WEBVTT
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Welcome to the course Time value of money-Concepts
and Calculations.
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This lecture is devoted to the introduction
of this course.
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The present massive open online course objectives
are to illustrate basics of mathematics of
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finance; that is time value of money.
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It is one of the basic theories of financial
management.
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The time value of money or in short TVM is
based on the idea that money available at
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the present time is worth more than the same
amount in the future, due to it is potential
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earning capacity.
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In a lighter way, we can say that a bird in
the hand is worth two in the bush.
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This quote principle, finance holds that provided
money can earn interest inflation is 0, any
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amount of money is worth more the sooner it
is receipt.
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This may sound simple, but it underpins the
concept of interest.
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The time value of money is impossible to ignore
when dealing with loans, investment analysis,
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capital budgeting and many other financial
decisions.
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It is a fundamental building block that the
entire field of finance is built upon.
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For example, if given a choice between receiving
Rupees 100 today or Rupees 100 a year after
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now, you should take the money today.
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Lets analysis why?
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Because you could invest that 100 and even
if you only earned a, 8 percent annual return
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on your investment you still would have 108
Rupees a year from now; obviously, more than
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Rupees 100 you would have received if you
have waited.
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If you did not invest that 100 at all, but
simply spent it, you should still be better
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off because of inflation the Rupees 100 usually
will have more buying power today than in
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the future clearly.
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The first option is more valuable based on
two fundamental concepts; one higher purchasing
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power and second better opportunity cost.
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Let us, explain what is higher purchasing
power?
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And what is opportunity cost?
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Higher purchasing power because of inflation
Rupees 100000 can be exchanged for more goods
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and services today than Rupees 100000 in 100
years.
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Putting another way just think back, to what
Rupees 100000 could buy you 100 years ago.
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Rupees 100000, in 1916 would be equivalent
to roughly Rupees 50,50,495 today, that is
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in 2016 taking 4 percent interest rate.
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Now the opportunity cost, a rupee received
today can be invested.
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Now, to earn interest resulting in a higher
value in the future in contrast a rupee received
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in the future cannot begin earning interest
until, it is received.
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This lost opportunity to earn interest is
the opportunity cost.
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For these reasons two fundamental principles
of time value of money are; the one more is
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better than less and the second sooner is
better than later.
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Why the time value of money is so important
in capital budgeting decisions?
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Time value of money is an important concept,
in financial management.
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It can be used to compare investment alternatives.
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And to solve problems involving loans, mortgages,
leases, savings and annuities and thus affects
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financial decisions.
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Let me explain it through examples.
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Suppose you take example consider a project
that requires Rupees 400000 investment today.
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In a negative cash flows shown in the diagram
and will return 100000 a year, for the next
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5 years shown by positive cash flow.
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On paper, it looks as if the project produces
Rupees 100000 profit because I am investing
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400000 today and I am getting 100000, 100000
each year for 5 years, that amounts to 5,00,000.
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So, 5,00,000 minus 400000 is 100000 profit,
but those future cash flows must be converted
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to present value to know the actual profit.
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So, I cannot calculate the actual profit like
this, I have to convert the future cash flows
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to present cash flow and calculate the profit.
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If it is does then, if the company uses a
discount rate of 10 percent, the present value
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of those cash flows actually comes out to
be 379078.92 that is less than 400000 costs.
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So, the project actually will lose money though
it appears that it is gaining about 100000.
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However, if the company is using a discount
rate of 5 percent, the present value is 432947.66
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meaning that the project is in profit.
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To decide between competing projects, time
value of money can be used to decide between
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competing projects.
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Companies apply the time value of money in
various ways to make yes or no decisions on
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capital projects as well as to decide between
competing projects.
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Two of the most popular methods are.
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Net present value and internal rate of return
or IRR; these methods are used take the decisions.
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In the first method, you add up the present
value of all cash flows involved in a project,
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if the total is greater than 0, the project
is worth doing.
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The higher the net present value, the better
is the project.
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In the IRR method, you start with the cost
of the project and determine the rate of return
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that would make the present value of the future
cash flows equal to your upfront cost.
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If that rate called the Internal Rate of Return
is greater than your discount rate, the project
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is worth doing.
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The higher the IRR, the better the project
is paying the bills.
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Another important factor in asserting time
value of money is the level of debt you carry.
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If you have significant costly debt, it is
more advantageous to get money in hand quickly.
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If you make payments on a 12 percent loan,
generating revenue quickly can help you to
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expedite payments on the debt.
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This reality warrants strong considerations
of investment with quick returns.
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Now the, we talk about the concept of time
value of money.
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The purpose of the section is to introduce,
the concepts, terminology and the mathematics
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of the time value of money.
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Understanding of this is crucial for understanding
all sorts of solutions to financial problems
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in personal finance, investments, banking
insurance, etcetera.
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The concepts include, why interest is charged?
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Rate of interest and it is role, time line
to show investment and receipts number of
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periods, compounding and discounting, analysis
of problems related to time value of money.
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Now, let us see the first one, why interest
is charged?
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Interest is charged by lenders has compensation
for the loss of the assets used and can be
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thought of as the price of money.
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If a borrower wants to spend more than his
actual cash on hand, he will need to find
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someone to lend him additional funds.
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In the case of lending money, the lender could
have invested the fund instead of lending
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them out.
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With lending a large asset, the lender may
have been able to generate income from the
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asset should they have decided to use it themselves.
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The interest rate charged to a borrower reflects
the level of risk that the particular borrower
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might default on the loan and to compensate
for inflation.
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Rate of interest and it is role.
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Rate of interest is defined as the amount
of interest earned by a unit of principal
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in a unit of time.
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It is usually expressed in percentage value
like, 5 percent or 10 percent interest rate
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per year.
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Further interest rates are expressed for a
unit of time or time period like per year
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per 6 months or per day etcetera.
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This figure shows that, how interest rate
grow the money?
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If you see, for i equal to 5, that is interest
rate equal to 5, the growth is slow and for
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i equal to 20 percent the growth is faster.
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The time unit is usually taken as 1 year for
example, if Rupees 1 to 100 were the compensation
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demanded for giving someone the use of Rupees
1,000 for a period of 1 year.
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The principal would be 1,000and the rate of
interest would be 100 divided by 1,000 which
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is equal to 0 point 1 or 10 percent per year.
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The time line, now from example we will draw
a time line.
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Consider an example; consider a project that
requires a 400000 investment today.
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So, 400000 will be shown as a negative cash
flow at 0 year.
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And will return 100000 a year for the next
5 years.
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So, in the next 5 years you will find that
we are showing positive cash flows 100000
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each.
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The time line is defined as a time line is
a graphical representation of the size and
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timing of the cash flows.
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Let us take a second example, in the picture
above in the right and side you can easily
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see that the problem consists of a 5 year
100 annuity.
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So, in all the 5 years, we are showing positive
cash flows of 100 each and a Rupees 1,000
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cash flow, that occurs at the end of the investment.
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So, on 5th year who were showing, 100 as well
as 1,000, 1,000 is returned at the top of
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100.
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So, this is how the cash flows are shown in
a time line.
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Number of periods: interest rate is always
defined for a unit period of time.
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That unit period of time may be, 1 year, may
be half year, may be quarter of a year, may
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be month day or hours as shown in this figure,
we have shown number of years and number of
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months and at 0 year is considered to be today.
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Now once thing you should remember, those
interests are always charged at the end of
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the time period.
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The total length of time, the investment is
held is given by number of time periods in
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a time value problem and is designated by
capital N. Capital N may be, number of years,
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capital N may be number of months, capital
N may be number of quarters and capital N
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may be number of any defined time period.
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Now, let us considered the concept of discounting
and compounding; now, at time equal to 0,
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if I am investing some money it will grow
if I move to the future and this is called
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compounding.
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And if I move to the past then, it will decrease
and this is called discounting.
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Compounding method is used to know the future
value of present money, while discounting
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is a way to compute the present value of future
money.
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Analysis of problem related to TVM, that is
time value of money.
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Every time value of money problem has five
variables.
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Variable number one is the present value or
PV, then the future value FV, third variable
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is number of periods capital N, fourth variable
is interest rate i and the fifth variable
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is annuity amount, which is shown by PMT.
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In many cases, one of these variables will
be equal to 0.
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So, the problem will effectively have only
one, only four variables.
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We will always know the value of all the four
except one variable that is, missing value.
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For which you have to solve the problem.
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Let us take an example to substantiate this.
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Suppose you invest Rupees 100000 today at
8 percent compounded annually.
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What will this investment be worth in 4 years?
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Now you do the analysis of this example.
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First of all, we know that our present value
PV is 100000.
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Since, this is what we are investing today.
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Next the rate i is given to us as 8 percent.
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Third, the number of periods end in this problem
is 4 years.
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So, that leaves 2 remaining variables out
of the 5, payment of annuity amount and future
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value.
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These 2 we do not know and out of these 2,
in this case 1 is 0.
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Which one out of these 2, we do not know while
it was not explicitly given to us.
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We do know that the payment PMT, in this problem
is 0.
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Whenever payment is not explicitly given to
us, it is implied that there is no payment.
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So, all that leaves us with is the future
value component, which can be now easily be
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solved because we have one equation and four
unknowns and out of these four unknowns three
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unknowns are known.
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So, one equation can be solved very easily
for single unknown.
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Now, the different topics which will be included
in the series of lectures on time value of
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money are interest rate.
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Interest rate is the amount charged expressed
as a percentage of principal by a lender to
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a borrower for the use of his asset.
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Interest rates are typically charged on an
annual basis known as the annual percentage
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rate.
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The second topic is the simple interest.
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Simple interest is computed only on the original
amount borrowed.
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It is the return on that principal for 1 time
period.
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The third is the compounding techniques.
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In this compounding techniques, there are
three sub headings; compounding annually,
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discrete annually, compounding and continuous
compounding.
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Now in complaint compounding is defined as,
in this interest is compounded when the amount
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earned on initial deposit.
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That is initial principal becomes part of
the principal at the end of the first compounding
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period.
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The terms principal refers to the amount of
money on which interest is received.
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Now present value is an amount today that
is equivalent to a future payment or series
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of payments that has been discounted by an
appropriate interest rate.
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The future amount can be a single sum that
will be received at the end of the last period
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or as a series of equally spaced payments
an annuity or both.
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Since money has time value, the present value
of a promised future amount is always less
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the future value.
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The future value is the amount of money that
an investment with a fixed compounded interest
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rate will grow to by some future debt.
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The investment can be single sum, deposited
at the beginning of the first period or a
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series of equally spaced payments or an annuity
or both.
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Since money has time value, we naturally expect
the future value to be greater than the present
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value.
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Now Annuity; an annuity is a contractual financial
product sold by financial institutions that
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is designed to accept and grow funds from
an individual and then upon annuitization
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pay out a stream of payments to the individual
at a later point of time.
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The period of time when annuities are being
funded and before payouts begin is referred
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to as the accumulation phase.
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For example, annuities are student loan payments,
car loan payments, insurance premiums, mortgage
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payments and retirement savings.
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Amortization, amortization is a method for
repaying a loan in equal installments.
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Part of each payment goes towards interest
and the remaining is used to reduce the principal.
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As the balance of the loan is gradually reduced
a progressive large portion of each payment
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goes towards reducing principals.
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Perpetuities, perpetuity is simply and annuity
that continuous forever.
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That is perpetually the only difference between
annuity and perpetuity is the ending period.
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For annuity payments last for a certain period
whereas, for perpetuity they continue indefinitely
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as represented by infinite.
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Cash flow, a cash flow diagram is a picture
of a financial problem that shows all cash
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inflows and outflows along with time line.
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It can help you to visualize a problem and
to determine it, determine if it can be solved
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by TVM method; valuation of bond, valuation
of financial asset bonds, and valuation of
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shares, valuation of financial asset shares.
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Thank you.