Henry is a student leaving high school considering what to do with his life. If he attends college next year, he will graduate with a degree with probability 0.9. With probability 0.1, he will attend for four years but not get his degree. The cost of attending college is $400,000. If he attends college, Henry will work for 50 years and then retire. If he earns a college degree, he will make $120,000 per year. If he attends college but does not earn a degree, he will make $50,000 per year. If he does not attend college, he will work for 54 years, earning $100,000 per year, and then retire.

a) Write out the equation for the net present value of Henry attending college. Note that you do not have enough information yet to solve it for a number.

b) Write a mathematical statement (i.e., an equation or inequality, with words as needed) to express under what circumstances Henry will choose to attend college.

c) Now imagine he does not know the probability of graduating with a degree, if he chooses to attend college. Write a mathematical statement expressing the probability of graduating with a degree, conditional on attending college, at which Henry is indifferent between attending and not attending college

Now let’s set the interest rate at 3%.

d) What is the present discounted value of the income Henry will make if he does not attend college? Show your work – write down the mathematical formula you use to generate this and the work you used to come to your final answer. You can use excel / google sheets to come up with the final numerical answer.

e) What is the present discounted value of the income Henry will make if he does attend college? Show your work. Write down the mathematical formula you use to generate this and the work you used to come to your final answer. You can use excel / google sheets to come up with the final numerical answer.