Page 147 - DMGT521_PROJECT_MANAGEMENT

Project Management

Notes is one and it is called the rule of 72. According to this rule of thumb the doubling period is
obtained by dividing 72 by the interest rate. For example, if the interest rate is 8 percent, the
doubling period is about 9 years (72/8). Likewise, if the interest rate is 4 percent the doubling
period is about 18 years (72/4). Though somewhat crude, it is a handy and useful rule of thumb.

9.4.2 Present Value of a Single Amount

The process of discounting, used for calculating the present value, is simply the inverse of
compounding. The present value formula can be readily obtained by manipulating the
compounding formula:

FV = PV (1 + r) n
n
n
Dividing both the sides of Eq. by (1 + r) , we get:
n
PV = FV [1/1 (1 + r) ]
n
n
The factor 1/1(1 + r) in Eq. (7.3) is called the discounting factor or the Present Value interest
factor (PVIF ).
rn
Example: What is the present value of 1,000 receivable 6 years hence if the rate of
discount is 10 percent?
The present value is:

1,000 × PVIF, 10%, 6 = 1,000 (0.5645) = 564.5
Present Value of an Uneven Series

In financial analysis we often come across uneven cash flow streams.
For example, the cash flow stream associated with a capital investment project is typically
uneven. Likewise, the dividend stream associated with an equity share is usually uneven and
perhaps growing.
The present value of a cash flow stream uneven or even may be calculated with the help of the
following formula:
A A A A
PV  1  2  3 + ….. + n n
n

(1+r) 1 (1+r) 2 (1+r) 3 (1 r)
where PV = present value of a cash flow stream
n
A = cash flow occurring at the end of year t
t
r = discount rate
n = duration of the cash flow stream

Future Value of Annuity

An annuity is a stream of constant cash flow (payment or receipt) occurring at regular intervals
of time. The premium payments of a life insurance policy,

Example: In general terms the future value of an annuity is given by the following
formula:
n-1
n-2
FVA = A (1+r) + A (1+r) + ... +A
n
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