In: Finance
Let D0,D1,D2,D3 and all be dividends in year 0,1,2,3 and so on
Value of cash dividends is as follows at the end of each year
D0=D1= $3.40
D2 = 3.4*(1.05) = 3.57
D3 = 3.4*(1.05^2) = 3.7485
D4 = D3*1.15 = 3.7485*1.15 = 4.3108
D5 = D4*1.1 = 4.7419
Required return, r is 12%
According to multistage Dividend growth model,
Price of stock, P is given by discounted future dividends
P = D1/(1+r) + D2/(1+r)^2 +D3/(1+r)^3 + D4/(1+r)^4 + D5/[(r-g)*(1+r)^4]
The last part if Gordon growth model value of stock at time 4, (of dividends from year 5 till perpetuity) which is discounted to present
P = 3.4/1.12 + 3.57/(1.12^2) + 3.7485/(1.12^3) + 4.3108/(1.12^4) + 4.7419/[(.12-.10)*(1.12^4)]
P = 3.0357+2.846+2.6681+2.7396+134.5327
P = $ 145.82
Thus, maximum price an investor should pay is $ 145.82. This is the value of stock today.
If we take initial growth period till year 4, the stock price at year 4 end is D5/(r-g)
= 4.7419/(0.12-0.10) = $237.09
If we take initial growth period till year 4, the present value of dividends is
3.4/1.12+ 3.57/(1.12^2) + 3.7485/1.12^3) + 4.3108/1.12^4
= 3.0357+2.846+2.6681+2.7396
= $11.29
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