IPO is referred to as the very first offering of securities or shares to the general public. Examples 3

4 Equity Common Stock Valuation Common stock represents an ownership interest in a corporation, but to a typical investor, a share of common stock is simply a piece of paper characterized by two features: It entitles its owner to dividends, but only if the company has earnings out of which dividends can be paid, and only if management chooses to pay dividends rather than retaining and reinvesting all the earnings. Stocks can be sold at some future date, hopefully at a price greater than the purchase price. If the stock is actually sold at a price above (below) its purchase price, the investor will receive a capital gain (loss). Recall the definition of fair value of financial assets, it is the present value of all the expected cash flows. In case of stocks, what do you think will be the future cash flows? 4

5 Equity Common Stock Valuation Depending upon the investment horizon of the investor, an investor is generally entitled to the following two cash flows in case of stocks: A regular cash stream in the form of dividends; The payment an investor receives when he sells the stock at some future date. In our discussion of bonds, we found the value of a bond as the present value of interest payments over the life of the bond plus the present value of the bond s face value: Bond Interest ( K d) Interest ( K d)... Interest n ( K d) Face n ( K d) Stock prices are likewise determined as the present value of a stream of cash flows and the basic stock valuation equation is similar to the bond valuation equation. 5

6 Equity Common Stock Valuation Think of yourself as an investor who buys a stock with the intention of holding it forever. In this case, what cash flows do you think you will receive? In such a case, you and your heirs will only receive a stream of dividend payments and the value of the stock today will be calculated as the present value of an infinite stream of dividends: Where, P 0 (Dividend) ( Ks) = P 0 = Fair value of the share or stock; (Dividend) = Dividend received at the end of this year or year ; (Dividend) n = Dividend received at the end of year n; K s = The required rate of return demanded by investors. (Dividend) ( Ks)... (Dividend) n ( Ks) n 6

7 Equity Common Stock Valuation What about the more typical case, where you expect to hold the stock for a finite period and then sell it what will be the value of P 0 in this case? Would the approach be any different? To see this, recognize that for any individual investor, the expected cash flows consist of expected dividend plus the expected sale price of the stock. However, the sale price the current investor receives will depend on the dividends some other investor expects in the future. In case if the investor has a two year investment horizon, then we will have: P 0 (Dividend) ( Ks) Where, (Price) = The fair value of the stock at the end of year, which is actually the present value of all the future dividends that an investor expects to receive after year (Dividend) ( Ks) (Price) ( Ks) 7

8 Finite Investment Horizon Examples IBF stock will pay a dividend this year of PKR.40 per share. It is expected that the price of the stock at the end of this year will be PKR30. Given a 3% required rate of return, what should be the fair value of the stock today? P 0 (Dividend) ( Ks).40 P0 ( 0.3).40 P0 (.3) P0 (Price) ( Ks) 30 ( 0.3) 30 (.3)

9 Finite Investment Horizon Examples IBF has already paid a dividend of PKR.40 last year. Based upon the historical payout, investors expect that the stock will pay a dividend of PKR.75 at the end of this year and PKR3 at the end of the next year. It is also expected that the price of the stock at the end of the next year will be PKR38. What do you think should be its fair value today if the required rate of return is 3%? (Dividend) P0 ( Ks).75 P0 ( 0.3) (Dividend) ( Ks) 3 ( 0.3) (Price) ( Ks) 38 ( 0.3) P

10 Equity Common Stock Valuation The General Dividend Discount Model If we extend the holding period of an investor indefinitely then the fair value of the stock simply becomes the present value of an infinite stream of dividends, represented by John Burt William s (938) original DDM formula: P 0 (Dividend) ( Ks) (Dividend) ( Ks)... (Dividend) n ( Ks) While the above mentioned general dividend discount model is theoretically correct, applying it in practice requires an accurate forecast of dividends for many periods into the future, a task for which we rarely expect to have sufficient information; To simplify the almost impossible task of making accurate forecasts, we can use of the following growth models: Gordon Constant Growth Model; Two-Stage Growth Model; The H-Model; Three-Stage Growth Model. n 0

11 Equity Common Stock Valuation Gordon Constant Growth Model The dividends disbursed by corporations can assume any pattern, in case of the Gordon Constant Growth Model however, it is assumed that dividends grow at a constant rate forever; In such a case, the general dividend discount model can be transformed into the following equation: P 0 D0( g) ( Ks) D0( g) ( Ks) D0( g) P0 Ks- g D P0 Ks- g... D0( g) n ( Ks) n

12 Equity Common Stock Valuation Gordon Constant Growth Model The equation that we just arrive d at is known as the Constant Growth Model or the Gorden Growth Model: D P0 Ks- g Here, P 0 = Fair value or intrinsic value of the stock today; D = D 0 (+g) = Dividend expected at the end of year or this year; K s = Investor s required rate of return; g = Sustainable dividend growth rate of the firm. The Gorden Growth Model assumes that: The firm expects to pay a dividend, D, in one year; Dividends grow indefinitely at a constant rate, g (Which may be less than zero); The growth rate, g, is less than the investor s required rate of return.

13 Equity Common Stock Valuation Gordon Constant Growth Model ABC Food Products just paid a dividend of PKR.5. Its stock has a required rate of return of 3.4%, and investors expect the company to grow at a constant 8% in the future. What do you think should be the price of its stock today? DEF Potato Chips paid a PKR per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4 percent per year. What is the expected dividend in each of the next 3 years? If the discount rate is percent, at what price will the stock sell? What is the expected price of the stock 3 years from now? If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments? 3

14 Equity Common Stock Valuation Multi-Stage Growth Models For most companies, the underlying assumption of the Gordon Growth Model that dividends are expected to grow at a constant rate forever is unrealistic; Owing to the competitive advantages they have developed or patents/trademarks they hold, corporations experience substantially higher growth rates for shorter periods. Subsequently as the market forces catches up, the growth rate of the firm decreases and stabilizes at a sustainable level. This illustration emphasizes upon two periods of different growth rates clearly deviating from the assumption laid down by the Gorden Growth Model; Similarly, we can develop multistage growth models depending upon the stages of growth we expect the firm to experience. However, it should be kept in mind that the appropriate model is the one which closely resembles the company s expected pattern of growth; Regardless of the stages we have included in our model, keep in mind that we are still forecasting dividends into the future and discounting them back to gauge the fair value of the share. 4

15 Equity Common Stock Valuation The Two-Stage Dividend Discount Model The most basic multistage model is a two-stage dividend discount model which assumes that the company grows at a higher rate for a relatively short period (The first stage) and then reverts back to a sustainable perpetual growth rate (The second stage); An illustration in which the two-stage model would apply is a situation in which a company has a patent that will expire after a certain number of years. For example, suppose a firm is expected to grow at 5% until the expiry of its patents in another 4 years then the firm is expected to revert to a long-term growth rate of 3% in perpetuity. The stock of this company should be modeled by a two-stage model with dividends growing at 5% until the expiry of patents and then at 3% forever (See pictorial in the next slide). 5

16 Dividend Growth Rate (g) 3% 5% SZABIST Equity Common Stock Valuation The Two-Stage Dividend Discount Model Stage Stage Time 6

17 Equity Common Stock Valuation The Two-Stage Dividend Discount Model Under the two-stage dividend discount model, the formula to calculate the fair value of the share is: P 0 D0( gs) ( K ) S... D0( gs) t ( K ) S t D0( g ( K ) S S t t ) ( g (K g S L L ) ) Here, P 0 D 0 K s t g s g L = Fair value or intrinsic value of the stock today; = Last dividend paid by the company; = Investor s required rate of return; = Length of the high growth period (In years); = Short-term dividend growth rate; = Long-term dividend growth rate. 7

18 Equity Common Stock Valuation The Two-Stage Dividend Discount Model GHI Recreation just paid a dividend of PKR per share. An analyst forecasts that because of being the first entrant in the market, the company is currently experiencing a growth rate of 0% which is expected to continue for another 5 years. However as competition mounts, the growth rate of the company is expected to fall down to a sustainable level of 8%. If investor demands a return of 8%, what do you think is the fair value of the stock today? JKL Distributors is a startup firm and currently pays no dividends. The company recently reported earnings of PKR.50 per share which are expected to grow at a rate of 5% for the next four years. It is in year 5 however, JKL is expected to distribute 0% of its earnings in the form of dividends. The dividends are then expected to grow at a constant rate of 5% forever. Calculate the fair value of the stock if the required rate of return is 5%. 8

19 Equity Common Stock Valuation The H-Model The problem with the basic two-stage dividend discount model is that it is usually unrealistic to assume that a stock will experience high growth for a short period and then the growth rate immediately falls to a sustainable level; The H-Model overcomes the drawback and uses a more realistic phenomenon. In this model, the growth rate starts out high and then linearly declines over the high-growth stage until it reaches the sustainable level; For example, consider a firm that generates high profit margins because of the little competition it faces in the industry and is experiencing a growth rate of 8%. However, it is expected that as competitors enter the market the growth rate of the firm will decline by 3% every year until it reaches 6% at the end of the fourth year when the industry matures and growth rate stabilizes (See pictorial in the next slide). 9

20 Dividend Growth Rate (g) 6% 8% SZABIST Equity Common Stock Valuation The H-Model Stage Stage Time 0

21 Equity Common Stock Valuation The H-Model Under the H-Model, the general dividend discount model transforms into the following equation: Here, P 0 D 0 K s H g s g L P = Fair value or intrinsic value of the stock today; = Last dividend paid by the company; = Investor s required rate of return; = (T/) = Half-life (In years) of the high growth period; = Short-term growth rate; = Long-term growth rate. 0 D0 ( g (K g S L ) ) L D 0 H (gs g (K g ) S L L )

22 Equity Common Stock Valuation The H-Model MNO Foods just paid a dividend of PKR per share. The growth rate of the firm, which is currently 0%, is expected to decline linearly over the next 0 years to a stable growth rate of 5%. If the required rate of return is 9%, what is the fair value of the stock? PQR Consultants paid of dividend of PKR.50 per share last year. Because of the patent it owns, the company is currently experiencing a growth rate of 5% which is expected to decline linearly over a period of 5 years to the long-term growth rate of 5%. Calculate the fair value of the stock if the required rate of return is 5%.

23 Equity The Sustainable Growth Rate The sustainable growth rate of the firm repeatedly mentioned in various valuation models is primarily dependent upon the following two factors: The amount of earning the company retains and reinvests; The rate of return the company earns on its equity (ROE). So, mathematically the sustainable growth rate is: g Return on Equity Retention Rate g Net Income Total Equity g Net Income Total Equity Retained Earnings Net Income Dividends Net Income 3

24 Equity Valuation of Preferred Stock A preferred stock is a hybrid, that is, it possesses certain characteristics of a bond and certain characteristics of a common stock. Like bonds, preferred stock has a par value and a fixed amount of dividends that must be paid before dividends can be paid on the common stock. As noted above, a preferred stock entitles its owners to regular, fixed dividend payments which lasts forever. So, preferred stock in essence is nothing but an example of a perpetuity where the value of the preferred stock today is: P Kp Where, D p = Dividends paid by the preferred stock K p = The required rate of return on the preferred stock 0 D p 4

25 Equity Components of Total Expected Return In case of common stock, an investor expects to generate return in the following two forms: Periodic payments that the investor receives; Capital gain that the investor expects to book upon selling the stock. Based upon the two sources of return, the total return of the stock can be represented as: Total Return Dividend Yield Capital Gains Yield Total Return Dividends Begining Price Capital Gains Beginning Price 5

26 Stock Valuation A Few Examples How can we say that price equals the present value of all future dividends when many actual investors may be seeking capital gains and planning to hold their shares for only a year or two? Explain. FM Products has issued preferred stock with an annual dividend of PKR8 that will last forever. If the discount rate is %, at what price should the preferred stock sell? At what price should the stock sell year from now? FM Cosmetics will pay a year-end dividend of PKR3 per share. Investors expect the dividend to grow at a rate of 4 percent indefinitely. If the stock currently sells for PKR30 per share, what is the required rate of return on the stock? If the expected rate of return on the stock is 6.5%, what is the stock price? FM Industries pays a dividend of PKR per quarter. The dividend yield on its stock is reported at 4.8 percent. What price is the stock selling at? 6

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