present value of a growing annuity
growingannuity(cash, rate, growth, nperiods)
amount of first payment
rate of growth of the payments
number of payments
The function growingannuity calculates the present value at period=0, of an annuity of nperiods payments, starting at period=1 with a payment of cash. The payments increase at a rate growth per period.
Since growingannuity used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[growingannuity]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[growingannuity].
I hold an investment that will pay me every year for 5 years starting next year. The first payment is 100 units, 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:
cf ≔ 100,100⋅1.03,100⁢1.032,100⁢1.033,100⁢1.034
or equivalently as
i ≔ 'i':
cf ≔ seq⁡futurevalue⁡100,0.03,i,i=0..4
Here, we deal with a more complicated example illustrating differential growth. We have an investment that will pay dividends of 1.12 units 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%? Solution: first part, the present value for the first 6 years is a growing annuity
part1 ≔ growingannuity⁡1.12,0.12,0.12,6
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
div_6 ≔ futurevalue⁡1.12,0.12,5
So, the growing perpetuity, will start with dividends of
div_7 ≔ futurevalue⁡div_6,0.08,1
Its value 6 years from now is
part2_6 ≔ growingperpetuity⁡div_7,0.12,0.08
Which has a present value of
part2 ≔ presentvalue⁡part2_6,0.12,6
Therefore the investment has a present value of
The Finance[growingannuity] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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