Discount factor
(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.
