Questions: Madison Tour, Inc., just paid a dividend of 3.15 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year, indefinitely. Assume investors require a return of 11 percent on this stock. What will the price be in 3 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Madison Tour, Inc., just paid a dividend of 3.15 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year, indefinitely. Assume investors require a return of 11 percent on this stock.

What will the price be in 3 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Transcript text: Madison Tour, Inc., just paid a dividend of $\$ 3.15$ per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year, indefinitely. Assume investors require a return of 11 percent on this stock. What will the price be in 3 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) $\square$

Solution

To determine the price of the stock in 3 years, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a stock with constant growth). The formula for the price of the stock at any time $ t $ is given by:

\[ P_t = \frac{D_{t+1}}{r - g} \]

where:

$ P_t $ is the price of the stock at time $ t $.
$ D_{t+1} $ is the dividend expected at time $ t+1 $.
$ r $ is the required rate of return (11% or 0.11 in this case).
$ g $ is the growth rate of the dividends (6% or 0.06 in this case).

First, we need to calculate the dividend expected in 3 years, $ D_4 $, because the price in 3 years, $ P_3 $, is based on the dividend in the following year:

Calculate the dividend in 1 year ($ D_1 $): \[ D_1 = D_0 \times (1 + g) = 3.15 \times (1 + 0.06) = 3.15 \times 1.06 = 3.339 \]
Calculate the dividend in 2 years ($ D_2 $): \[ D_2 = D_1 \times (1 + g) = 3.339 \times 1.06 = 3.53934 \]
Calculate the dividend in 3 years ($ D_3 $): \[ D_3 = D_2 \times (1 + g) = 3.53934 \times 1.06 = 3.7517004 \]
Calculate the dividend in 4 years ($ D_4 $): \[ D_4 = D_3 \times (1 + g) = 3.7517004 \times 1.06 = 3.976802424 \]

Now, use the Gordon Growth Model to find the price of the stock in 3 years ($ P_3 $):

\[ P_3 = \frac{D_4}{r - g} = \frac{3.976802424}{0.11 - 0.06} = \frac{3.976802424}{0.05} = 79.53604848 \]

Rounding to two decimal places, the price of the stock in 3 years will be:

\[ P_3 = 79.54 \]

Therefore, the price of the stock in 3 years is expected to be \$79.54.

Was this solution helpful?