Time Value of Money, calculation of Interest both with simple and compound rates, PV value, FV value,

1. PRESENTATION
Title: Time Value of Money
Subject: Corporate Finance
Contents:
 What is the 'Time Value of Money - TVM’
 Why Money Has Time Value?
 Interest Rate
 Simple Interest Calculation
 Compound Interest Calculation
 Present Value & Future Value
 Future Value Calculation
 Present Value Calculation
 Present Value of a Future Payment

2. What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that
money available at the present time is worth more
than the same amount in the future due to its
potential earning capacity.
Time Value of Money can help investors to compare
different investment alternatives.

3. Why Money Has Time Value?
Suppose you were given the choice between receiving 5000$ today or 5000$ in 10 years. Which
option would you rather select? Clearly the first option is more valuable for the following
reasons:
 Purchasing power: Because of inflation, 5000$ can be used to buy more goods and services
today than 5000$ in 10 years from now.
 Opportunity Cost: A rupee received today can be invested now to earn interest, this can
result in a higher value in the future. Sooner is better than later.
 Risk Vs Return: If you are giving your money to be used by another person / company, that
means you are taking the risk associated with it, which is known as ‘default risk’ (you may or
may not get back your payments). So, you expect return / interest to compensate the risk
 Individuals prefer current consumption to future consumption.

4. Interest Rate
Interest calculation is of two types:
 Simple Interest Rate:
Interest is earned only on the principal amount.
 Compound Interest Rate:
Interest is earned on both the principal and accumulated
interest of prior periods.
Money earning an interest rate is said to be compounding in value.
The interest rate is the percent of principal charged by the lender for the use of its money.
The principal is the amount of money lent. Banks pay you an interest rate on deposits
because they borrow that money from you.

5. Simple Interest Calculation
To calculate interest on a specified amount of loan for a particular period of time, we need:
 Principle Amount
 Number of Years/Months/Days
 Interest Rate
To calculate the amount of Interest we use following formula:
Total Interest = (Principle Amount) x (Interest Rate) x (Number of Years)
Total Amount Payable at the end of the period = (Principle Amount + Interest Amount)
Ex: 5000$ bearing an interest rate of 10% for a period of 5 Years.
Interest = 5000$ * 10% * 5  Interest = 2500$
Total Amount Payable = 5000$ + 2500$  Total Amount Payable = 7500$

6. Compound Interest Calculation
have originated in 17th-century Italy, compound interest can be thought of as “interest
on interest,” and will make a sum grow at a faster rate than simple interest, which is
calculated only on the principal amount.
“Compound interest is the most powerful force in the universe”. Albert Einstein
To calculate Compound Interest Rate we use following formula:
Compound Interest = [Principle x (1 + Interest Rate)n] – Principle Amount
Ex: 5000$ bearing 10% compound interest rate for a period of 5 years:
Interest = [5000$ x (1 + 10%)5] – 5000 $  8052.55 – 5000 = 3052.55$

7. Present Value & Future Value
Time value of money calculations involve Present value (what a cash flow would be worth to you
today) and Future value (what a cash flow will be worth in the future).
So at the most basic level, the time value of money demonstrates that, all things being equal, it
is better to have money now rather than later.
The basic principles of TVM are compounding and discounting methods.
Compounding is about the future value of today’s investment, where as discounting is the today’
value (PV) of money to be received in the future (FV – Future Value)
To make the concept clear we use an example for which we calculate future values.

8. You have won a cash prize! You have two payment options: A - Receive $10,000 now OR B -
Receive $10,000 in three years. Which option would you choose?
by receiving $10,000 today, you are poised to increase the future value of your money by
investing and gaining interest over a period of time. For Option B, you don't have time on your
side, and the payment received in three years would be your future value. To illustrate, we
have provided a timeline:
If you are choosing Option A, your future value will be $10,000 plus any interest acquired over
the three years. The future value for Option B, on the other hand, would only be $10,000.
Future Value Calculation:

9. To answer this question we have to find out the future value of 10000 $, for that we need to
consider a specific rate of interest.
If you choose Option A and invest the total amount at a simple annual rate of 4.5%, the
future value of your investment at the end of the first year is $10,450, which of course is
calculated by multiplying the principal amount of $10,000 by the interest rate of 4.5% and
then adding the interest gained to the principal amount:
Future value of investment at end of first year = ($10,000 x 0.045) + $10,000
= $10,450
If the $10,450 left in your investment account at the end of the first year is left untouched
and you invested it at 4.5% for another year, how much would you have? To calculate this
we use following formula:

10. To calculate the future value of amount 10000 $ we replace values in the formula as follows:
So if we receive the amount of 10000 $ today and invest it at a rate of 4.5% for next 3 years at
the end of the period we will receive an amount of 11411$ which shows a return on
investment of 1411.66$.
So in option B after 3 years we are going to receive only 10000$, so 10000$ become our future
value and not the present value. To Illustrate it better we calculate the present value of 10000$
which is going to be received within next 3 years.

11. Present Value Calculation:
If you received $10,000 today, the present value would of course be $10,000 because present
value is what your investment gives you now if you were to spend it today. If $10,000 were to be
received in 3 years, the present value of the amount would not be $10,000 because you do not
have it in your hand now, in the present. To find the present value of the $10,000 you will
receive in the future, you need to pretend that the $10,000 is the total future value of an
amount that you invested today. In other words, to find the present value of the future $10,000,
we need to find out how much we would have to invest today in order to receive that $10,000 in
the future.
To find out the present value we use following formula:

12. Present Value of a Future Payment
What if the payment in three years is more than the amount you'd receive today? Say you could
receive either $15,000 today or $18,000 in four years. Which would you choose? The decision is
now more difficult. If you choose to receive $15,000 today and invest the entire amount, you
may actually end up with an amount of cash in four years that is less than $18,000. You could
find the future value of $15,000, but since we are always living in the present, let's find the
present value of $18,000 if interest rates are currently 4%. The equation for present value is the
following:
From the above calculation we now know our choice is between receiving $15,000 or $15,386.48
today. Of course we should choose to postpone payment for four years!