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- 1. Lecture 11 Topic: Stock Valuation Agenda: I. Stock valuation methods II. Factors that affect stock prices III. Stock risk IV. Stock performance measurement V. Stock market efficiency
- 2. I. Stock valuation methods ~ Valuation of Common Stock: Theoretically, stock value should be equal to the present value of all cash flows (dividends and expected future value) generated by the stock. If we hold a stock forever, Then Value of Stock = P^0 = PV of expected future dividends P^0 = D1 / (1+Ks)1 + D2 / (1+Ks)2 +D3 / (1+Ks)3 + ….+ D∞ / (1+Ks)∞ Notations in stock valuation model: P0 : actual market price of stock today. Dt : expected dividend at the end of period t. P^t : expected market price of stock at the end of period t. • P^0 >=< P0. • P^0 is called intrinsic, or theoretical, value of the stock today. P0 is actual market price, but P^0 is the intrinsic value today based on a particular investor’s estimate. An investor would buy the stock only if her or his estimate of P^0 were equal to or greater than P0. Ks: minimum acceptable, or required, rate of return on the stock. It can be estimated by CAPM. Ki = Krf + (KM-Krf) × βi Total risk = diversifiable risk + un-diversifiable risk Stand-alone risk unsystematic risk systematic risk Firm specific risk market risk
- 3. ~ Stock Valuation Models Based on different assumptions of dividend growth, we may categorize stock valuation model into 3 forms— 1) Zero Growth Form 2) Constant Growth Form 3) Non-constant Form 1. Zero Growth Model: if g=0, D0 = D1 = D2 =…= D∞ = D P^0 = D1 / (1+Ks)1 + D2 / (1+Ks)2 +D3 / (1+Ks)3 + ….+ D∞ / (1+Ks)∞ = D / (1+Ks)1 + D / (1+Ks)2 +D / (1+Ks)3 + ….+ D / (1+Ks)∞ = D / Ks (just as perpetuity) It implies: * K^s = D / P0 ● Valuation of Preferred Stock: Preferred stocks are a hybrid somewhere between a bond and a common stock. Like bonds, preferred stocks have a par value and a fixed amount of dividend which must be paid before dividends can be paid on the common stock. Like stocks, preferred stock dividends can be omitted without throwing the company into bankruptcy. Suppose the payments (dividends) last forever, Vps is found as follows: Vps = Dps /Kps Kps = Dps /Vps Where Vps is the value of preferred stock Dps is dividend for each period Kps is periodic required rate of return.
- 4. 2. Constant (Normal) Growth Model: (GORDON MODEL) if g ≠0, and g is a constant. D1 = D0 (1+g)1 D2 = D1 (1+g)1 = D0 (1+g)2 : Dn = D0 (1+g)n P^0 = D0 (1+g)1 / (1+Ks)1 + D0 (1+g)2/ (1+Ks)2 + ….+ D0 (1+g)∞ / (1+Ks)∞ = D1 / (Ks - g) ● In this model, Ks must larger than g. ● This model implies: K^s = D1 / P0 + g. In this case, g equals capital gain, because K^s = D1 / P0 + (P^1 - P0) / P0 ● Growth in dividend occurs primarily as a result of growth in EPS. The amount of earnings tends to grow over time is due to 1) inflation 2) the amount of earnings the company retains and reinvests, 3) the rate of return the company earns on its equity (ROE). ● K^s: expected rate of return which an investor who buys the stock expects to receive. * Ks >=<K^s: An investor would buy the stock only if her or his estimate of K^s is equal to or greater than Ks. * Expected total return = K^s = D1 / P0 + (P^1 - P0) / P0 Dividend Gain: D1 / P0, or Dt / Pt-1 Capital Gain: (P^1 - P0)/ P0, or (P^t - Pt-1)/ Pt-1
- 5. 3. Supernormal (Non-constant) Growth Model: ~ If g increases over time, in other words, when firms grow much faster than the economy as a whole, they are called supernormal growth firms and have supernormal growth rates. ~ Firms typically go through life cycles. During the early part of their lives, their growth is much faster than that of the economy as a whole; then they match the economy growth; and finally their growth is slower than that of the economy. ~ For example, Automobile manufacturers in the 1920s and computer software firms in the 1990s are examples of firms in the early part of the cycle. In order to find out the stock prices for supernormal companies, we can break down our stock valuation model into 2 parts: P^0 = [ D0 (1+gs)1 / (1+Ks)1 + D0 (1+gs)2/ (1+Ks)2 + ….+ D0 (1+gs)s / (1+Ks)s ] + P^s/ (1+Ks)s P^s = Ds (1+gn) / Ks-gn. gs: super-growth rate s: number of super-growth years. gn: normal-growth rate after the super growth rate period. Abnormal Growth=gs Normal Growth = gn 0 1 2 3 S ∞ |------------ |-------------|-------------|------------ |-----------------------……… ---------| 0 D1 D2 D3 DS D∞ P^s = DS × (1+gn) / (Ks - gn)
- 6. Example: Super-normal growth model ~ D0 =$1, for next two periods: g=20%, after the first two periods: g= 6%, β =1.5 Rf=4.75% RM=10% D1=1(1+20%) D2=1.2(1+20%) =1.2 =1.44 D3=1.44(1+6%) =1.5264 P^2=D3/(Ks-g) =1.5264/(12.625% - 6%) =23.04 P^0 = 1.2/(1+12.625%) + (1.44 +23.04)/(1+12.625%)2 = 20.37
- 7. If a company’s policy is not to pay any dividend, we can not use this valuation model. We should use other approach which depends on earning ability. If Dividend is not available: BVt = BVt-1 + NIt - Dt Dt = BVt-1 + NIt - BVt = NIt – (BVt - BVt-1) = NIt – [BVt-1(1+k) - BVt-1] = NIt – k BVt-1 P ^t = (NIt – ks BVt-1) / (Ks - g) (Modified Gordon Model)
- 8. II. Factors that affect stock prices Stock market Equilibrium: Equilibrium is the condition under which the expected return on a security is equal to its required return. The reason that stock price will be stable in equilibrium point is because: Ks > K^s, investors will sell the stock; Ks < K^s, investors will buy the stock. Thus, only when Ks = K^s (or P0 = P^0), investors will think that the price is reasonable and no transaction will occur. Changes in Equilibrium Stock Prices: Can equilibrium prices change over time? Yes, they change over time. The equilibrium prices are affected by all factors in CAPM and Gordon Model: Ki = Krf + (KM - Krf) βi. Required rate of return. K^s = D1 / P0 + g. Expected rate of return. Example: Krf will change when inflation or real risk free rate changes. Market risk premium will change when risk aversion changes. βi will change when companies’ management decisions change. g and D will change when dividend policies change. * Ideally, equilibrium ordinarily exists for any given stock, Ks = K^s, and P0 = P^0. However, because expectations and economy situations keep changing, stock prices are changing overtime to adjust to new information. Firm-specific factors Interest rate Industrial conditions Risk levels Expectations: Dividend policy Monetary policy Risk levels Stock offerings Inflation Stock repurchases Economic growth Acquisitions Divestitures
- 9. III. Stock Risk Risk The chance that an unfavorable event will occur It reflects the uncertainty about future returns ~ Risk measurement Risk can be measured by the fluctuation of the stock price. 1) Volatility of a stock (the dispersion of the price movements) ~ Variance Example: 2) Sensitivity of stock returns to market returns ~ β Example:
- 10. IV. Stock Performance Measurement The performance of a stock can be measured by its excess return divided by its risk It measures the “reward” for taking 1 unit of risk associated with a stock. 1) Sharpe Index: (R-Rf)/σ Example: Avg. Return Rf Volatility (σ) Sharpe Index A 20% 6% 8% 1.75 B 10% 6% 2.5% 1.60 2) Treynor Index: (R-Rf)/β Example: Avg. Return Rf Volatility (σ) Sharpe Index A 20% 6% 2 7% B 10% 6% 0.5 8%
- 11. V. Stock Market Efficiency Stock markets are efficient, if stock prices can instantly and correctly reflect all the available information in the markets. All information: past, public, and inside information Public and past information Strong form Semi-strong form Past information Weak form

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