CIMA BA1 Syllabus D. The Financial Context Of Business - Annuity and perpetuity formulae - Notes ^{4 / 4}

Annuity

An annuity is a fixed (constant) periodic payment or receipt which continues either for a specified time or until the occurrence of a specified event, e.g. ground rent.

Illustration

$100 will be received at the end of every year for the next 3 years. 

If cost of capital is 10%, what is the PV of these amounts together?

Solution

Strictly speaking it is:
Yr 1 $100 / 1.1 = $91
Yr 2 $100/1.1 ^ 2 = $83
Yr 3 $100/1.1 ^ 3  = $75

All added together = $249

This is easier is to calculate using an annuity discount factor - this is simply the 3 different discount factors above added together

So using normal discount factors:

Yr 1 0.909
Yr 2 0.826
Yr 3 0.751

All added together 2.486 = Annuity factor (or get from annuity table)

So $100 x 2.486 = $248.6 = $249

Perpetuity

Perpetuity is a periodic payment or receipt continuing for a limitless period.

Calculating the PV of a perpetuity:

Cash flow
---------------
Interest rate

Illustration

What is the present value of an annual income of $50,000 for the foreseeable future, given an interest rate of 5%? 

Solution

50,000 / 0.05 = $1,000,000