The firm projects a rapid growth of 40 percent for the next two years and then a growth rate of 20 percent for the following two years. After that, the firm expects a constant-growth rate of 8 percent. The firm expects to pay its first dividend of $1.25 a year from now. If your required rate of return on such stocks is 20 percent, what is the current price of the stock

The price of the stock today is $15.63

Explanation:

The three stage Dividend Discount model will be used to calculate the price of this stock as the dividends are growing at three different growth rates. These dividends will be discounted back to calculate the price of the stock today.

The price per share today under this model will be:

P0 = D1 / (1+r) + D2 / (1+r) ^2 + ... + Dn / (1+r) ^n + [Dn * (1+gC) / (r - gC) ] / (1+r) ^n

Where,

D1 is the dividend expected for the next period of Year 1. gC is the constant growth rate or third stage growth rate that will last forever.

P0 = 1.25 / (1+0.2) + 1.25 * (1+0.4) / (1+0.2) ^2 + 1.25 * (1+0.4) * (1+0.2) / (1+0.2) ^3 + 1.25 * (1+0.4) * (1+0.2) ^2 / (1+0.2) ^4 +

[1.25 * (1+0.4) * (1+0.2) ^2 * (1+0.08) / (0.2 - 0.08) ] / (1+0.2) ^4

The P0 = $15.625 rounded off to $15.63