3.3 Perpetuities
Perpetuities are annuities which provide cash flows for an infinite period, an example of which is non-redeemable preference shares paying a fixed dividend. The formula used is:
PV = PMTr
An investor wants to buy 1 000 non-redeemable 9% preference shares of R1 each. If the interest rate which he applies is 12%, what is the present value of the investment?
In essence the investor is buying a future cash flow in perpetuity amounting to 9% of R1 000 which is R90. This problem requires the principal amount to be determined.
PV = PMTr = 900.12 = R750
The investor who requires a return of 12% will therefore be prepared to pay no more than R750 which is the present value of the investment.
