Question

Question 8
Dividends on CCN corporation are expected to grow at a 9% per year. Assume that the discount rate on CCN is 12% and that the expected dividend per share in one year is $0.50. CCN has just paid a dividend, so the next dividend is the $0.50 to be paid one year from now.

Calculate the expected price per share 14 years from now. Assume that a dividend has just been paid.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer 1

To calculate the expected price per share of CCN corporation 14 years from now, we can use the Gordon Growth Model (also known as the Dividend Discount Model) which is defined as:

\[
P = \frac{D} {r - g}
\]

Where:
- \( P \) = Price of the stock today
- \( D \) = Dividend in the next period
- \( r \) = Discount rate (required rate of return)
- \( g \) = Growth rate of dividends

Since we need the expected price per share 14 years from now, we will first calculate the expected dividend at that time.

1. Calculate the expected dividend 14 years from now:

The formula for the dividend in \( n \) years with a growth rate \( g \) is:

\[
D_n = D_0 \times (1 + g)^n
\]

Where:
- \( D_0 = 0.50 \) (the next dividend)
- \( g = 0.09 \) (growth rate of 9%)
- \( n = 14 \) (years)

\[
D_{14} = 0.50 \times (1 + 0.09)^{14}
\]
\[
D_{14} = 0.50 \times (1.09)^{14}
\]

Let's calculate \( (1.09)^{14} \):

\[
(1.09)^{14} \approx 4.124
\]

Now we can find:

\[
D_{14} \approx 0.50 \times 4.124 \approx 2.062
\]

2. Now we can calculate the expected price per share 14 years from now:

Using the Gordon Growth Model:

\[
P_{14} = \frac{D_{15}} {r - g}
\]

To find \( D_{15} \), we need to calculate the dividend for the next year after year 14:

\[
D_{15} = D_{14} \times (1 + g) = 2.062 \times (1 + 0.09)
\]
\[
D_{15} \approx 2.062 \times 1.09 \approx 2.24958
\]

Now substituting \( D_{15} \) back into the price formula:

\[
P_{14} = \frac{2.24958}{0.12 - 0.09}
\]
\[
P_{14} = \frac{2.24958}{0.03} \approx 74.986
\]

Thus, the expected price per share 14 years from now is:

\[
\text{P}_{14} \approx 74.99
\]

The final answer is:

\[
74.99
\]