The DDM and Common Stock Valuation Some

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

Assume beta = 1. 2, k. RF = 7%, and k. M = 12%. What is the required rate of return on the firm’s stock? Use the SML to calculate ks: ks= k. RF + (k. M – k. RF)b. Firm = 7% + (12% – 7%) (1. 2) = 13%.

D 0 was $2. 00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. ks = 13%. 0 g = 6% 1 D 0 = 2. 00 2. 12 13% 1. 8761 1. 7599 1. 6509 2 2. 247 3 2. 382

What’s the stock’s market value? D 0 = 2. 00, ks = 13%, g = 6%. Constant growth model: D 1 $2. 12 P 0 = = ks – g 0. 13 – 0. 06 = $2. 12 0. 07 = $30. 29.

What is the stock’s market value one ^ year from now, P 1? • D 1 will have been paid, so expected dividends are D 2, D 3, D 4 and so on. Thus, D 2 $2. 247 P 1 = = ks – g 0. 13 – 0. 06 Could also $32. 10. follows: = find P 1 as ^ ^ ^ P 1 = P 0(1. 06) = $32. 10.

Find the expected dividend yield, capital gains yield, and total return during the first year. D 1 $2. 12 Dividend yld = = = 7. 0%. P 0 $30. 29 ^ P 1 – P 0 $32. 10 – $30. 29 Cap gains yld = = $30. 29 P 0 = 6. 0%. Total return = 7. 0% + 6. 0% = 13. 0%.

Rearrange model to rate of return form: D 1 $ $ + g. P 0 = to k s = ks - g P 0 ^ Then, ks = $2. 12/$30. 29 + 0. 06 = 0. 07 + 0. 06 = 13%.

^ What would P 0 be if g = 0? The dividend stream would be a perpetuity. 0 2 3 2. 00 13% 1 2. 00 PMT $2. 00 P 0 = = = $15. 38. k 0. 13 ^ . . .

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%. • Can no longer use constant growth model. • However, growth becomes constant after 3 years.

Nonconstant growth followed by constant growth: 0 k = 13% 1 s g = 30% D 0 = 2. 00 2 g = 30% 2. 600 3 g = 30% 3. 380 4 g = 6% 4. 394 . . . 4. 658 2. 301 2. 647 3. 045 46. 116 54. 109 ^ = P 0 $ P 3 = 4. 658. = $66. 54 0. 13 - 0. 06

What is the expected dividend yield and capital gains yield at t = 0? At t = 4? $2. 60 Div. yield 0 = = 4. 81%. $54. 11 Cap. gain 0 = 13. 00% – 4. 81% = 8. 19%.

• 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%.

Suppose g = 0 for t = 1 to 3, and then g is ^ a constant 6%. What is P 0? 0 ks=13% g = 0% 2. 00 1. 77 1. 57 1. 39 20. 99 25. 72 1 2 g = 0% 2. 00 3 g = 0% 2. 00 4 g = 6% 2. 00 . . . 2. 12 $ = 30. 29. P 3 = 0. 07

What is D/P and capital gains yield at t = 0 and at t = 3? t = 0: D 1 $2. 00 = = 7. 78%. P 0 $25. 72 CGY = 13% – 7. 78% = 5. 22%. t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%.

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: D 0 ( + g ) 1 D 1 $ = P 0 = ks - g $2. 00(0. 94) $1. 88 = = = $9. 89. 0. 13 – (-0. 06) 0. 19

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.

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.

Using the Free Cash Flow Method • 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.

Issues Regarding the Free Cash Flow Method • 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. (More. . . )

FCF Method Issues Continued • 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 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 k = 10% 1 2 3 4 g = 6% -5 -4. 545 8. 264 15. 026 398. 197 416. 942 10 20 . . . 21. 20 530 = = *TV 3 0. 04 *TV 3 represents the terminal value of the firm, at t = 3.

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.