Answer:
closest to $100
Step-by-step explanation:
To find the value of a share of KTI's stock using the Dividend Discount Model (DDM), we can use the formula:
\[P = \frac{D_1}{r - g}\]
Where:
- \(P\) = Value of the stock
- \(D_1\) = Expected dividend per share next year
- \(r\) = Equity cost of capital
- \(g\) = Growth rate of dividends
We're given that KTI will pay out $1.50 of its $5 earnings per share as dividends, so \(D_1 = 1.50\).
To find the growth rate (\(g\)), we can use the sustainable growth rate formula:
\[g = \text{Return on new investments} \times \text{Plowback ratio}\]
The plowback ratio (\(b\)) is the portion of earnings retained to fund future growth. It's calculated as \(1 - \text{Dividend payout ratio}\).
Plugging in the values:
\[b = 1 - \frac{1.50}{5} = 1 - 0.30 = 0.70\]
\[g = 0.15 \times 0.70 = 0.105\]
Now, we can calculate the value of the stock:
\[P = \frac{1.50}{0.12 - 0.105}\]
\[P = \frac{1.50}{0.015}\]
\[P = 100\]
So, the value of a share of KTI's stock is closest to $100.
