Page 67 - DMGT302_FUNDAMENTALS_OF_PROJECT_MANAGEMENT

Fundamentals of Project Management

Notes Compound and Simple Interest

So far we have assumed that the money is invested at compound interest which means that each
interest payment is reinvested to earn further interest in future periods. By contrast, if no
interest is earned on interest, the investment earns only simple interest. In such a case the
investment grows as follows:
Future value = Present value [1 + Number of years × Interest rate]

Doubling Period

Investors commonly ask the question: How long would it take to double the amount at a given
rate of interest? To answer this question we have to calculate the future value interest and we
find that when the interest rate is 12 percent it takes about 6 years to double the amount, when
the interest is 6 percent it takes about 12 years to double the amount, so on and so forth. Is there
a rule of thumb which dispenses with the use of the future value interest factor table? Yes, there
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.

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:
PV = FV [1/1 (1 + r) ]
n
n
n
The factor 1/1(1 + r) 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 per cent?
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 1 2 3 n
(1+r) (1+r) (1+r) (1 + r)

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