Question $3$:

Dr$.$ Michael Casey of Medical Research Corporation $($MRC$)$ was thrilled with the response he had received from drug companies for his latest discovery, a unique electronic stimulator that reduces the pain from arthritis. The process had yet to pass rigorous Federal Drug Administration $($FDA$)$ testing and was still in the early stages of development, but the interest was intense. He received the three offers described below. $($Unless otherwise specified, use a $10$ percent interest rate throughout this analysis.$)$

Offer I $-$ $$1,100,000$ now plus $$220,000$ from year $6$ through $15.$ Also, if the product did over $$100$ million in cumulative sales by the end of year $15,$ he would receive an additional $$3,500,000.$ Dr$.$ Casey thought there was a $70$ percent probability this would happen.

Offer II $-$ Thirty percent of the buyer's gross profit on the product for the next four years. The buyer in this case was GSK Pharmaceutical. GSK$\text{'}$s gross profit margin was $60$ percent. Sales in year one were projected to be $$5$ million and then expected to grow by $40$ percent per year.

Offer III $-$ A trust fund would be set up for the next eight years. At the end of that period, Dr$.$ Casey would receive the proceeds. The trust fund called for semiannual payments for the next eight years of $$200,000($a total of $$400,000$ per year$).$ The payments would start immediately. Since the payments come at the beginning of each period instead of the end. Assume the annual interest rate on this annuity is $10$ percent annually. Determine the present value of the trust fund's final value.