Final answer:
Using the Gordon Growth Model and given the P/E ratio, earnings per share, and dividend information, the expected stock price can be calculated. However, since complete financial information is not provided, the exact expected stock price for Avalanche Inc. in 6 years cannot be determined.
Step-by-step explanation:
To calculate the expected stock price in 6 years for Avalanche Inc., which currently has a P/E ratio of 9.77, earned $4.35 per share, and paid a $1.25 dividend last year, we'll use the Gordon Growth Model. The model requires the expected growth rate, which is given as 13%.
Here's the formula:
Expected Stock Price = (Dividends per Share * (1 + Growth Rate)) / (Discount Rate - Growth Rate)
To find the discount rate, also known as the required rate of return, we can rearrange the P/E ratio formula:
Discount Rate = (Earnings per Share / Stock Price)
With the P/E ratio of 9.77 and earnings of $4.35 per share, the stock price can be assumed to be:
Stock Price = Earnings per Share * P/E Ratio = $4.35 * 9.77
Thus, we need to perform the calculations with the information provided and the formula above. As we do not possess all the necessary financial data in this hypothetical scenario, we are unable to provide the exact expected stock price for Avalanche Inc. after 6 years. For accurate predictions, historical data, financial statements, and additional market conditions would be required.