Question

Question 5 [4 points] Suppose the interest rate is 5%. You inherit a trust (a perpetuity) that will eventually pay you $10,000 a year forever. You will receive the first $10,000 payment exactly three years from today. a. What is the trust worth at the moment you start collecting payments (i.e. in three years from today) (1 point] b. What is the trust worth today? (1.5 points c. A bank offers to exchange your trust for another stream of yearly payments that also lasts forever but whose first payment will be made exactly one year from today instead of three. What is the highest yearly payment that the bank is willing to offer you in exchange for your trust? [1.5 points]

Answer 1

Value today of a perpetuity that start payment exactly 1 year from now and interest rate i is given by

PV = PMT/i

So, value today of a perpetuity starting today = PMT + PMT/i

a). So, value of trust after 3 years = 10000 + 10000/0.05 = $210000

b). Trust value today can be calculated using PV formula

PV = FV/(1+i)^t

So, trust value today = 210000/1.05^3 = $181405.90

c). For a similar perpetuity, that starts paying exactly one year from now, annual payment = PV*i

So, highest yearly payment the bank is willing to offer in exchange for the trust = 181405.90*0.05 = $9070.29