- Submitted By: stepmaria
- Date Submitted: 01/06/2009 1:55 PM
- Category: Business
- 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?

ANSWER

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.

ANSWER

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.

ANSWER

NPV = -500000 + 1 x 50000

(1+.09)³ 0.09

= -500000 + 428991

= -71009