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The DDM and Common Stock Valuation

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 k s :.

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The DDM and Common Stock Valuation

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  1. The DDMand 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, kRF =7%, and kM =12%. What is the required rate of return on the firm’s stock? Use the SML to calculate ks: ks= kRF + (kM – kRF)bFirm = 7% + (12% – 7%) (1.2) = 13%.

  3. D0 was $2.00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. ks = 13%. 0 1 2 3 g = 6% D0 = 2.00 2.12 2.247 2.382 13% 1.8761 1.7599 1.6509

  4. What’s the stock’s market value? D0 = 2.00, ks = 13%, g = 6%. Constant growth model: D1 $2.12 P0 = = ks – g 0.13 – 0.06 $2.12 = = $30.29. 0.07

  5. What is the stock’s market value one year from now, P1? ^ • D1 will have been paid, so expected dividends are D2,D3, D4 and so on. Thus, Could also find P1 as follows: D2 $2.247 ^ P1 = = ks – g 0.13 – 0.06 = $32.10. ^ ^ P1 = P0(1.06) = $32.10.

  6. Find the expected dividend yield, capital gains yield, and total return during the first year. D1 $2.12 Dividend yld = = = 7.0%. P0 $30.29 ^ P1– P0 $32.10 – $30.29 Cap gains yld = = $30.29 P0 = 6.0%. Total return = 7.0% + 6.0% = 13.0%.

  7. D D $ $ 1 1 = = + P to k g . - 0 s k g P s 0 Rearrange model to rate of return form: ^ Then, ks = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%.

  8. What would P0 be if g = 0? ^ The dividend stream would be a perpetuity. 0 1 2 3 13% ... 2.00 2.00 2.00 ^ PMT k $2.00 0.13 P0 = = = $15.38.

  9. If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P0? k is still 13%. ^ • Can no longer use constant growth model. • However, growth becomes constant after 3 years.

  10. Nonconstant growth followed by constant growth: 0 1 2 3 4 ... ks = 13% g = 30% g = 30% g = 30% g = 6% D0 = 2.00 2.600 3.380 4.394 4.658 2.301 2.647 3.045 4.658 . $ P = = $66.54 46.116 3 . 13 - 0 . 06 0 ^ 54.109 = P0

  11. What is the expected dividend yield and capital gains yield at t = 0? At t = 4? $2.60 $54.11 Div. yield0 = = 4.81%. Cap. gain0 = 13.00% – 4.81% = 8.19%.

  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. Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P0? ^ 0 1 2 3 4 ... ks=13% g = 0% g = 0% g = 0% g = 6% 2.00 2.00 2.00 2.00 2.12 1.77 1.57 2.12 1.39 $ = = P 30.29. 20.99 3 0 . 07 25.72

  14. What is D/P and capital gains yield at t = 0 and at t = 3? D1 $2.00 $25.72 = = 7.78%. t = 0: P0 CGY = 13% – 7.78% = 5.22%. t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%.

  15. If g =-6%, would anyone buy the stock? If so, at what price? Firm still has earnings and still pays dividends, so P0 > 0: ( ) + D 1 g D $ 0 1 = = P - - 0 k g k g s s $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. 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. ^

  19. 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...)

  20. 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.

  21. 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 1 2 3 4 ... k = 10% g = 6% -5 10 20 21.20 -4.545 8.264 15.026 21.20 0.04 530 = = *TV3 398.197 416.942 *TV3 represents the terminal value of the firm, at t = 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.

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