Constant Growth Common Stock: What Is The Value Of A Common

Constant-Growth Common Stock What is The Value Of A Common Sto

Problem 1 constant Growth Common Stockwhat Is The Value Of A Common Sto

Problem 1 constant Growth Common Stockwhat Is The Value Of A Common Sto

Problem 1 Constant-Growth Common Stock What is the value of a common stock if the firm's earnings and dividends are growing annually at 10%, the current dividend is $1.32, and investors require a 15% return on investment? What is the stock's rate of return if the market price of the stock is $35?

Paper For Above instruction

Determining the value of a common stock under constant growth assumptions is a foundational element in financial valuation. The most widely used method for this is the Gordon Growth Model (also known as the Dividend Discount Model for a perpetually growing dividend), which is especially applicable when a company's dividends are expected to grow at a steady rate indefinitely. This model provides a straightforward formula to assess the intrinsic value of a stock based on expected future dividends, growth rate, and required rate of return.

In this specific scenario, the firm’s dividends are expected to grow annually at 10%. The current dividend (D₀) is given as $1.32. The required rate of return (r) that investors demand is 15%. Using the Gordon Growth Model, the value of the stock (P₀) can be calculated as:

P₀ = D₁ / (r - g)

where D₁ is the dividend expected one year from now, calculated as D₀ × (1 + g).

Calculating D₁: D₁ = $1.32 × (1 + 0.10) = $1.452

Applying the formula: P₀ = $1.452 / (0.15 - 0.10) = $1.452 / 0.05 = $29.04

Hence, the intrinsic value of the stock, based on these assumptions, is approximately $29.04.

To evaluate the stock’s current rate of return based on the market price, we can reverse engineer the expected return that would justify the current stock price of $35. This can be approximated by the dividend yield plus the growth rate, which aligns with the Gordon Model’s assumptions:

Expected Rate of Return (r̂) = (D₁ / P₀) + g = ($1.452 / $35) + 0.10 ≈ 0.0415 + 0.10 = 0.1415 or 14.15%.

This expected return of approximately 14.15% is slightly below the 15% required return, indicating that at a $35 market price, the stock offers a slightly lower yield than what investors demand, which could suggest it is somewhat overvalued or that market expectations are adjusting.

Financial Theory and Implications

The use of the Gordon Growth Model assumes that dividends will grow at a constant rate indefinitely. While it simplifies valuation, it relies heavily on the accuracy of the growth rate and the required rate of return estimates. In real-world scenarios, companies’ earnings and dividends might not grow at a fixed rate forever, necessitating more complex models or multi-stage growth valuations. Nonetheless, for stable, mature companies, the Gordon Model remains a valuable tool for estimating stock value and assessing investment attractiveness.

Conclusion

Based on the provided data, the intrinsic value of the company’s stock is approximately $29.04, calculated using the dividend discount model with a 10% growth rate and a 15% investor return requirement. The current market price of $35 implies an estimated return of about 14.15%, slightly below the required rate, which may influence investment decisions and market perceptions. Investors and analysts should consider other factors, including market conditions, company fundamentals, and broader economic indicators, when making investment choices related to this stock.

References

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