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Correct Answer: 14.1%
to determine the estimated cost of common equity for terra corporation, the dividend-yield-plus-growth approach, also known as the gordon growth model, is used. this method estimates the cost of equity by considering the dividend expected to be paid in the next period, the current stock price, and the expected growth rate in dividends.
let's break down the calculation as follows:
1. **dividend for next period (d1)**: this is the forecasted dividend for the next period, which is given as $2.11.
2. **current stock price (p0)**: this is the current market price per share of the stock, which is given as $23.12.
3. **growth rate (g)**: this is the constant rate at which dividends are expected to grow indefinitely, given as 5%. it is important to express this growth rate as a decimal in calculations, which is 0.05.
the formula for the cost of equity (ke) using the dividend-yield-plus-growth approach is:
\[ ke = \left(\frac{d1}{p0}\right) + g \]
where:
- \( \frac{d1}{p0} \) is the dividend yield
- \( g \) is the growth rate of dividends
plugging in the values:
\[ ke = \left(\frac{2.11}{23.12}\right) + 0.05 \]
first, calculate the dividend yield:
\[ \frac{2.11}{23.12} = 0.0913 \text{ (or 9.13%)} \]
then, add the growth rate to the dividend yield:
\[ 0.0913 + 0.05 = 0.1413 \text{ (or 14.13%)} \]
thus, the estimated cost of common equity is approximately 14.1%. this percentage reflects the expected return that investors demand for investing in the equity of terra corporation, accounting for both the yield from expected future dividends and the growth in these dividends. this rate is crucial for the company in making decisions regarding financing and investment, ensuring that any projects undertaken meet or exceed this cost of equity to add value to the shareholders.
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