growingannuity(cash, rate, growth, nperiods)

I hold an investment that will pay me every year for 5 years starting next year. The first payment is 100 U, and each payment is expected to grow by 3% each year. If the interest rate is 11%, what is the present value of the investment.

This can also be calculated as follows:

The cash flows are given by:

or equivalently as

Here, we deal with a more complicated example illustrating differential growth. We have an investment that will pay dividends of 1.12 U starting one year from now, growing at 12 % per year for the next 5 years. From then on, it will be growing at 8%. What is the present value of these dividends if the required return is 12%? Sol: first part, the present value for the first 6 years is a growing annuity

The fact that this is 6 times the present value of the first dividend is because the growth rate is equal to the required return. The second part, is a (deferred) growing perpetuity. Six years from now, the dividends will be

So, the growing perpetuity, will start with dividends of

Its value 6 years from now is

Which has a present value of

Therefore the investment has a present value of

33 Units.

Finance[annuity]