Annuity factor: Difference between revisions
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<span style="color:#4B0082">'''Example 1'''</span> | <span style="color:#4B0082">'''Example 1: Present value calculation'''</span> | ||
Annuity factor = 1.833. | Annuity factor = 1.833. | ||
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= 1.833 x 10 | = 1.833 x 10 | ||
= $18. | = $'''18.33'''m | ||
=== Annuity factor | === Annuity factor === | ||
The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as: | The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as: | ||
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<span style="color:#4B0082">'''Example 2'''</span> | <span style="color:#4B0082">'''Example 2: Annuity factor calculation'''</span> | ||
When the periodic cost of capital (r) = 6%, | When the periodic cost of capital (r) = 6%, | ||
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= ( 1 - 1.06<sup>-2</sup> ) / r | = ( 1 - 1.06<sup>-2</sup> ) / r | ||
= 1.833 | = '''1.833''' | ||
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= 0.9434 + 0.8900 | = 0.9434 + 0.8900 | ||
= 1.833 | = '''1.833''' | ||
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<span style="color:#4B0082">'''Example 3'''</span> | <span style="color:#4B0082">'''Example 3: Loan installment'''</span> | ||
$20m is borrowed at an annual interest rate of 6%. | $20m is borrowed at an annual interest rate of 6%. | ||
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20 / 1.833 | 20 / 1.833 | ||
= $10.9m | = '''$10.9m''' | ||
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== Other resources == | |||
[[Media:2014_11_Nov_-_Ever_deceasing_circles.pdf| Ever decreasing circles, The Treasurer, 2014]] | [[Media:2014_11_Nov_-_Ever_deceasing_circles.pdf| Ever decreasing circles, The Treasurer, 2014]] | ||
Revision as of 14:10, 2 December 2015
Financial maths.
(AF).
Annuity factors are used to calculate present values of annuities, and equated instalments.
The simplest type of annuity is a finite series of identical future cash flows, starting exactly one period into the future.
Present value calculations
An annuity factor can be used to calculate the total present value of a simple fixed annuity.
The Annuity Factor is the sum of the Discount factors 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,r
Sometimes also known as the Present Value Interest Factor of an Annuity (PVIFA).
Present value
The present value of the annuity is calculated from the Annuity Factor (AF) as:
= AF x Time 1 cash flow.
Example 1: Present value calculation
Annuity factor = 1.833.
Time 1 cash flow = $10m.
Present value is:
= AF x Time 1 cash flow
= 1.833 x 10
= $18.33m
Annuity factor
The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as:
AF(n,r) = (1 - ( 1 + r )-n ) / r
Where
n = number of periods
r = periodic cost of capital.
Example 2: Annuity factor calculation
When the periodic cost of capital (r) = 6%,
and the number of periods in the total time under review (n) = 2.
Annuity factor is:
= ( 1 - ( 1 + r )-n ) / r
= ( 1 - 1.06-2 ) / r
= 1.833
This figure is also the sum of the related Discount Factors (DF):
AF2 = DF1 + DF2
= 1.06-1 + 1.06-2
= 0.9434 + 0.8900
= 1.833
Equated instalments
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 3: Loan installment
$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:
20 / 1.833
= $10.9m
The Annuity Factor is sometimes also known as the Annuity formula.
See also
- Annuity
- Annuity formula
- CertFMM
- Discount factor
- Perpetuity factor
- Present value
- Instalment
- Equated instalment
- Principal
