# Discount factor

*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* DF_{n,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.