The price you and your sister would pay for the stock today may not necessarily be the same. The price of a stock is determined by various factors such as supply and demand dynamics, market sentiment, company performance, and future growth prospects.
Since you plan to sell the stock after one year, your decision may be influenced more by short-term factors and expectations for the stock's performance within that timeframe. On the other hand, your sister, who plans to hold the stock for five years, may be more focused on long-term factors and potential growth over that extended period.
Therefore, your investment horizon and differing strategies may lead to different valuations of the stock, which can result in paying different prices for the stock today. It is possible that you might be willing to pay a lower price since your holding period is shorter and you may have different return expectations compared to your sister.
Ultimately, the specific circumstances, market conditions, and individual investment considerations will determine whether you and your sister would pay the same price for the stock today or not.