20 August 2024
Summary
TLDRThis educational video script introduces the concept of the time value of money and its significance in financial management, particularly for long-term projects. It explains how the purchasing power of money diminishes over time due to factors like inflation, interest, and risk. The script delves into the mechanics of compounding and discounting, illustrating how to convert future cash flows into present values using formulas and tables. It also outlines the Net Present Value (NPV) technique for evaluating investments, emphasizing its role in maximizing shareholder wealth.
Takeaways
- đĄ The concept of time value of money is essential in financial management, as it accounts for the reduction in purchasing power over time due to factors like inflation and interest rates.
- đ The time value of money is crucial for evaluating long-term projects, as it helps to assess future cash flows in today's terms, allowing for informed decision-making.
- đ° Present value (PV) is the current worth of a future sum of money or cash flow, while future value (FV) is the value of money at a future date, calculated using compounding.
- đą Compounding is the process of converting present value to future value, using the formula FV = PV * (1 + r)^n, where r is the interest rate and n is the number of periods.
- đ Discounting is the reverse of compounding, converting future value to present value, which is essential for evaluating investments and projects today.
- đ The discount factor is used to adjust future cash flows to their present value, and it can be found using the formula 1 / (1 + r)^n or from a present value table.
- đ Understanding the difference between compounding and discounting is fundamental to financial calculations, with compounding adding value over time and discounting reducing it.
- đŠ Net Present Value (NPV) is a method used to evaluate investments, calculated by subtracting the present value of cash outflows (like initial investments) from the present value of cash inflows.
- đ NPV provides an absolute measure of the value that a project is expected to create, with a positive NPV indicating an increase in shareholder wealth.
- đ The script provides a step-by-step explanation of how to calculate future value, present value, and NPV, emphasizing the importance of these concepts in financial decision-making.
- đ The use of a present value table is demonstrated as a quick method to determine discount factors for different interest rates and periods, simplifying the calculation process.
Q & A
What is the concept of time value of money?
-The time value of money is the concept that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This concept is fundamental in finance as it takes into account the reduction in purchasing power over time, often due to inflation and other economic factors.
Why is the time value of money important in financial management?
-In financial management, the time value of money is crucial because it helps in evaluating the profitability of investments that span multiple years. It allows decision-makers to compare the value of cash flows occurring at different times, bringing them to a common basis for making informed investment decisions.
What is the difference between present value and future value?
-Present value refers to the current worth of a future sum of money or cash flow, given a specified rate of return. Future value, on the other hand, is the value of money at a future date, calculated by compounding the current value by the rate of interest over time.
How does inflation affect the time value of money?
-Inflation erodes the purchasing power of money over time. As prices rise, the same amount of money buys fewer goods and services in the future compared to the present, which is why future money is worth less in today's terms.
What is compounding and how is it related to the time value of money?
-Compounding is the process of calculating the interest on a principal sum of money semiannually, quarterly, or annually, and adding it to the principal so that interest is earned on the initial principal and also on the accumulated interest. It is related to the time value of money as it demonstrates how money grows over time when interest is added to the principal.
What is discounting and how does it differ from compounding?
-Discounting is the process of finding the present value of a future cash flow. Unlike compounding, which calculates the future value of money, discounting converts future cash flows into present values, adjusting for the time value of money.
How is the discount factor used in calculating present value?
-The discount factor is used to convert a future cash flow into its present value. It is calculated as (1 + r)^-n, where r is the interest rate and n is the number of periods. Multiplying the future cash flow by the discount factor gives the present value of that cash flow.
What is the formula for calculating the future value of an investment?
-The formula for calculating the future value of an investment is Future Value = Present Value * (1 + r)^n, where r is the interest rate and n is the number of periods the money is invested or borrowed for.
Can you explain the concept of Net Present Value (NPV)?
-Net Present Value (NPV) is a financial metric that calculates the difference between the present value of cash inflows and the present value of cash outflows over a period of time. It is used to analyze the profitability of an investment or project. A positive NPV indicates that the investment is expected to generate more cash than the cost, thus creating value for the shareholders.
How does the risk associated with future cash flows affect the time value of money?
-Risk associated with future cash flows is incorporated into the time value of money through the discount rate. Higher perceived risk may lead to a higher discount rate, which in turn results in a lower present value of future cash flows, reflecting the increased uncertainty and potential for loss.
What is the significance of using a present value table in financial calculations?
-A present value table provides a quick reference for discount factors at different interest rates and time periods. It simplifies the calculation of present values by allowing users to look up the appropriate discount factor instead of calculating it manually, thus saving time and reducing the potential for calculation errors.
Outlines
đ° Time Value of Money and Discounted Cash Flow Concepts
This paragraph introduces the fundamental concept of the time value of money, explaining how the purchasing power of money decreases over time due to factors like inflation and the potential for earning interest. It emphasizes the importance of this concept in financial management, especially when evaluating long-term projects. The speaker discusses the difference between present value, which is the value of money today, and future value, which is the value at a future point in time. The paragraph also covers compounding, which is the process of converting present value to future value using a compound factor, and sets the stage for the concept of discounting, which is the reverse process used to evaluate future cash flows in today's terms.
đ Understanding Discounting and Calculating Present Value
The second paragraph delves into the specifics of discounting, which is essential for financial decision-making. It explains that discounting involves converting future cash flows into present values to facilitate current investment decisions. The speaker outlines the formula for discounting, which involves a discount factor calculated as (1 + r)^-n, where r is the interest rate and n is the number of periods. The paragraph also illustrates how to use a present value table to find the appropriate discount factor for a given interest rate and time period. It provides an example of calculating the present value of a future receivable, demonstrating three different methods to ensure understanding and reinforcing the concept of discounting as a tool for evaluating future cash flows in today's terms.
Mindmap
Keywords
đĄTime Value of Money
đĄDiscounted Cash Flows
đĄPresent Value
đĄFuture Value
đĄCompounding
đĄDiscounting
đĄInflation
đĄRisk
đĄNet Present Value (NPV)
đĄInterest Rate
đĄInvestment Decision
Highlights
Introduction to the concept of discounted cash flow techniques such as NPV and discounted payback period.
Explanation of the time value of money and its practical implications in financial management.
The impact of inflation on the purchasing power of money over time.
Importance of bringing future cash flows into today's terms for decision-making purposes.
Definition of present value and its relation to future value in financial calculations.
The concept of compounding as the conversion of present value to future value.
The formula for calculating future value using the compound factor.
Factors that cause the reduction in the purchasing power of money, including interest, inflation, and risk.
The process of discounting to convert future value to present value for project evaluation.
The use of discount factors in financial calculations and how to apply them.
Explanation of the present value table and its utility in exams.
Demonstration of calculating present value using different methods and verifying consistency.
Introduction to the Net Present Value (NPV) technique for project evaluation.
Description of how NPV is calculated by taking the net of present values of inflows and outflows.
The significance of NPV in determining the absolute monetary impact on shareholder wealth.
Emphasis on the importance of NPV as a key metric in financial decision-making.
The potential for NPV to be a comprehensive topic in financial management exams.
Transcripts
it is discounted
Cas okay guys let's continue chapter
number three it is discounted Cas for
techniqu so the three npv ir and
discounted payback period right now to
understand first what is discounted
let's talk about time value of money
concept the time value of money concept
is again a very practical concept it is
with time the power of your money is
going to reduce if let's say for example
last year you were able to buy a t-shirt
for $100 this year you'll have to pay
$110 to buy the same t-shirt the reason
because now the work or the purchasing
part of your $100 has reduced so with
time due to inflation the purchasing
power of your money reduces now why is
it that we have time value of money here
in financial management see we are
talking about projects that are going to
last for a number of years 20 years 30
years 40 years right so we will be
having cash flows coming from these
projects in the future right what we
have to do is make the decision today
about a cash flow that's going to come
after 30 years we have to make the
decision today so in order to make the
decision today I have to bring that cash
flow into today's terms because I know
the value of the cash flow after 30
years is not equal to the value of that
cash flow today so what we have to do is
we have to bring all the F cash flows
into today's terms because this is where
I have to make the decision and that's
how we're going to use the time value of
money Concept in investment opis and
financial management so there are two
very important terms one is present
value present value refers to the value
today and we have the future value
future value refers to the value in the
future let's say the value after 30
years or 20 years or after one year
that's the future value bringing it to
today's term will be the present value
now like I said $100 of today might be
equal to $110 of tomorrow so your
present value is always less than your
future value fine now why is there a
reason or what what might be the things
that cause your purchasing power of
money to reduce so the potential for
earning interest or the cost of Finance
is one of the reasons why the purchasing
power reduces very important is the
inflation and then the effect of risk
because we have to take the project on
in the future and because of the future
being involved there are a lot of
uncertainities and risks so we have to
incorporate that using the time manage
money concept as well right so our
future is not equal to the present
that's what the main concept is now to
incorporate this we have the concept of
compounding and discounting compounding
is actually the main concept discounting
is using compounding for All Purpose
what is compounding compounding is let's
say for example today that is Time Zero
you have a present value of $100 you
want to see how much would this $100 be
equal to after one year that is
calculating the future value so this
conversion of present to future is known
as
compounding I repeat the conversion of
present to future is compounding we've
discussed your future value is always
higher than the present value so it
means I have to add something to the
present value to come up to the future
value the formula for this is future
value equals your present value into the
compound factor and the compound factor
is 1 + r ra to the power n now where n
is your number of periods one year two
year 3 years that's n r is your rate of
interest or the rate by which you have
to compound whereas this entire thing is
known as the compound Factor 1 + r rais
to the^ 10 let's say for example my
present value was $100 the rate of
interest is 10% so 1 plus 0.1 I want to
know the value of this after one year so
what will be the future value then 110
so 100 into 1.1 to the^ one that's going
to give us $110 so what is compounding
converting present value into future
value by multiplying it with 1 plus r
n is always it's if you're going from
present to Future that's always
compounding right but in our case we
won't be using compounding we'll be
taking compounding as the basic concept
and we'll go the other way around
because we have to bring everything to
the present value right okay let's have
a look at this question it says an
investment of 500 to be made today so
what is this present value in an account
earning 5% in trust that's your R what
will be the value of the account after 3
years that's your n guys online please
let me know your answers for this what
it be the future value given a certain
present value multip 1 plus r the N guys
online do type in your answers or you
can also speak up if you want
exent yes answer
excellent Mohammed yes Mar s answers
pleas okay so what's the present value
that's 500 into 1 plus r is excellent 5%
so that's 0.05 to the power n is 3 so
that will approximately give us 579 as
the future value now like I said this is
just a concept on the basis of which
we're going to build up the concept of
discounting that will will be using in
financial management so we know we have
to take up a project in the future that
will come up with a lot of future cash
flows right in year one there will be a
revenue then year two Revenue year three
year 20 Revenue I have the cash FL in
the future but I have to decide about
this project today so I don't need the
cash fls of the future rather I need the
value of all those cashs in the present
so that I'm able to make the decision
today so that's what discounting is
going from the future to the present
converting the future value into the
present value that's what discounting is
and this is what we'll be using the
formula is future value into the
discount factor and the discount factor
is 1 + r ra^ minus n since we know the
present Val is less than future we'll
have to take something out right so
which is why it will be minus n here 1 +
r^ minus n is your discount Factor
another way to calculate the same is
present value equals future value
divided 1 plus r ra to the^ n would give
you the same answer correct
okay now let me show you this table here
the present value table like I said it
will be there with you in the exam it's
a shortcut for the discount factors they
have given you an answer for 1 plus r^
minus n for up to 20% for 15 years I
tell you how to use it let's have a look
at this question it says what is the
present value of 65,000 this 65,000 is
my receivable in 6 years time this is my
n if the applicable interest rate is
seven let's do it using all three
different ways number one present value
equals future value into 1 plus r the
powerus N future value is R is 7% n is 6
use your calculators what do we
get
43312 1.07 power - 6 * by 65,000 so
that's 4335 anyone of you is not getting
the answer please let me know now second
way was present value equals future
value divided by 1 + R ra^ 8 so future
vales again 65,000 divid 1 + r ra^ 6
just quickly try it out and see if
you're getting a similar answer this is
the first and the last time we'll be
using all three methods here just to
familiarize you with the fact that they
going give you similar
answers
43,000
300 correct Third Way is present value
equals future value into discount Factor
future Val is again 65,000 now the
discount Factor please pay attention
here how are you going to read the table
so what's my R 7% so what I have to
focus on is 7% from here correct what's
your n so in the period go for six now
see which one matches 6 years and 7%
That's your discount factor I repeat you
have to look down 7% and across six
years correct so what's the discount
Factor 0. 666 see what you get as an
answer
90 similar answer almost just slight
differ because that is a rounded of
version and it is totally acceptable is
that c good with all the three possible
ways of calculating it Okay so we've
seen how to convert a future value into
a present value because the decision has
to be made today and that's known as
discounted now we'll start off with the
techniques the first technique was Net
Present
Value let's say for example I have to
evaluate a project that has a life of 25
years for which they've given me that at
t z you'll have to spend 1 million on
this that's my initial investment and
accumulatively they're saying from T1 to
T5 T25 right from T1 to T25 they've
given me that the present value of
inflows would be equal to
$500,000 it's a very simple basic
version that I'm bringing of n me so the
different mean today you going to spend
1 million and in future accumulated
you're going to earn ,500,000 in today's
terms right that's a present value so
what the Net Present Value Net Present
Value is as literal as it name it's a
net of present values present values so
you're going to take present value of
inflows what's
that minus present value of outflow
what's the present value of outflow for
me what am I going to spend today 1
million so what's the net of present
values that's npv this is the net of
your present Valu as simple as this it
has a lot to it npv can be a
full-fledged 20 mark question in your
exam this is just a start what is it
it's the net of present value of inflows
and outflows correct now what is this
500,000 represent
in absolute terms so this is the only
technique that gives us an answer in
absolute terms that is in dollars in
absolute terms if the project is
accepted the wealth of shareholders
because who's going to get all the
growth the shareholders the wealth of
shareholders will Max
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