Question

This week we learned computations and the time value of money. Briefly explain the time value of money, its methods, and how it applies to NPV. When computations are performed, it is important to justify your work by showing how the answer was determined via narrative, calculations, and formulas. Presentation is also very important and is a quality aspect in addition to utilizing a table to present data and answers.

Answer 1

Concept of Time Value of Money

Let’s start a discussion on Time Value of Money by taking a very simple scenario. If you are

offered the choice between having ` 10,000 today and having ` 10,000 at a future date, you

will usually prefer to have ` 10,000 now. Similarly, if the choice is between paying ` 10,000

now or paying the same ` 10,000 at a future date, you will usually prefer to pay ` 10,000

later. It is simple common sense. In the first case by accepting ` 10,000 early, you can simply

put the money in the bank and earn some interest. Similarly in the second case by deferring

the payment, you can earn interest by keeping the money in the bank.

Therefore the time gap allowed helps us to make some money. This incremental gain is time

value of money.

Now let me ask a question, if the bank interest was zero (which is generally not the case),

what would be the time value of money? As you rightly guessed it would also be zero.

As we understood above, the interest plays an important role in determining the time value of

money. Interest rate is the cost of borrowing money as a yearly percentage. For investors,

interest rate is the rate earned on an investment as a yearly percentage.

Simple Interest & Compound Interest

Simple Interest: It may be defined as Interest that is calculated as a simple
percentage of the original principal amount. Please note the word “Original”. The formula for
calculating simple interest is:
SI = P0 (i)(n)
Where,
SI = simple interest in rupees
P0 = original principal
i = interest rate per time period (in decimals)
n = number of time periods
If we add principal to the interest i.e. P0 + P0 (i)(n), we will get the total future value (FV).
Compound Interest: If interest is calculated on original principal amount it is simple
interest. When interest is calculated on total of previously earned interest and the original
principal it compound interest. Naturally, the amount calculated on the basis of compound
interest rate is higher than when calculated with the simple rate.

Future Value:

This also known as terminal value. The accrued amount FVn on a
principal P after n payment periods at i (in decimal) rate of interest per payment period is given
by:
n 0 FV P (1 i) , n
Where,
Annual rate of interest r i . Number of payment periods per year k
= +
= =
(1 + i)n is known as future value factor or compound value factor.
n
0 n
r So FV P 1 ,when compounding is done k times a year at an annual interest rate r. k
  = +    
Or
0 i,n n
n i,n
FV = P (FVIF ),
Where,
FVIF is the future value interest factor at i% for n periods equal (1 + i) .
Computation of FVn shall be quite simple with a calculator. However, compound interest tables
as well as tables for (1+i)n at various rates per annum with (a) annual compounding; (b)
monthly compounded and (c) daily compounding are available.

Effective Rate of Interest (EIR)

It is the actual equivalent annual rate of interest at which an investment grows in value when
interest is credited more often than once a year.

Present Value
Let’s first define Present Value. Simple definition is “Present Value” is the current value of a
“Future Amount”. It can also be defined as the amount to be invested today (Present Value) at
a given rate over specified period to equal the “Future Amount”.
If we reverse the flow by saying that we expect a fixed amount after n number of years, and
we also know the current prevailing interest rate, then by discounting the future amount, at the
given interest rate, we will get the present value of investment to be made.
Discounting future amount converts it into present value amount. Similarly, compounding
converts present value amount into future value amount.
Therefore, we can say that the present value of a sum of money to be received at a future
date is determined by discounting the future value at the interest rate that the money could
earn over the period. This process is known as Discounting.
The present value interest rate or the future value interest rate is known as the discount rate.
This discount rate is the rate with which the present value or the future value is traded off. A
higher discount rate will result in a lower value for the amount in the future. This rate also
represents the opportunity cost as it captures the returns that an individual would have made
on the next best opportunity.
Since finding present value is simply the reverse of finding Future Value (FV), the formula for
Future Value (FV) can be readily transformed into a Present Value formula. Therefore the P0,
the Present Value becomes:-
P = 0 FVn (1 + i) −n
Where, FVn = Future value n years hence
i = Rate of interest per annum
n = Number of years for which discounting is done.
As mentioned earlier, computation of P may be simple if we make use of either the calculator
or the Present Value table showing values of (1+i) −n for various time periods/per annum
interest rates. For positive i, the factor (1 + i) −n is always less than 1, indicating thereby, future
amount has smaller present value.