Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 24 percent for the next three years, with the growth rate falling off to a constant 7 percent thereafter. If the required return is 11 percent, and the company just paid a dividend of $2.05, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

The current price per share is $84.16

Explanation:

The dividend discount model (DDM) estimates the value of a share/stock based on the present value of the expected future dividends from the stock. We will use the two stage growth model of DDM here as the growth in dividends of the stock is divided into two stages.

The formula for current price under two stage growth model is,

P0 = D0 * (1+g1) / (1+r)  +  D0 * (1+g1)^2 / (1+r)^2 + ... + D0 * (1+g1)^n / (1+r)^n  +

[( D0 * (1+g1)^n * (1+g2)) / (r - g2)] / (1+r)^n

Where,

g1 is initial growth rate

g2 is the constant growth rate

r is the required rate of return

So, the price of the stock today will be,

P0 = 2.05 * (1+0.24) / (1+0.11)  +  2.05 * (1+0.24)^2 / (1+0.11)^2  +  

2.05 * (1+0.24)^3 / (1+0.11)^3  + [( 2.05 * (1+0.24)^3 * (1+0.07)) / (0.11 - 0.07)] / (1+0.11)^3

P0 = $84.1556 rounded off to $84.16

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