Growing annuity factor: Difference between revisions
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By analogy with the simple annuity factor abbreviated as AF(n,r) ''or'' AF<SUB>n,r</SUB> | By analogy with the simple annuity factor abbreviated as AF(n,r) ''or'' AF<SUB>n,r</SUB> | ||
the growing annuity factor can be abbreviated as GAF(n,r,g) ''or'' AF<SUB>n,r,g</SUB> | |||
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<span style="color:#4B0082">'''Example 2: Growing annuity factor calculation'''</span> | <span style="color:#4B0082">'''Example 2: Growing annuity factor calculation'''</span> | ||
When the periodic cost of capital (r) = 6% | When the periodic cost of capital (r) = 6% | ||
growth rate (g) per period = 1% | growth rate (g) per period = 1% | ||
and the number of periods in the total time under review (n) = 2 | and the number of periods in the total time under review (n) = 2 | ||
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* [[Annuity]] | * [[Annuity]] | ||
* [[Annuity factor]] | * [[Annuity factor]] | ||
* [[ | * [[Cumulative Discount Factor]] (CumDF) | ||
* [[Discount factor]] | * [[Discount factor]] | ||
* [[Equated instalment]] | |||
* [[Growing perpetuity factor]] | |||
* [[Instalment]] | |||
* [[Perpetuity factor]] | * [[Perpetuity factor]] | ||
* [[Present value]] | * [[Present value]] | ||
* [[Principal]] | * [[Principal]] | ||
[[Category:The_business_context]] | |||
Latest revision as of 15:25, 1 July 2022
Financial maths.
(GAF).
Growing annuity factors are used to calculate present values of growing annuities.
The simplest type of growing annuity is a finite series of growing future cash flows, starting exactly one period into the future, and growing at a constant percentage rate per period.
Present value calculations
A growing annuity factor can be used to calculate the total present value of a growing annuity.
The Growing Annuity Factor is the sum of the adjusted Discount factors for maturities 1 to n inclusive, when the cost of capital is the same for all relevant maturities.
The discount factors need to be adjusted because of the growth of the cash flows.
By analogy with the simple annuity factor abbreviated as AF(n,r) or AFn,r
the growing annuity factor can be abbreviated as GAF(n,r,g) or AFn,r,g
Present value
The present value of the growing annuity is calculated from the Growing Annuity Factor (GAF) as:
= GAF x Time 1 cash flow.
Example 1: Present value calculation
Annuity factor = 1.842.
Time 1 cash flow = $10m.
Present value is:
= AF x Time 1 cash flow
= 1.842 x 10
= $18.42m
Growing annuity factor calculation
The growing annuity factor for 'n' periods at a periodic yield of 'r' and a periodic growth rate of 'g' is calculated as:
AF(n,r,g)
= (1 / (r-g) )
- x (1 - ( (1+g) / (1+r) )n )
Where
n = number of periods
r = periodic cost of capital
g = periodic growth rate from Time 1 period in the future
Example 2: Growing annuity factor calculation
When the periodic cost of capital (r) = 6%
growth rate (g) per period = 1%
and the number of periods in the total time under review (n) = 2
The growing annuity factor is:
= (1 / (r-g) )
- x (1 - ( (1+g) / (1+r) )n )
= (1 / (0.06 - 0.01) )
- x (1 - ( (1.01) / (1.06) )2 )
= (20)
- x (0.0921)
= 1.842
