Discount factor

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(DF).


The purpose of Discount factors is to answer questions of the type:

"What is the value today (Time 0) of a promise to receive £100m at Time 1 year (one year into the future)."


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)-1


Commonly abbreviated as DF(n,r) or DFn


where

n = number of periods, and

r = periodic cost of capital.


Examples

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)-n

= 1.06-1

= 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:

£100m x 0.9434

= £94.34m.


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

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

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.)


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.

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

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


See also