Rojas Craig
03/25/2024 · Elementary School
uper Carpeting Inc. just paid a dividend \( \left(D_{0}\right) \) of \( \$ 2.64 \), and its dividend is expected to grow, at a constant rate \( (g) \) of \( 3.85 \% \) per year. f the required return \( \left(r_{s}\right) \) on Super's stock is \( 9.63 \% \), then the intrinsic, or theoretical market, value of Super's shares is per sha
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To calculate the intrinsic value of Super Carpeting Inc.'s shares, we can use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth). The formula for the intrinsic value \( P_0 \) of a stock is given by:
\[
P_0 = \frac{D_1}{r_s - g}
\]
Where:
- \( D_1 \) is the expected dividend next year,
- \( r_s \) is the required return,
- \( g \) is the growth rate of the dividend.
First, we need to calculate \( D_1 \), which is the dividend expected next year. Since the most recent dividend \( D_0 \) is \( \$2.64 \) and it is expected to grow at a rate of \( 3.85\% \), we can calculate \( D_1 \) as follows:
\[
D_1 = D_0 \times (1 + g) = 2.64 \times (1 + 0.0385) = 2.64 \times 1.0385
\]
Calculating \( D_1 \):
\[
D_1 = 2.64 \times 1.0385 \approx 2.743
\]
Now we can substitute \( D_1 \), \( r_s \), and \( g \) into the Gordon Growth Model formula:
\[
P_0 = \frac{2.743}{0.0963 - 0.0385}
\]
Calculating the denominator:
\[
0.0963 - 0.0385 = 0.0578
\]
Now substituting back into the formula:
\[
P_0 = \frac{2.743}{0.0578} \approx 47.38
\]
Thus, the intrinsic, or theoretical market, value of Super Carpeting Inc.'s shares is approximately **$47.38** per share.
Quick Answer
The intrinsic value of Super Carpeting Inc.'s shares is approximately $47.38 per share.
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