Before the value at risk can be estimated you need to know the probability that the $10000 that is being invested to start your new business would actually lead to a profit making proposition. Assuming you could lose all of the $10000 or it becomes double with an equal probability, the VaR is 100%.
Though in the two cases you have described the value of risk is less important than what the $10000 means to you. For a person earning $100000 losing the entire $10000 is not going to lead to a major change in his life. He could live on $90000 with approximately the same level of comfort as he could on $100000. But your losing the last $10000 you have could mean your ending up on the street with no food. On the other hand, if your business venture succeeds the same $10000 could change your entire life. It is a risk that you have to decide if you are willing to take on.