Equity Valuation – Dividend Growth Rate

Practice Question

Intro to Finance
Equity Valuation
Dividend
Short Answer

Two years ago, Lucas bought a stock for $27.12 a share of Battery Co. When she purchased the stock, the company had just paid a $1.58 dividend, and the dividend is expected to grow at a rate of x. Given a required return of 16% on this investment, what is the growth rate (x) of the Battery Co. stock?

Answer +
Final Answer: 9.6% (or 0.096)
Explanation +

Step 1: Identify Variables

  • Price (\( P_0 \)) = 27.12
  • Dividend just paid (\( D_0 \)) = 1.58
  • Required return (\( r \)) = 16% or 0.16

Step 2: Use the Dividend Discount Model (DDM)

\[ P_0 = \frac{D_1}{r - g} \quad \text{and} \quad D_1 = D_0(1 + g) \]

Step 3: Substitute into the DDM

\[ 27.12 = \frac{1.58(1 + g)}{0.16 - g} \]

Step 4: Solve for \( g \)

\[ 27.12(0.16 - g) = 1.58(1 + g) \\ 4.3392 - 27.12g = 1.58 + 1.58g \\ 2.7592 = 28.7g \Rightarrow g = \frac{2.7592}{28.7} \approx 0.0961 \]

Conclusion: The dividend growth rate \( g \) is approximately 9.6%.