Growing annuity factor - Revision history

imported>Doug Williamson: Classify page.

2022-07-01T15:25:09Z

Classify page.

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	* [[Present value]]		* [[Present value]]
	* [[Principal]]		* [[Principal]]

			[[Category:The_business_context]]

imported>Doug Williamson: Mend link.

2022-06-25T16:38:37Z

Mend link.

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	* [[Annuity]]		* [[Annuity]]
	* [[Annuity factor]]		* [[Annuity factor]]
	* [[~~CumDF~~]]		* [[Cumulative Discount Factor]] (CumDF)
	* [[Discount factor]]		* [[Discount factor]]
	* [[Equated instalment]]		* [[Equated instalment]]

imported>Doug Williamson: Links ordering.

2021-04-07T11:03:07Z

Links ordering.

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	* [[CumDF]]		* [[CumDF]]
	* [[Discount factor]]		* [[Discount factor]]
			* [[Equated instalment]]
			* [[Growing perpetuity factor]]
			* [[Instalment]]
	* [[Perpetuity factor]]		* [[Perpetuity factor]]
	* [[Present value]]		* [[Present value]]
	* [[Instalment]]
	* [[Equated instalment]]
	* [[Principal]]		* [[Principal]]

imported>Doug Williamson: Removed link

2016-11-16T14:33:15Z

Removed link

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	* [[Annuity]]		* [[Annuity]]
	* [[Annuity factor]]		* [[Annuity factor]]
	* [[CertFMM]]
	* [[CumDF]]		* [[CumDF]]
	* [[Discount factor]]		* [[Discount factor]]

imported>Doug Williamson: Layout.

2016-07-20T06:20:53Z

Layout.

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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>		the growing annuity factor can be abbreviated as GAF(n,r,g) ''or'' AF<SUB>n,r,g</SUB>

imported>Doug Williamson: Punctuation.

2016-04-04T11:27:03Z

Punctuation.

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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

imported>Doug Williamson: Create the page. Source: FMM course formulae.

2016-04-04T08:47:11Z

Create the page. Source: FMM course formulae.

New page

''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 factor]]s 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

= $'''18.42'''m

=== 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'''

== See also ==
* [[Annuity]]
* [[Annuity factor]]
* [[CertFMM]]
* [[CumDF]]
* [[Discount factor]]
* [[Perpetuity factor]]
* [[Present value]]
* [[Instalment]]
* [[Equated instalment]]
* [[Principal]]