Annuity factor: Difference between revisions
imported>Doug Williamson (Categorise the page and link with technical skills pages.) |
imported>Doug Williamson (Updated entry. Source ACT Glossary of terms) |
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(AF). | (AF). | ||
1. | |||
A method for calculating the total present value of a simple fixed [[annuity]]. | |||
Mathematically, the Annuity Factor is the cumulative [[Discount factor]] for maturities 1 to n inclusive, when the [[cost of capital]] is the same for all relevant maturities. | Mathematically, the Annuity Factor is the cumulative [[Discount factor]] for maturities 1 to n inclusive, when the [[cost of capital]] is the same for all relevant maturities. | ||
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'''Example''' | |||
For example, when the Annuity factor | For example, when the Annuity factor = 1.833 and the Time 1 cash flow = $10m, then: | ||
and the Time 1 | |||
Present value = AF x Time 1 cash flow | Present value = AF x Time 1 cash flow | ||
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= 1.833 x $10m | = 1.833 x $10m | ||
= | = $18.33m | ||
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'''Example''' | |||
For example, when the periodic cost of capital (r) = 6% and the number of periods in the total time under review (n) = 2, then: | For example, when the periodic cost of capital (r) = 6% and the number of periods in the total time under review (n) = 2, then: | ||
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The Annuity Factor is sometimes also known as the Annuity formula. | 2. | ||
Annuity factors are also used to calculate equated loan instalments. | |||
For a loan drawn down in full at the start, the equated loan instalment is given by: | |||
Instalment = Principal/Annuity factor | |||
'''Example''' | |||
$20m is borrowed at an annual interest rate of 6%. | |||
The loan is to be repaid in two equal annual instalments, starting one year from now. | |||
The annuity factor is 1.833 (as before). | |||
The loan instalment is: | |||
$20m/1.833 | |||
= $10.9m | |||
The Annuity Factor is sometimes also known as the ''Annuity formula''. | |||
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* [[Perpetuity factor]] | * [[Perpetuity factor]] | ||
* [[Present value]] | * [[Present value]] | ||
* [[Instalment]] | |||
* [[Equated instalment]] | |||
* [[Principal]] | |||
[[Category:Financial_management]] | [[Category:Financial_management]] | ||
Revision as of 11:15, 19 November 2014
Financial maths.
(AF).
1.
A method for calculating the total present value of a simple fixed annuity.
Mathematically, the Annuity Factor is the cumulative Discount factor for maturities 1 to n inclusive, when the cost of capital is the same for all relevant maturities.
Commonly abbreviated as AF(n,r) or AFn
Also known as the Present Value Interest Factor of an Annuity (PVIFA).
Present value calculation
The present value of the annuity is calculated from the Annuity Factor (AF) as:
= AF x Time 1 cash flow.
Example
For example, when the Annuity factor = 1.833 and the Time 1 cash flow = $10m, then:
Present value = AF x Time 1 cash flow
= 1.833 x $10m
= $18.33m
Annuity factor calculation
The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as:
AF(n,r) = 1/r x [1-(1+r)-n]
where
n = number of periods, and
r = periodic cost of capital.
Example
For example, when the periodic cost of capital (r) = 6% and the number of periods in the total time under review (n) = 2, then:
Annuity factor = 1/r x [1-(1+r)-n]
= 1/0.06 x [1-(1 + 0.06)-2]
= 1.833
This figure is also the sum of the two related Discount Factors:
AF2 = DF1 + DF2
= 1.06-1 + 1.06-2
= 0.9434 + 0.8900
= 1.833
2.
Annuity factors are also used to calculate equated loan instalments.
For a loan drawn down in full at the start, the equated loan instalment is given by:
Instalment = Principal/Annuity factor
Example
$20m is borrowed at an annual interest rate of 6%.
The loan is to be repaid in two equal annual instalments, starting one year from now.
The annuity factor is 1.833 (as before).
The loan instalment is:
$20m/1.833
= $10.9m
The Annuity Factor is sometimes also known as the Annuity formula.
