CIMA P2 Syllabus B. Capital Investment Decision Making - Annuities & Perpetuities - Notes ^{7 / 8}

Lets us now look at discounting a future cash-flow that is constant every year for a specified number of years (an annuity).

Illustration

100 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?

• Strictly speaking it is:
  Yr 1 100 x 1/ 1.1 = 91
  Yr 2 100 x 1/1.1 power of 2 = 83
  Yr 3 100 x 1/1.1 power of 3 = 75

  All added together = 249

Annuity Discount Factors

This is easier is to calculate using an annuity discount factor - this is simply the 3 different discount factors above added together - again luckily this is given to us in the exam (in the annuity table)

• So using normal discount factors:

  yr 1 1/1.1 = 0.909
  yr 2 1/1.1/1.1 = 0.826
  Yr 3 1/1.1/1.1/1.1 = 0.751
  All added together 2.486 = Annuity factor (or get from annuity table!)

  So 100 x 2.486 = 248.6 = 249

Perpetuities

This is a constant amount received forever

Calculating the PV of a perpetuity:

Cashflow / Interest rate

• Illustration 

  What is the PV of an annual income of 50,000 for the forseeable future, given an interest rate of 5%?

  Answer 
  50,000 / 0.05 = 1,000,000

Perpetuity starting in the future

Don’t panic!

Just calculate the perpetuity as normal - then discount the answer down (discount factor for 3 years -  for example - if the perpetuity started at year 3)