Subjects finance

Implied Growth Rate E95Eff

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1. **State the problem:** We need to calculate the implied growth rate $g$ using the given dividend growth model formula: $$P_0 = \frac{D_0(1+g)}{r-g}$$ where $P_0 = 24.25$, $D_0 = 1.10$, and $r = 0.085$. 2. **Write the equation with given values:** $$24.25 = \frac{1.10(1+g)}{0.085 - g}$$ 3. **Multiply both sides by the denominator to clear the fraction:** $$24.25(0.085 - g) = 1.10(1 + g)$$ 4. **Distribute terms:** $$24.25 \times 0.085 - 24.25g = 1.10 + 1.10g$$ $$2.06125 - 24.25g = 1.10 + 1.10g$$ 5. **Bring all terms involving $g$ to one side and constants to the other:** $$2.06125 - 1.10 = 1.10g + 24.25g$$ $$0.96125 = 25.35g$$ 6. **Solve for $g$ by dividing both sides by 25.35:** $$g = \frac{0.96125}{25.35}$$ $$g = 0.0379$$ 7. **Interpretation:** The implied growth rate $g$ is approximately 0.0379 or 3.79%.