### Syllabus D4e)

Explain and illustrate compounding and discounting

### Compounding & Discounting

#### Compounding

We have already looked at compounding in previous section.

Just a reminder that the formula for compounding is:

FV = PV (1+r) ^ n

#### Discounting

Discounting is compounding in reverse.

It starts with a future amount of cash and converts it into a present value.

A present value is the amount that would need to be invested now to earn the future cash flow, if the money is invested at the ‘cost of capital’.

Hence, when looking at whether we should invest in something we will be looking at future cash flows coming in.

We want to know what these future cash flows are worth now, in today’s money ideally.

PV = FV

---------

(1 + r) ^ n

r - rate of interest

n - number of time periods

#### Illustration

A business is to receive $100 in one year’s time and the interest rate/discount rate is 10%.

What is the PV of that money?

**Solution**

PV = 100 /1.10 ^ 1

PV = $90.9

#### Example

A business is to receive $100 in two years’ time and the interest rate/discount rate is 10%.

What is the PV of that money?

**Solution**

PV = $100 /1.10 ^ 2

PV = $82.6

#### Discount Rate

The present value can also be calculated using a discount factor (saving all the dividing by 1.1 etc.)

The discount factor can be calculated as:

1/ (1+r) ^ n

r - rate of interest

n - number of time periods

So, the discount factor for 10% in 3 years is:

1/1.1 ^ 3 = 0.751

There are also tables that give you a list of these ‘discount factors’ – a copy of these tables is included at the end of these notes.

Hence, to calculate a present value for a future cash flow, you simply multiply the future cash flow by the appropriate discount factor.

#### Illustration

What is the present value of $133 received at the end of 3 years, using a cost of capital of 10%

**Solution**

$133 x 0.751 = $100