# Annuities and Perpetuities

## Annuities and Perpetuities

• Submitted By: stepmaria
• Date Submitted: 01/06/2009 1:55 PM
• Words: 306
• Page: 2
• Views: 498

ANNUITIES - PERPETUITIES
An annuity is a financial instrument that pays a constant amount every certain period (eg every year) for an x number of periods. In order to calculate the present value of an annuity the same principle is used as before:
d/(1+r) + d/(1+r)² + d/(1+r)³ + ………..d/(1+r)ⁿ
This equation can also be expressed as d (1 - 1 )
r (1+r)ⁿ
Where d = Payment at the end of each year starting at the end of the year
r = Cost of capital

As can be seen from the above formula if n is increased to infinity the present value is given by the formula 1
r

EXAMPLE
A company with a cost of capital of 14% is considering an investment in a project costing \$500.000 that would yield cash inflows of \$100.000 a year in perpetuity. Should the project be undertaken?

YEAR Cash flow Disc. Factor Present value
0 -500000 1 -500000
1 - ∞ 100000 1/0.14 = 7.14 714000
NPV 214000

The project should be undertaken since it gives a positive NPV.

EXAMPLE
A project requires an initial capital outflow of \$1000.000 and is expected to produce net cash inflows of \$90000/year starting at the end of the second year. Calculate the NPV of the project assuming 8% cost of capital.

NPV = -1000000 + 1 x 90000
(1+0.08) 0.08
= -1000000 + 1041667
= 41667

EXAMPLE
A project requires an initial capital outflow of \$500000 and is expected to produce net cash inflows of \$50000/year starting at the end of the fourth year. Calculate the NPV of the project and advise management as to whether they should go ahead with the project assuming a 9% cost of capital.