To value the stock of Big Time Cell Phone Corporation after the announcement using the Gordon Growth Model (also known as the Dividend Discount Model), we need to calculate the expected future dividend and the stock price based on the new growth rate.
Step 1: Determine the Expected Future Dividend
The dividend for Year 1 after the cut has been given as $2.07. To find the expected dividend in Year 2 (D2), we can use the new growth rate of 3.80%.
The formula for the expected dividend in Year 2 is:
\[ D2 = D1 \times (1 + g) \]
Where:
- \(D1\) = Year 1 Dividend ($2.07)
- \(g\) = Growth rate (3.80% or 0.038)
Calculating the Year 2 dividend:
\[ D2 = 2.07 \times (1 + 0.038) = 2.07 \times 1.038 = 2.15 \]
Step 2: Calculate the Expected Stock Price Using the Gordon Growth Model
The Gordon Growth Model formula to determine the price of the stock today (P0) is given by:
\[ P0 = \frac{D1}{r - g} \]
Where:
- \(D1\) = Year 1 Dividend ($2.07)
- \(g\) = Growth rate (3.80% or 0.038)
- \(r\) = Required rate of return (this needs to be estimated or provided)
For the sake of this calculation, we can assume the required rate of return is the same as before, which might have been lower due to the previous growth expectations. For this illustration, let's assume \(r = 6.50%\) (0.065), a common estimate for a stable company like Big Time.
Calculating the price using the assumed \(r\):
\[ P0 = \frac{2.07}{0.065 - 0.038} = \frac{2.07}{0.027} \approx 76.67 \]
Conclusion
Based on the assumptions and calculations using the Gordon Growth Model with the new dividend and growth expectations:
- Expected Year 2 Dividend (D2): $2.15
- Estimated Stock Price (P0): $76.67
The actual stock price might differ based on market reactions, investor sentiment, and other external factors, but this calculation provides a theoretical price based on the new dividend cut and growth rate. Always validate the required rate of return, as it can significantly affect the outcome.
1 answer