Growing annuity factor and Period costs: Difference between pages

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imported>Doug Williamson
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imported>Doug Williamson
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''Financial maths''
''Cost and management accounting.''


(GAF).  
Period costs are costs that are incurred with the passing of time, rather than with the production of services or products.


Growing annuity factors are used to calculate present values of growing annuities.  
Examples include administration overheads, marketing overheads and finance overheads.


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.


== See also ==
* [[Direct costs]]
* [[Direct production cost]]
* [[Indirect costs]]
* [[Management accounting]]
* [[Overheads]]
* [[Production overheads]]


 
[[Category:Accounting,_tax_and_regulation]]
== Present value calculations ==
[[Category:The_business_context]]
 
 
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'' AF<SUB>n,r</SUB>
 
the growing annuity factor can be abbreviated as GAF(n,r,g) ''or'' AF<SUB>n,r,g</SUB>
 
 
 
=== Present value ===
 
The [[present value]] of the growing annuity is calculated from the Growing Annuity Factor (GAF) as:
 
= GAF x Time 1 cash flow.
 
 
<span style="color:#4B0082">'''Example 1: Present value calculation'''</span>
 
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) )<sup>n</sup> ''')'''
 
 
Where
 
n = number of periods
 
r = periodic cost of capital
 
g = periodic growth rate from Time 1 period in the future
 
 
<span style="color:#4B0082">'''Example 2: Growing annuity factor calculation'''</span>
 
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) )<sup>n</sup> ''')'''
 
 
=  '''('''1 / (0.06 - 0.01) ''')'''
 
::x '''('''1 - ( (1.01) / (1.06) )<sup>2</sup> ''')'''
 
 
=        '''('''20''')'''         
 
::x        '''('''0.0921''')'''
 
= '''1.842'''
 
 
 
== See also ==
* [[Annuity]]
* [[Annuity factor]]
* [[CumDF]]
* [[Discount factor]]
* [[Perpetuity factor]]
* [[Present value]]
* [[Instalment]]
* [[Equated instalment]]
* [[Principal]]

Revision as of 17:24, 10 February 2019

Cost and management accounting.

Period costs are costs that are incurred with the passing of time, rather than with the production of services or products.

Examples include administration overheads, marketing overheads and finance overheads.


See also