Suppose that you have $1,000 at hand that you can place in a bank gaining 5% annually in interest; assume that this interest rate is your personal discount rate. Your friend asks you to lend him $1,000 so he can buy a new gadget that he does not really need. He promises to pay back the full amount, plus interest, in a certain amount of time. Assume that you really do not think that your friend should buy this new gadget, except, of course, if you were to make a profit out of it.
(a) Your friend offers to pay you back $1,006 in one year. What should you do? Demonstrate how much money you would make if you were to place your $1,000 in the bank and compare it with the amount of money you would make if you were to accept your friend’s offer.
(b) Your friend offers to pay you back $1,060 in one year. What should you do? Demonstrate.
(c) Your friend offers to pay you back $500 in one year, another $400 in two years, and $200 in three years. What should you do? Demonstrate.
(d) Your friend offers to pay you back $200 in one year, another $400 in two years, and $500 in three years. What should you do? Demonstrate.
(e) Suppose instead that your friend just saw a publicity for this gadget he really does not need but really wants, and that this gadget will come into the market in x years and will cost $1,000. Your friend is worried that he will spend his money on other useless gadgets before this one comes out, so he offers to pay you $y each year if you agree to give him $1,000 in x years when the gadget gets on the market. Assume you can still earn 5% annual interest by placing the money your friend gives you in a bank, and that in x years you have to withdraw all of the money from the bank; assume again that this interest rate is your personal discount rate.
(i) If x = 1, that is, your friend pays you $y today, and you pay him back $1,000 in a year. For what amount of money y will you be indifferent between accepting or refusing his offer?
(ii) If x = 5, for which amount of money y will you be indifferent between accepting or refusing his offer?
(iii) Suppose now that instead of giving you the money each year, your friend gives you only $y today. If x = 10, for which amount of money y will you be indifferent between accepting or refusing your friend’s offer?
