1. Stock Valuation 1Finance - Pedro Barroso

2. Present Value of Common Stocks The value of any asset is the present value of its expected future cash flows Stock ownership produces cash flows from – Dividends – Capital Gains Valuation of different types of stocks – Zero Growth – Constant Growth – Differential Growth 2Finance - Pedro Barroso

3. Present Value of Common Stocks We can think of value of a stock as the present value of future dividends (D = DPS: Dividend per share): 3Finance - Pedro Barroso

4. Case 1: Zero Growth Assume that dividends will remain at the same level forever  Since future cash flows are constant, value of a zero growth stock is present value of perpetuity: 4Finance - Pedro Barroso

5. Case 2: Constant Growth Value of a constant growth stock is the present value of a growing perpetuity (Gordon Model) Assume that dividends will grow at a constant rate (g) forever, i.e. 5Finance - Pedro Barroso

6. Constant Growth Example Big D, Inc., will pay a dividend of $0.50 per share a year from today. It is expected to increase its dividend by 2% per year. If investors require a return of 15%, what is the stock value? 6Finance - Pedro Barroso

7. Case 3: Differential Growth Assume that dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter … 0 1 2 … NN+1 … 7Finance - Pedro Barroso

8. Case 3: Differential Growth We can value this as the sum of: an N-year annuity growing at rate g 1 present value of a perpetuity growing at rate g 2 that starts in year N+1 8Finance - Pedro Barroso

9. A Differential Growth Example A stock will pay a dividend of $2 a year from today. The dividend is expected to grow at 8% for 2 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%. 9Finance - Pedro Barroso

10. With Cash Flows … 0 1 234 0 1 2 3 Constant growth phase beginning in year 4 is a growing perpetuity D 4 = 2.333 x 1.04 = 2.43 D 5 = 2.333 x 1.04 2 D 6 = 2.333 x 1.04 3... 10Finance - Pedro Barroso

11. With the Formula 11Finance - Pedro Barroso

12. Estimates of Parameters The value of a stock depends upon its growth rate (g) and its discount rate (R) Where does g come from? g = Retention ratio × Return on Equity (ROE) g = (1 – Payout) × Return on Equity (ROE) where Payout = DPS/EPS, Retention ratio (plowback) = 1 - Payout 12Finance - Pedro Barroso

13. Where does R come from? Discount rate can be broken into two parts. – Dividend yield (D 1 / P 0 ) – Growth rate (in dividends) Later, CAPM to estimate discount rate 13Finance - Pedro Barroso

14. Growth Opportunities Growth opportunities are opportunities to invest in positive NPV projects Value of a firm can be the sum of the value of a firm that pays out 100% of its earnings (EPS) as dividends and the net present value of the growth opportunities (NPVGO) 14Finance - Pedro Barroso

15. DGM and NPVGO We have two ways to value a stock: – Dividend discount model (DDM) – Sum of its value as a “cash cow” plus the per share value of its growth opportunities 15Finance - Pedro Barroso

16. NPVGO Model: Example Firm has EPS of $5 at the end of the first year, payout ratio of 30%, discount rate of 16%, and ROE of 20% – Dividend year 1: D 1 = 5 × 0.3 = 1.5 – Growth rate in dividends: g = (1 – 0.3) × 20% = 14% From dividend growth model, stock value is: 16Finance - Pedro Barroso

17. NPVGO Model: Example First, we must calculate the value of the firm as a cash cow Second, we calculate the value of the growth opportunities 17Finance - Pedro Barroso

18. NPVGO Model: Example Finally, 18Finance - Pedro Barroso NPV growths at 14% rate (0.9975/0.875 – 1)

19. Price-Earnings Ratio Analysts frequently relate earnings per share to price Price-earnings ratio is calculated as the current stock price divided by next year (annual) EPS (i.e., number of years to recover investment) 19Finance - Pedro Barroso Using constant dividend growth model:

20. Price-Earnings Ratio Increases with: – payout – growth Decreases with: – discount rate (riskless interest rate + risk premium) Compare P/E across firms to assess if: – stock is cheap (low P/E) or – expensive (high P/E) but firms must be comparable in payout, growth and risk (for example, firms in the same industry) 20Finance - Pedro Barroso

21. Stock Quotes 21Finance - Pedro Barroso

22. Stock Quotes 22Finance - Pedro Barroso

23. Dividends 23Finance - Pedro Barroso

24. Price-Earnings Ratio 24Finance - Pedro Barroso