Question

You can purchase a fifteen-year annuity, that pays $26,500 a year. The first payment starts nine years from today. What is a fair market price today if your opportunity cost of investment is 5%?

A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust (a local bank) to pay the lumpsum payout to the trust and have trust pay the annual payments. The first winner of the lottery chooses the annuity and will receive $200,000 a year for the next twenty years. The local government will give the trust $1,500,000 to pay for this annuity. What investment rate must the trust earn to break-even on this arrangement?

Answer 1

a.Present value=Future cash flows*Present value of discounting factor(rate%,time period)

=26500/1.05^9+26500/1.05^10+26500/1.05^11+26500/1.05^12+26500/1.05^13+26500/1.05^14+26500/1.05^15+26500/1.05^16+26500/1.05^17+26500/1.05^18+26500/1.05^19+26500/1.05^20+26500/1.05^21+26500/1.05^22+26500/1.05^23

=$186172.07(Approx)

b.Let investment rate be x%

At this rate;present value of annuity=1,500,000

1,500,000=200000/1.0x+200000/1.0x^2+...............+200000/1.0x^20

Hence x=investment rate=11.94%(Approx)