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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 DDMand Common Stock Valuation • Some quick examples, courtesy of Harcourt • The Effect of Evolving Growth Rates • Valuation via Operating Cash Flow
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%.
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
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
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.
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%.
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%.
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.
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.
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
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%.
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 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
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%.
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.
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 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.
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.