Woidtke Manufacturing's stock currently sells for $38 a share. The stock just paid a dividend of $2.40 a share (i.e., D0 = $2.40), and the dividend is expected to grow forever at a constant rate of 10% a year. What stock price is expected 1 year from now? Do not round intermediate calculations. Round your answer to the nearest cent.

The stock is a constant growth stock as it dividends are expected to grow at a constant rate. Thus, the constant growth model of DDM will be used to calculate the price of the stock. The formula under constant growth model to calculate the price of the stock today is,

P0 = D1 / r - g

Where,

D1 is D0 * (1+g) or the dividend expected for the next period
r is the required rate of return
g is the growth rate of dividends

First we need to calculate the required rate of return.

38 = 2.4 * (1+0.1) / (r - 0.1)

38 * (r - 0.1) = 2.64

38r - 3.8 = 2.64

38r = 2.64 + 3.8

r = 6.44 / 38

r = 0.1694736842 or 16.94736842%

As, we use D1 to calculate P0 or the price of the stock today, we will use D2 to calculate the price of the stock one year from now.

P1 = 2.4 * ( 1+0.1)^2 / (0.1694736842 - 0.1)

P1 = $41.80