2-3 Growing Perpetuities and Annuities

Growing Perpetuities

If you have a perpetuity that has

• a discount rate of 10% a year
• an annual amount of 1$

Because of the previous chapters we will know that the present value of this perpetuity is: $PV=\frac{annualamount}{discountrate}=\frac{1}{0,10}=10\mathrm{\$}$

When a perpetuity grows on a annual basis with a certain percentage the new formula will be $PV=\frac{annualamount}{discountrate-growrate}$. Let's keep the sample as above but a growth rate of 7%. The new present value will be $PV=\frac{1}{0,10-0.07}=\frac{1}{0,03}=33,3\mathrm{\$}$.