A stock just paid an annual dividend of $2.50 per share yesterday (assume the st

Question

A stock just paid an annual dividend of $2.50 per share yesterday (assume the stock pays dividends once per year).   You project that the stock’s 3-year growth rate in dividends will be 8% per year (applies to the dividend one year from now, 2 years from now, and 3 years from now). Then, starting 4 years from now, you expect that the dividend will be 3.5% larger than its prior year dividend level, with this annual growth rate of 3.5% to continue forever. The effective annual discount rate for this stock is 8.5% per annum.

--Based on a dividend discount model, what do you estimate as the fair market value for this stock?

--Starting at year 4, how much do you expect the stock price to appreciate every year?         

Explanation / Answer

Current Dividend                              2.5 Cash flow from Dividend 1 year from now will be      2.5(1.08)-growing @ 8% 2.7 Cash flow from Dividend 2 yrs. from now will be    2.7(1.08) 2.916 Cash flow from Dividend 3 yrs. from now will be    2.916(1.08) 3.14928 From Year 4 dividend growth % will be - 8*(103.5/100 ) = 8.28% So, Dividend after year 4 will be 3.14928( 1.0828) =   3.41004 Since this growth rate is constant henceforth, PV of all future cash flows @ end of 3 years is calculated using the formula PV= Dividend/share /(Required discount rate- growth rate of dividend) ie. 3.41004 / (0.085 - 0.0828) = 1550.018 To find the value of the firm, we find the PV of all these cash flows @ 8.5% Year Cash flow PV F @ 8.5% PV @ 8.5% 1 2.7 0.92166 2.488482 2 2.916 0.84946 2.477025 3 3.14928 0.78291 2.465603 3 1550.0182 0.78291 1213.525 TOTAL PV of the cash flows= 1220.956 So, value of the firm = $ 1220.96 Starting at year 4, the stock price is expected to appreciate @ the growth rate of dividend        ie. 3.5% over the previous year - every year Workings PRICE % increase Share price @ year 4 end 3.41(1+0.035) /(.085-.035) D0(1+g) /k-g 70.587 Share price @ year 5 end 73.058 0.035 Share price @ year 6 end 75.615 0.035 Share price @ year 7 end 78.261 0.035 ie.3.5%

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