Annuity factor: Difference between revisions

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An annuity factor is a method for calculating the total present value of a simple fixed [[annuity]].  
An annuity factor can be used to calculate 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.
The Annuity Factor is the sum of the [[Discount factor]]s for maturities 1 to n inclusive, when the [[cost of capital]] is the same for all relevant maturities.





Revision as of 14:32, 28 June 2015

Financial maths.

(AF).

Annuity factors are used to calculate present values of annuities, and equated instalments.


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

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 calculation

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

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:

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

$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