On the eve of the Summer Olympic Games, Nike is trying to decide whether or not to offer a sponsorship contract to Usain Bolt, a sprinter. Nike will pay Bolt a sponsorship fee of $1 million. If Usain Bold comes in first in the 100-meter run, Nike will pay an additional bonus fee of $0.5 million, and it estimates that the present value of the resulting increase in future sales will amount to $6 million. Otherwise, Nike will pay no bonus fee. If Usain Bolt comes in second, the present value of the increase in future sales will amount to $2 million, and if he comes in third, it will amount to $1 million. How should Nike value this deal? Assume that the probability of Bolt finishing first is 10%, and of him finishing second and third is 15% and 20%, respectively. (4 points)