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 DF_n

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

• Annuity factor
• Compounding factor
• Factors
• Present value