Discount factor: Difference between revisions

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(DF).  
''Financial maths.''


'''1.'''


The purpose of Discount factors is to answer questions of the type:
(DF).


"What is the value today (Time 0) of a promise to receive £100m at Time 1 year (one year into the future)."
A discount factor is a number less than one, that we multiply a single future cash flow by, to work out its present value as:


PV = DF x future cashflow.


'''1.'''
Strictly, the number less than one which we multiply a future cash flow by, to work out its present value as:


PV = DF x future cashflow.
The periodic discount factor is calculated from the periodic [[yield]] as:


DF = (1 + periodic yield)<SUP>-n</SUP>


The periodic discount factor is calculated from the periodic yield as:
''(= 1 / (1 + periodic yield)<SUP>n</SUP>)''


DF = (1 + periodic yield)<SUP>-1</SUP>


Commonly abbreviated as DF(n,r) ''or'' DF<SUB>n,r</SUB>


Commonly abbreviated as DF(n,r) ''or'' DF<SUB>n</SUB>
Where:


n = number of periods.


where
r = periodic yield (or periodic cost of capital).


n = number of periods, ''and''


r = periodic cost of capital.


<span style="color:#4B0082">'''Example 1: Discount factor calculation'''</span>


Periodic yield or cost of capital (r) = 6%.


'''''Examples'''''
Number of periods in the total time under review (n) = 1.


For example, when the periodic cost of capital (r) = 6% and the number of periods in the total time under review (n) = 1, then:


Discount factor = (1+r)<sup>-n</sup>
Discount factor = (1 + r)<sup>-n</sup>


= 1.06<sup>-1</sup>
= 1.06<sup>-1</sup>


= '''0.9434'''
= 0.9434.




Continuing this example, the present value (today, Time 0) of a promise to receive £100m at Time 1 year hence (one year into the future) is calculated at a rate of 6% per annum as:
The greater the time delay, the smaller the Discount Factor.
 
£100m x 0.9434


= £94.34m.


<span style="color:#4B0082">'''Example 2: Increasing number of periods delay'''</span>


The greater the time delay, the smaller the Discount Factor.
Periodic yield or cost of capital = 6%.  


For example, when the periodic cost of capital = 6% as before, but the number of periods delay increases to 2, then:
The number of periods delay increases to 2.


Discount factor = (1+r)<sup>-n</sup>
Discount factor = (1 + r)<sup>-n</sup>


= 1.06<sup>-2</sup>
= 1.06<sup>-2</sup>


= '''0.8890'''
= 0.8890.


''(A smaller figure than the 0.9434 we calculated previously for just one period's delay.)''
''(A smaller figure than the 0.9434 we calculated previously for just one period's delay.)''


Continuing this case, the present value (today, Time 0) of a promise to receive £100m at Time 2 years hence (two years into the future) is calculated at a rate of 6% per annum as:
£100m x 0.8890
= £88.90m.




'''2.'''  
'''2.'''  


Loosely and historically, the yield or cost of capital used for the purpose of calculating Discount Factors.   
Historically, the yield or cost of capital used for the purpose of calculating Discount Factors, as defined above.   


For example the 6% rate applied in definition 1. above.
For example the 6% rate applied in definition 1. above.
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== See also ==
== See also ==
* [[Annuity factor]]
* [[Annuity factor]]
* [[Certificate in Treasury Fundamentals]]
* [[Certificate in Treasury]]
* [[Compounding effect]]
* [[Compounding factor]]
* [[Compounding factor]]
* [[Cumulative Discount Factor]]
* [[Day count conventions]]
* [[Discount]]
* [[Discounted cash flow]]
* [[Expected credit loss]]
* [[Factors]]
* [[Factors]]
* [[Present value]]
* [[Present value]]
[[Category:Cash_management]]
[[Category:Liquidity_management]]

Latest revision as of 00:03, 7 July 2022

Financial maths.

1.

(DF).

A discount factor is a number less than one, that we multiply a single future cash flow by, to work out its present value as:

PV = DF x future cashflow.


The periodic discount factor is calculated from the periodic yield as:

DF = (1 + periodic yield)-n

(= 1 / (1 + periodic yield)n)


Commonly abbreviated as DF(n,r) or DFn,r

Where:

n = number of periods.

r = periodic yield (or periodic cost of capital).


Example 1: Discount factor calculation

Periodic yield or cost of capital (r) = 6%.

Number of periods in the total time under review (n) = 1.


Discount factor = (1 + r)-n

= 1.06-1

= 0.9434.


The greater the time delay, the smaller the Discount Factor.


Example 2: Increasing number of periods delay

Periodic yield or cost of capital = 6%.

The number of periods delay increases to 2.

Discount factor = (1 + r)-n

= 1.06-2

= 0.8890.

(A smaller figure than the 0.9434 we calculated previously for just one period's delay.)


2.

Historically, the yield or cost of capital used for the purpose of calculating Discount Factors, as defined above.

For example the 6% rate applied in definition 1. above.


See also