To determine if the project was good for shareholders, we can use the Gordon Growth Model (also known as the Dividend Discount Model) to evaluate the expected value of the stock before and after the dividend cut and the change in growth rate.
- Before the announcement, the expected annual dividend was \( D_0 = 3.10 \) and was expected to grow at \( g_1 = 2.50% \).
The expected dividend for year 1 (\( D_1 \)) would be: \[ D_1 = D_0 \times (1 + g_1) = 3.10 \times (1 + 0.025) = 3.10 \times 1.025 = 3.175 \]
Using Gordon Growth Model: \[ P_0 = \frac{D_1}{r - g_1} \] Where \( P_0 \) is the current price ($18.74), \( r \) is the required rate of return, and \( g_1 \) is 2.5%. Rearranging gives us a way to estimate \( r \).
Assuming \( P_0 = 18.74 \): \[ 18.74 = \frac{3.175}{r - 0.025} \] Multiplying both sides by \( r - 0.025 \) gives: \[ 18.74(r - 0.025) = 3.175 \] \[ 18.74r - 0.4685 = 3.175 \] \[ 18.74r = 3.6435 \] \[ r \approx 0.1941 \text{ (or 19.41%)} \]
- After the announcement, the new expected dividend is \( D_1 = 2.15 \) and the new growth rate is \( g_2 = 3.85% \).
Applying the Gordon Growth Model again: \[ D_1 = 2.15 \] \[ P_1 = \frac{D_1}{r - g_2} = \frac{2.15}{0.1941 - 0.0385} = \frac{2.15}{0.1556} \approx 13.82 \]
Conclusion: Prior to the announcement, the stock was valued at $18.74, and after the announcement, the estimated value drops to approximately $13.82. Given this significant reduction in the valuation of the stock, the project had a negative impact on shareholders.
Answer: NO
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