The Concept of Time Value
As we know, time has value.
Like the proverb says, time is money.
Let’s think about it, which one would you prefer to receive?
$10,000 today, or $10,000 in five years’ time?
I believe that your answer is definitely, today.
But the question is, why?
We want to receive the money now, but not after five years.
That’s because, $1 today is worth more than $1 in the future.
As a basic principle of time value, money available at the present time is worth more.
than the same amount in the future, due to its potential earning capacity.
So, after receiving $10,000 today, we may use this portion of money to invest, and earn
return from it.
Another point, the concept of time value of money is important, because it allows the
comparison of cash flows from different periods.
We will explain about it later in this video.
Okay, another question for you.
Let say, your father has offered to give you some money and asked you to choose one of
the following two alternatives.
$1,000 today, or $1,100 one year from now.
Which one would be your choice?
Before making your decision, it is important to know that, the answer depends on what rate
of interest you could earn on any money you receive today.
From $1,000 to $1,100, there is an increase of $100, or 10% interest rate.
So, if you could deposit $1,000 today at 12% per year, you would prefer to be paid today,
because you could earn more interest on your own.
What if you could only earn 5% on fixed deposit?
You would be better off if you chose the $1,100 in one year.
Simply speaking, your decision depends much on what rate of interest you could earn after.
receiving the money.
Future Value
What is future value, FV?
FV translates $1 today into its equivalent in the future.
This process is called compounding.
Present Value
What about present value, PV?
PV translates $1 in the future into its equivalent today.
This process is called discounting.
For the calculation of time value of money questions, there are four computational aids.
Computational Aids
First, use the equations.
Second, use the financial tables.
Third, use financial calculators.
Fourth, use electronic spreadsheets, such as Microsoft Excel.
The Timeline
Before that, make sure you know how to draw a timeline.
CF is the cash flow.
T means time, usually in years or in months.
i is the interest rate.
The timeline is one of the most important tools for solving complicated problems.
Assumptions
For applying this, there are some assumptions.
First, unless otherwise stated, t = 0, represents today.
This is the decision point.
Second, unless otherwise stated, cash flows occur at the end of a time interval.
Third, cash inflows are treated as positive amounts, while cash outflows are treated as
negative amounts.
Fourth, compounding frequency is the same as the cash flow frequency.
Compounding frequency could be annually, semiannually, quarterly, monthly, weekly or daily.
The cash inflows and outflows of a firm can be described by its general pattern.
Basic Patterns of Cash Flow
The three basic patterns include, a single amount, an annuity, or a mixed stream.
As shown in the table, project A is a single amount cash flow, in which only one cash inflow
on year 1.
Project B is an annuity, because there are repeating cash inflows from Year 1 to Year
3.
Project C is a mixed stream, as from Year 1 to Year 6, the cash inflows are all different.
These are the three basic patterns of cash flow that you will find in the questions of
time value of money.
Future Value vs Present Value
Let’s look at this question.
Suppose a firm has an opportunity to spend $15,000 today on some investments that will
produce $17,000 spread out over the next five years as follows, as shown in the table.
What do you think, is this a wise investment?
Pay $15,000, earn back $17,000.
In fact, we are not sure.
The returns of $17,000 are not a one-off payment, but they are spread out over the next five
years.
To make the right investment decision, we need to compare the cash flows at a single
point in time.
Either, we convert all the cash flows to Year 5 to get the future value, or we convert all
the cash flows back to Year 0 to get the present value.
We can only compare the cash flows at a single point in time, which means on Year 0 for PV,
or on Year 5 for FV.
Cash flows from different years are not comparable, as they have different time value.
Simple Interest
Next, there are two types of interest.
First is simple interest.
Interest paid or earned is based on the original amount, or principal borrowed or lent.
As shown in the table, every year the interest is calculated based on $100, which is the
original principal.
So, you don’t earn interest on interest.
compound interest
The second type is compound interest.
Interest paid or earned is based on any previous interest earned, as well as on the principal.
borrowed or lent.
