1. Mixtastic, a firm that sells a subscription for a mix-at-home cocktail kit, projects it will earn $100K in profit each year, and each year it has an 80% chance of surviving until the next year. Under these assumptions, what is the value of the firm today? In case the firm only expects to start earning profit in three years, then approximately by what percentage does its present value decrease? 2. Stuffitt, the "AirBnB for storage units," expects to earn $5 million in profit per year, once it is up and running. Currently, the expected start date is two years from now, but with a $2 million additional investment, Stuffitt could go "live" in one year. Whether or not Stuffitt is "live," it always has a 60% chance of surviving until the following year. Calculate the value if they open in two years and the value if they open in one year. Is it worthwhile to make the investment (i.e. is the difference greater than $2 million)? 3. For Mixtastic in Problem 1, suppose the firm will earn $100K a year starting immediately. What if, instead of an 80% chance of surviving each year, it only has a 50% chance? And what if it has an 80% chance, but annual profit is only $50K? Calculate the value of the firm in these two scenarios. Which is better: double the profit or 30% better odds to last for another year? 4. For Stuffitt in Problem 2, suppose the firm will earn $5 million a year starting in two years. What if, instead of a 60% chance of surviving each year, it has a 75% chance? And what if it has a 60% chance, but annual profit is $10 million? Calculate the value of the firm in these two scenarios. Which is better: double the profit or 15% better odds to last for another year