ch-03 (time value of money)

3-1 Excel BooksFinancial Management tools and techniques Dr Pradip Kumar Sinha

Copyright © 2009, Dr Pradip Kumar Sinha

PART – I

Time Value of MoneyCH-3CH-3

Introduction to Financial ManagementIntroduction to Financial Management

3Chapter

Time Value

of Money

Time Value

of Money



PART – I



Cont….

Interest Interest is a fee that is paid for having the use of money e.g., interest on mortgages for having the use of bank’s money.

The compensation for waiting is the time value of money, called interest.

Interest is usually paid in proportion and the period of time over which the money is used.

The interest rate is typically stated as a percentage of the principal per period of time.

Principal the amount of money that is lent or invested is called principal.

Simple Interest that is paid solely on the amount of the principal is called simple interest. Simple interest is usually associated with loans or investments that are short-term in nature. The computatuion of simple interest is based on the following formula:

Simple interest = principal × interest rate per time period × number of time period



PART – I



Compound Interest: Compound Interest occurs when interest earned

during the previous period itself earns interest in the next and subsequent

periods.

Future Value of Re. 1

A sum of money invested today at compound interest accumulates to a

larger sum called the amount or future value.

The future value varies with the interest rate, the compounding frequency

and the number of periods. If the future value of Re. 1 principal investment is

known, we can use it to calculate the future value of any amount invested.



PART – I



Compound Discount

Finding the present value of future receipts involves discounting the future

value to the present.

Discounting is the opposite of compounding. It involves finding the present

value of some future amount of money that is assumed to include interest

accumulations.

Present Value of Re. 1

Knowing the present value of Re. 1 is useful because it enables us to find the

present value of any future payment.



PART – I



Cont….

Annuities

An annuity is a series of equal payments made at equal time intervals, with

compounding or discounting taking place at the time of each payment.

Each annuity payment is called a rent.

There are several types of annuities, out of which in an ordinary annuity each

rent is paid or received at the end of each period.

There are as many rents as there are periods. Installment purchases, long-

term bonds, pension plans, and capital budgeting all involve annuities.



PART – I



Cont….

Future Value of Annuity of Re.1

The future value of an annuity or amount of annuity is the sum accumulated

in the future from all the rents paid and the interest earned by the rents.

The abbreviation FV is used for the future value of an annuity to differentiate

it from the lower case fv used for the future value of Re.1.

To obtain a table of future values of annuities, we assume payments of Re.1

each period made into a fund that earns 8 per cent interest compounded

each period.

The following diagram illustrates an annuity of four payments of Re.1, each

paid at the end of each period, with interest of 8 per cent compounded each

period. 8% interest per period

Re.1 Re.1 Re.1 Re.1

P 1 2 3 4 n FV

Time Periods



PART – I



Cont….

Notice that there are four rents and four periods, each rent is paid at the end of

each period. At the end of the first period, Re.1 is deposited and earns interest for

three periods. The next rent earns interest for two periods, and so on. The

amount at the end of the fourth period can be determined by calculating the future

value of each individual Re.1 deposit as follows:

Future value of Re. 1 at 8% for 3 periods = Rs. 1.25971

Future value of Re. 1 at 8% for 2 periods = Rs. 1.16640

Future value of Re. 1 at 8% for 1 period = Rs. 1.08000

The fourth rent of Re. 1 earns no interest = Re. 1.0000

Total for 4 rents Rs. 4.50611

The formula for the future value of an annuity of Re.1 can be used to produce

tables for a variety of periods and interest rates

FV =n(1+1) –1

Fv = i



PART – I



Cont….

Present Value of Annuity of Re.1

The present value of an annuity is the sum that must be invested today at

compound interest in order to obtain periodic rents over some future time.

We use the abbreviation PV for the present value of an annuity.

The present value of an ordinary annuity of Re.1 can be illustrated as

follows:

Interest

Re.1 Re.1 Re.1 Re.1

PV 1 2 3 4 n

Time Periods



PART – I



Cont….

With each rent available at the end of each period, when compounding takes

place, the number of rents is the same as the number of periods. By discounting

each future event to the present, we find the present value of the entire annuity.

Present value of Re.1 discounted for 1 period at 8% = Re. 0.92593

Present value of Re.1 discounted for 2 periods at 8% = 0.85734



Present value of annuity of 4 rents at 8% Rs. 3.31213

The first rent is worth more than others because it is received earlier. Table on

present value of annuities may be used to solve problems in this regard. The

formula used to construct the table is:

PV =n

11–

(1+i)i



PART – I



Present Value of an Infinite Life Annuity: Perpetuities

An annuity that goes on for ever is called a perpetuity.

The present value of a perpetuity of Rs. C amount is given by the simple

formula: C/i where i is the rate of interest.

As the length of time for which the annuity is received increases, the annuity

discount factor increases but as length gets very long, this increase in the

annuity factor slows down. In fact, as annuity life becomes infinitely long the

annuity discount factor approaches an upper limit. Such a limit is 1/i.

ch-03 (time value of money)

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