Question

In exchange for $1000 today, the bank promises to pay you $25 per year forever (assuming you live forever). Your opportunity cost of capital is 5% compounded annually. If the first payment from the bank is scheduled to arrive next year, what effective annual interest rate is the bank paying out on this perpetuity? From a purely financial perspective, should you give $1000 to the bank or invest your money elsewhere?

Answer 1

Effective annual Interest Rate on the Perpetuity = Annual Payment promised / Price of Perpetuity = $ 25 / $ 1000 = 0.025 or 2.5%

The bank is paying out 2.5% annually on this perpetuity. This is less than our opportunity cost of capital which is 5%.

Present Value of the Perpetuity = Annual Payment promised / Opportunity Cost of Capital = $ 25 / 0.05 = $ 500

If the bank had asked us to invest $500 instead of $1000, then we would have considered investing in this perpetuity (because then we would have earned 5% per annum). However, the effective interest rate paid out by the bank = 2.5% is less than our Opportunity Cost of Capital = 5%.

Hence, from a purely financial perspective we should not invest $1000 in this bank's perpetuity but rather invest it elsewhere.