To analyze the impact of the dividend change and expected growth rate on the stock price of Big Time Cell Phone Corporation, we'll use the Gordon Growth Model (also known as the Dividend Discount Model). This model states that the price of a stock is equal to the next year's dividend divided by the difference between the discount rate and the growth rate.
Steps Involved in Pricing the Stock:
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Identify the Variables:
- New dividend (Year 1 Dividend, D1) = $2.18
- Dividend growth rate (g) = 3.73% or 0.0373
- Current stock price prior to announcement (P0) = $16.61
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Estimate the Discount Rate: To utilize the Gordon Growth Model, we also need to estimate the required rate of return (discount rate) for the stock. However, we don’t have this directly provided. We can infer it based on the information before the announcement:
- Old dividend (D0) = $3.07
- Assuming the initial growth rate (prior announcement) was 2.50% or 0.025.
- The expected price of the stock before the announcement can be set equal to the estimated divident discount:
\[ P_0 = \frac{D_1}{r - g} \] Where \( D_1 = D_0 \times (1 + g) = 3.07 \times (1 + 0.025) = 3.07 \times 1.025 = 3.15\)
Rearranging the formula to find r: \[ 16.61 = \frac{3.15}{r - 0.025} \] So, \[ r - 0.025 = \frac{3.15}{16.61} \] \[ r - 0.025 = 0.189 \] Thus, \[ r = 0.189 + 0.025 = 0.214 \text{ or } 21.4% \]
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Recalculate the Price with the New Dividend: Now with the new dividend ($2.18) and expected growth rate (3.73%), we can estimate the new stock price \( P \):
\[ P = \frac{D_1}{r - g} = \frac{2.18}{0.214 - 0.0373} \]
Performing the calculation: \[ r - g = 0.214 - 0.0373 = 0.1767 \] Therefore, \[ P = \frac{2.18}{0.1767} \approx 12.34 \]
Conclusion:
The estimated new stock price, given the cut in dividends and a new growth rate of 3.73%, is approximately $12.34 per share. This indicates that the market is likely to price the stock lower following the dividend cut and the new growth projections.
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