1. The DDM and Common Stock Valuation Some quick examples, courtesy of Harcourt –The Effect of Evolving Growth Rates –Valuation via Operating Cash Flow

2. Assume beta = 1.2, k RF = 7%, and k M = 12%. What is the required rate of return on the firm’s stock? k s = k RF + (k M – k RF )b Firm = 7% + (12% – 7%) (1.2) = 13%. Use the SML to calculate k s :

3. D 0 was $2.00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. k s = 13%. 01 2.247 2 2.382 3 g = 6% 1.8761 1.7599 D 0 = 2.00 1.6509 13% 2.12

4. = What’s the stock’s market value? D 0 = 2.00, k s = 13%, g = 6%. Constant growth model: P 0 = = D1D1 k s – g 0.13 – 0.06 $2.12 0.07 $30.29.

5. D 1 will have been paid, so expected dividends are D 2, D 3, D 4 and so on. Thus, Could also find P 1 as follows: k s – g 0.13 – 0.06 P 1 = = What is the stock’s market value one year from now, P 1 ? ^ ^ ^ D2D2 $2.247 ^ = $32.10. P 1 = P 0 (1.06) = $32.10.

6. Find the expected dividend yield, capital gains yield, and total return during the first year. Dividend yld = = = Cap gains yld = = Total return = 7.0% + 6.0% = 13.0%. D1D1 P0P0 P 1 – P 0 P0P0 ^ $30.29 $2.12 7.0%. $32.10 – $30.29 $30.29 = 6.0%.

7. Rearrange model to rate of return form: .P D kg D P g s 0 11 0    tok s Then, k s = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%. ^

8. P 0 = = = $15.38. What would P 0 be if g = 0? The dividend stream would be a perpetuity. 2.00 0123 13%... ^ PMT k $2.00 0.13 ^

9. Can no longer use constant growth model. However, growth becomes constant after 3 years. If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P 0 ? k is still 13%. ^

10. Nonconstant growth followed by constant growth: 0 2.301 2.647 3.045 46.116 1234 k s = 13% 54.109 = P 0 g = 30% g = 6% D 0 = 2.00 2.600 3.380 4.394 4.658 ... $66.54P 3 4.658 13006    0... ^

11. What is the expected dividend yield and capital gains yield at t = 0? At t = 4? Div. yield 0 = = 4.81%. Cap. gain 0 = 13.00% – 4.81% = 8.19%. $2.60 $54.11

12. During nonconstant growth, D/P and capital gains yield are not constant, and capital gains yield is less than g. After t = 3, g = constant = 6% = capital gains yield; k = 13%; so D/P = 13% – 6% = 7%.

13. 25.72 Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P 0 ? 0 1.77 1.57 1.39 20.99 1234 k s =13% g = 0% g = 6% 2.00 2.00 2.00 2.00 2.12.  P 3 2.12 007 30.29.  ^...

14. t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%. $2.00 $25.72 What is D/P and capital gains yield at t = 0 and at t = 3? t = 0: D1D1 P0P0 = = 7.78%. CGY = 13% – 7.78% = 5.22%.

15. If g = -6%, would anyone buy the stock? If so, at what price? Firm still has earnings and still pays dividends, so P 0 > 0:   P D kg D g kg ss 0 1 0 1 =  =   $2.00(0.94) $1.88 0.13 – (-0.06) 0.19 = = = $9.89.

16. What is the annual D/P and capital gains yield? Capital gains yield = g = -6.0%, Dividend yield= 13.0% – (-6.0%) = 19%. D/P and cap. gains yield are constant, with high dividend yield (19%) offsetting negative capital gains yield.

17. Free Cash Flow Method The free cash flow method suggests that the value of the entire firm equals the present value of the firm’s free cash flows (calculated on an after-tax basis). Recall that the free cash flow in any given year can be calculated as: NOPAT – Net capital investment.

18. Once the value of the firm is estimated, an estimate of the stock price can be found as follows: –MV of common stock (market capitalization) = MV of firm – MV of debt and preferred stock. –P = MV of common stock/# of shares. Using the Free Cash Flow Method ^

19. Free cash flow method is often preferred to the dividend growth model--particularly for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends. Issues Regarding the Free Cash Flow Method (More...)

20. Similar to the dividend growth model, the free cash flow method generally assumes that at some point in time, the growth rate in free cash flow will become constant. Terminal value represents the value of the firm at the point in which growth becomes constant. FCF Method Issues Continued

21. 416.942 FCF estimates for the next 3 years are -$5, $10, and $20 million, after which the FCF is expected to grow at 6%. The overall firm cost of capital is 10%. 0 -4.545 8.264 15.026 398.197 1234 k = 10% g = 6% -5 10 2021.20 21.20 0.04... *TV 3 represents the terminal value of the firm, at t = 3. 530 = = *TV 3

22. If the firm has $40 million in debt and has 10 million shares of stock, what is the price per share? Value of equity = Total value – Value of debt = $416.94 – $40 = $376.94 million. Price per share = Value of equity/# of shares = $376.94/10 = $37.69.