# 1 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Fin2808: Investments Spring, 2010 Dragon Tang Lectures 13 & 14 Equity Valuation Models March.

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1 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Fin2808: Investments Spring, 2010 Dragon Tang Lectures 13 & 14 Equity Valuation Models March 9&11 ， 2010 Readings: Chapter 18 Practice Problem Sets: 1,5,7,14, 16,17

2 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation How to make money in stocks?

3 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation How to make money in stocks? Capital gains: buy low/sell high –Growth companies Dividend yields: income stream –Matured (value) companies

4 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Equity Valuation Objectives: Calculate the intrinsic value of a firm using either a constant growth or multistage dividend discount model. Calculate the intrinsic value of a stock using a dividend discount model in conjunction with a price/earnings ratio. Assess the growth prospects of a firm from it P/E ratio.

5 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Balance Sheet Valuation Methods Book Value Liquidation Value Replacement Cost

6 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Expected Holding Period Return If E(HPR) > Required Rate of Return(RRR), the stock is a good deal. RRR is from a pricing model, e.g. CAPM: In market equilibrium, E(HPR) = RRR.

7 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Intrinsic Value versus Market Price V 0 (intrinsic value) > P 0 (market price)  buy V 0 (intrinsic value) < P 0 (market price)  sell or sell short In market equilibrium, V 0 = P 0 k is the market capitalization rate which equates V 0 and P 0 If V 0  P 0, then EMH implies the estimate of k is wrong Intrinsic value --The present value of a firm’s expected future net cash flows discounted by the required rate of return.

8 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Dividend Discount Models One Period Case: Multi-period Case: Where D 1,…, D H and P H are expected values

9 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Dividend Discount Models Example: Whitewater Rapids Company is expected to have dividends grow at a rate of 12% for the next three years. In three years, the price of the stock is expected to be \$ 74.46. If Whitewater just paid a dividend of \$2.00 and its level of risk requires a discount rate of 10%, what is the intrinsic value of Whitewater stock?

10 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Dividend Discount Models Dividend discount model (infinite horizon):

11 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Constant Growth DDM (Gordon’s Model)

12 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Constant Growth DDM Example: Whitewater Rapids Company is expected to have dividends grow at a constant rate of 6% for the foreseeable future. If Whitewater just paid a dividend of \$2.81 and its level of risk requires a discount rate of 10%, what is the intrinsic value of Whitewater stock?

13 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Market Capitalization Rate If V 0 = P 0 : Dividend Yield Capital Gains Yield Gordon’s Model: If g = 0: Perpetuity

14 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Implications of this Model If D 1 increases, then V 0 increases. If k decreases, then V 0 increases. If g increases, then V 0 increases. If D 1 increases X%, then V 0 will increase X%. g = the capital gains yield

15 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Dividend Payout Ratio and Plowback Ratio Dividend Payout Ratio: Percentage of earnings paid out as dividends Plowback (or Earning Retention) Ratio: Fraction of earnings retained and reinvested in the firm

16 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Stock Prices and Investment Opportunities If a firm retains earnings and reinvest them in a profitable investment opportunity, dividend may grow “faster”. If a firm pays out all dividends nothing gets re-invested, nothing growths.

17 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Figure 12.1 Dividend Growth for Two Earnings Reinvestment Policies

18 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Plowback Ratio and Growth Where: ROE = Return on Equity b = Plowback Ratio (or Earning Retention Ratio)

19 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Stock Prices and Investment Opportunities Present value no-growth (b=0 or ROE=k) Present value of growth Opportunities PVGO > 0 if ROE>k PVGO <0 if ROE<k

20 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Estimating Growth Example: Takeover Target has a plowback ratio of 60% and an ROE of 10%. If it expects earnings to be \$ 5 per share, what is the present value of Takeover’s growth opportunities if the appropriate capitalization rate is 15%? What is the PVGO?

21 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Life Cycles and the Constant Growth Model Changing growth rates: temporary high (or low) growth permanent constant growth

22 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Changing Growth Rate Example: Whitewater Rapids Company is expected to have dividends grow at a rate of 12% for the next three years. In three years, the dividends will settle down to a more sustainable growth rate of 6% which is expected to last “forever.” If Whitewater just paid a dividend of \$2.00 and its level of risk requires a discount rate of 10%, what is the intrinsic value of Whitewater stock?

23 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Price-Earning (P/E) Ratios Ratio of Stock price to its earnings per share Useful for firm valuation: Problems: –Forecasts of E –Forecasts of P/E

24 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation P/E Ratios and Growth If PVGO = 0:

25 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Numerical Example: No Growth E 0 = \$2.50 g = 0 k = 12.5% P 0 = D/k = \$2.50/.125 = \$20.00 P/E = 1/k = 1/.125 = 8

26 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation P/E Ratios and ROE P/E ratio rises with ROE but not necessarily with b 1/k ROE<k ROE>k b P/E

27 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Numerical Example with Growth b = 60% ROE = 15% (1-b) = 40% E 1 = \$2.50 (1 + (.6)(.15)) = \$2.73 D 1 = \$2.73 (1-.6) = \$1.09 k = 12.5% g = 9% P 0 = 1.09/(.125-.09) = \$31.14 P/E = 31.14/2.73 = 11.4 P/E = (1 -.60) / (.125 -.09) = 11.4

28 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Figure 12-3 P/E Ratio of the S&P 500 Index and Inflation

29 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Caveat with P/E Ratios High plowback ratio (b) High Growth Rate (g) (g = ROE*b) BUT High g (if due to high b) High P/E ratio Practitioners: high P/E as proxy of high dividend growth (g)

30 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation P/E ratio and Risk Holding everything equal: High risk (k), Low P/E. Why do small-risky firm have high P/E?

31 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Pitfalls in P/E Analysis Earnings are based on accounting data Current price and current earnings Future expected earnings is more appropriate In P/E formula, E is an expected trend In financial pages, E is the actual past period's earnings

32 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Figure 12-6 P/E Ratios

33 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Combining P/E and DDM

34 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation The Aggregate Stock Market: Earning Multiplier Approach

35 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Other Valuation Ratios & Approaches Price-to-book Price-to-cash flow Price-to-sales Present Value of Free Cash Flow

36 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Summary Valuation approaches: -Balance sheet values -Present value of expected future dividends DDM states that the price of a share of stock is equal to the present value of all future dividends discounted at the appropriate required rate of return Constant growth model DDM: P/E ratio is an indication of the firm's future growth opportunities Models used for the firm can be used to forecast the behavior of the aggregate stock market

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