City Foods, is a firm that is experiencing rapid growth. The firm just paid a dividend of $2.00 yesterday. They expect to see their dividend grow at a twenty percent rate for the next two years and then level out at a continuous six percent growth rate. City Food's required rate of return is twelve percent. What is the most you would pay for City Foods' common stock now

The maximum that should be paid for the stock today is $45 per share.

Explanation:

To calculate the current share price or the maximum that should be paid for the stock today, we will use the dividend discount model approach.

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 * (1+0.20) / (1+0.12)  +  2 * (1+0.20)^2 / (1+0.12)^2  +    

[( 2 * (1+0.20)^2 * (1+0.06)) / (0.12 - 0.06)] / (1+0.12)^2

P0 = $45

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