To determine the current price $X$ of Electric Violet stock, we can use the dividend discount model (DDM). We need to calculate the present value of the expected dividends over the specified time frame, including the perpetuity starting after year 5.

1. Calculate the present value of dividends in years 2, 4, and 5:

   • $D_2 = 4.53$
   • $D_4 = 5.68$
   • $D_5 = 6.44$

   Using the formula for present value: $PV = \frac{D}{(1 + r)^t}$ where $r = 0.143$.

   $PV(D_2) = \frac{4.53}{(1 + 0.143)^2} \approx 3.45$ $PV(D_4) = \frac{5.68}{(1 + 0.143)^4} \approx 3.23$ $PV(D_5) = \frac{6.44}{(1 + 0.143)^5} \approx 3.21$

2. Calculate the perpetuity starting after year 5: After year 5, the dividend grows at a rate of 2.4%. The dividend at year 6 can be calculated as: $D_6 = D_5 \times (1 + g) = 6.44 \times (1 + 0.024) \approx 6.59$

   The present value of the perpetuity starting at year 6 is given by: $PV = \frac{D_6}{r - g} = \frac{6.59}{0.143 - 0.024} \approx 52.19$

   We need to discount this back to present value: $PV(PV) = \frac{52.19}{(1 + 0.143)^5} \approx 27.47$

3. Sum the present values: $X = PV(D_2) + PV(D_4) + PV(D_5) + PV(PV)$ $X \approx 3.45 + 3.23 + 3.21 + 27.47 \approx 37.36$

Thus, the current price $X$ of Electric Violet stock is approximately $37.36.

Do you want details on any specific part, or do you have further questions? Here are some related questions to consider:

1. How do changes in the expected return affect the stock price?
2. What impact does the growth rate of dividends have on valuation?
3. Can the dividend discount model be applied to other types of investments?
4. How do you determine if a stock is overvalued or undervalued?
5. What are the risks associated with relying on dividend projections?

Tip: Always consider the sensitivity of stock price calculations to changes in growth rates and discount rates.