Question

1. You are offered a security that will pay $3,000 a year for twenty years and, also, $100,000 at the end of twenty-year period (last payment is $3,000 + $100,000). You did some research and found that if you invest in a similar risk security you can get a 9% annual return.

   1. What is the maximum amount you will be willing to pay for such a security?

   2. If you learn that this security will actually pay $3,000 a year in perpetuity (instead of 20 payments + $100,000), what is the maximum price you would pay for it?

Answer 1

The maximum price paid for the security is equal to the present value of future cash flows

= 3,000*PVAF(9%, 20 years) + 100,000*PVF(9%, 20 years)

= 3,000*9.1285 + 100,000*0.1784

= $45,225.5

Maximum price = 3,000/9%

= $33,333.33