1. 8-1 Chapter 8 Outline Common Stock Valuation – Cash Flows Dependent – Dividend Growth Model Stock price quotes

2. 8-2 Issues in Share Valuation If you buy a share of stock, you can receive cash in two ways – The company pays dividends – You sell your shares, either to another investor in the market or back to the company As with bonds, the price of the stock is the present value of these expected cash flows Uncertainty of cash flows Indefinite life

3. 8-3 Developing The Model The price of the stock is really just the present value of all expected future dividends + present value of selling price P 0 = D 1 /(1+R) + P 1 /(1+R) (if sell at end period 1) P 0 = D 1 /(1+R) + D 2 /(1+R) 2 + P 2 /(1+R) 2 (if sell at end period 2) P 0 = D 1 /(1+R) + D 2 /(1+R) 2 + D 3 /(1+R) 3 + P 3 /(1+R) 3 (sell per. 3) Or.. Just the present value of future dividends P 0 = D 1 /(1+R) + D 2 /(1+R) 2 + D 3 /(1+R) 3 + ….. (indefinite life) So, how can we estimate all future dividend payments?

4. 8-4 Three Special Cases Constant dividend – The firm will pay a constant dividend forever Constant dividend growth – The firm will increase the dividend by a constant percent every period Supernormal growth – Dividend growth is not consistent initially, but settles down to constant growth eventually

5. 8-51 Zero Growth/constant Dividend D 1 = D 2 = D 3.…= D t constant dividend or zero growth P 0 = D 1 / R Suppose a stock is expected to pay the same $0.50 dividend every quarter indefinitely and the required return is 10% with quarterly compounding. What is the price? – P 0 = 0.50 / (0.025) = $20 (yearly figures:$2/0.10)

6. 8-6 Dividend Growth Model – constant growth Dividends are expected to grow at a constant percent per period (g%) It is also called Gordon Growth Model. D 0 < D 1 < D 2 …D t-1 < D t D t =D t-1 (1+g) or D1 D2 D3 D t =D 0 (1+g) t With a little algebra, this reduces to:

7. 8-7 DGM – Example 1 Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? – D 0 = 0.50 – g = 2% – R = 15% – P 0 = ?

8. 8-8 DGM – Example 2 Suppose Pirates Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the share price today? – Dividend = $2 g = 5% R = 20% P 0 = ? – Why isn’t the $2 in the numerator multiplied by (1+.05) in this example?

9. 8-9 Share Valuation - Example 8.3 p238 Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? D1 = $4, g = 6%, R = 16%, P 0 = ? P 0 = 4 / (.16 -.06) = $40

10. 8-10 Share Valuation - Example 8.3 p238 continued.. What is the price expected to be in year 4? – D 5 = D 1 (1+g) 4 – P 4 = 4(1+.06) 4 / (.16 -.06) = 5.05/0.10 = 50.50

11. 8-11 Using the DGM to Find R Start with the DGM: Rearrange and solve for R Components of R: Dividend Yield (D 1 /P 0 ) + Capital Gains Yield (g)

12. 8-12 Finding the Required Return - Example Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? – R = [1(1.05)/10.50] +.05 = 15% What is the dividend yield? – 1(1.05) / 10.50 = 10% What is the capital gains yield? – g =5%

13. © 2012 Pearson Prentice Hall. All rights reserved. 7-13 Common Stock Valuation: Variable-Growth Model/Supernormal Growth The zero- and constant-growth common stock models do not allow for any shift in expected growth rates. The variable-growth model is a dividend valuation approach that allows for a change in the dividend growth rate. To determine the value of a share of stock in the case of variable growth, we use a four-step procedure.

14. © 2012 Pearson Prentice Hall. All rights reserved. 7-14 Common Stock Valuation: Variable-Growth Model (cont.) Step 1. Find the value of the cash dividends at the end of each year, D t, during the initial growth period, years 1 though N. D t = D 0 × (1 + g 1 ) t

15. © 2012 Pearson Prentice Hall. All rights reserved. 7-15 Common Stock Valuation: Variable-Growth Model (cont.) Step 2. Find the present value of the dividends expected during the initial growth period.

16. © 2012 Pearson Prentice Hall. All rights reserved. 7-16 Common Stock Valuation: Variable-Growth Model (cont.) Step 3. Find the value of the stock at the end of the initial growth period, P N = (D N+1 )/(r s – g 2 ), which is the present value of all dividends expected from year N + 1 to infinity, assuming a constant dividend growth rate, g 2.

17. © 2012 Pearson Prentice Hall. All rights reserved. 7-17 Common Stock Valuation: Variable-Growth Model (cont.) Step 4. Add the present value components found in Steps 2 and 3 to find the value of the stock, P 0.

18. © 2012 Pearson Prentice Hall. All rights reserved. 7-18 Common Stock Valuation: Variable-Growth Model (cont.) The most recent annual (2012) dividend payment of Warren Industries, a rapidly growing boat manufacturer, was $1.50 per share. The firm ’ s financial manager expects that these dividends will increase at a 10% annual rate, g 1, over the next three years. At the end of three years (the end of 2015), the firm ’ s mature product line is expected to result in a slowing of the dividend growth rate to 5% per year, g 2, for the foreseeable future. The firm ’ s required return, r s, is 15%. Steps 1 and 2 are detailed in Table 7.3 on the following slide.

19. © 2012 Pearson Prentice Hall. All rights reserved. 7-19 Table 7.3 Calculation of Present Value of Warren Industries Dividends (2013–2015)

20. © 2012 Pearson Prentice Hall. All rights reserved. 7-20 Common Stock Valuation: Variable-Growth Model (cont.) Step 3. The value of the stock at the end of the initial growth period (N = 2015) can be found by first calculating D N+1 = D 2016. D 2016 = D 2015  (1 + 0.05) = $2.00  (1.05) = $2.10 By using D 2016 = $2.10, a 15% required return, and a 5% dividend growth rate, we can calculate the value of the stock at the end of 2015 as follows: P 2015 = D 2016 / (r s – g 2 ) = $2.10 / (.15 –.05) = $21.00

21. © 2012 Pearson Prentice Hall. All rights reserved. 7-21 Common Stock Valuation: Variable-Growth Model (cont.) Step 3 (cont.) Finally, the share value of $21 at the end of 2015 must be converted into a present (end of 2012) value. P 2015 / (1 + r s ) 3 = $21 / (1 + 0.15) 3 = $13.81 Step 4. Adding the PV of the initial dividend stream (found in Step 2) to the PV of the stock at the end of the initial growth period (found in Step 3), we get: P 2012 = $4.14 + $13.82 = $17.93 per share

22. © 2012 Pearson Prentice Hall. All rights reserved. 7-22 Common Stock: Authorized, Outstanding, and Issued Shares Authorized shares are the shares of common stock that a firm ’ s corporate charter allows it to issue. Outstanding shares are issued shares of common stock held by investors, this includes private and public investors. Treasury stock are issued shares of common stock held by the firm; often these shares have been repurchased by the firm. Issued shares are shares of common stock that have been put into circulation. Issued shares = outstanding shares + treasury stock

23. © 2012 Pearson Prentice Hall. All rights reserved. 7-23 Common Stock: Authorized, Outstanding, and Issued Shares (cont.) Golden Enterprises, a producer of medical pumps, has the following stockholder ’ s equity account on December 31 st.