Question

Synovec Corp. is experiencing rapid growth. Dividends are expected to grow at 25 percent per year during the next three years, 15 percent over the following year, and then 8 percent per year indefinitely. The required return on this stock is 14 percent, and the stock currently sells for $72 per share. What is the projected dividend for the coming year?

Answer 1

According to Dividend discount model, the price of stock today is the present value of all future dividends.

According to constant growth model, if dividends grow at a constant rate of g% every year and discount rate is r%,then stock price today,P0 is

P0 = D1/(r-g)

Let latest dividend given be X. Dividend in coming year will be 1.25X and that is the answer required.

Let dividends in coming years 1,2,3,4,5 be D1,D2,D3,D4,D5 respectively.

D1 =1.25X

D2= 1.25^2 X

D3 = 1.25^3 X

D4= (1.25^3)* 1.15 X

D5= (1.25^3)*(1.15)* 1.08X

According to constant growth model, Price at year 4 will be P4 = D5/(r-g)

Substitute r as 14% and g as 8%

P4 = 2.4258X/(0.14-0.08)

According to Dividend discount model,

P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + P4/(1+r)^4

72 = 1.25X/1.14 + 1.5625X/(1.14)^2 + 1.9531X/(1.14^3) + 2.2461X/(1.14^4) + 2.4258X/[(0.14-0.08)*(1.14^4)]

72 = 1.09649X + 1.20229X + 1.31830X + 1.32987X + 23.93762X

Or 72 = 28.8846X

Or X = 2.492573

Thus dividend just given ,X is $2.49 and dividend next year would be 2.49*1.25 = $3.12

Projected dividend next year is $3.12.

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