20 August 2024

Summary

This 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

• 💡 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.
• 🕒 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.
• 💰 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.
• 🔢 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.
• 📉 Discounting is the reverse of compounding, converting future value to present value, which is essential for evaluating investments and projects today.
• 📊 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.
• 📚 Understanding the difference between compounding and discounting is fundamental to financial calculations, with compounding adding value over time and discounting reducing it.
• 🏦 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.
• 📈 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.
• 📝 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.
• 📑 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

00:00

💰 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.

05:01

📈 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.

Keywords

💡Time Value of Money

The time value of money is a financial concept that states that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. It is the core theme of the video, explaining why future cash flows must be discounted to their present value to make informed investment decisions. For example, the script mentions that the purchasing power of $100 reduces over time due to inflation, thus emphasizing the importance of this concept.

💡Discounted Cash Flows

Discounted cash flows (DCF) are the projected cash flows from an investment, discounted back to their present value using a discount rate. This concept is crucial in the video, as it helps in evaluating the profitability of long-term projects by converting future cash flows into today's terms. The script uses DCF to illustrate how to determine the value of a project's cash inflows and outflows over its lifetime.

💡Present Value

Present value is the current worth of a future sum of money or a series of cash flows given a specified rate of return. It is a fundamental concept in the video, as it is used to bring future cash flows into today's terms, allowing for a comparison of their value at the present time. The script explains that the present value is always less than the future value, as demonstrated in the compounding and discounting examples.

💡Future Value

Future value is the amount of money that a sum of money will grow to at a given annual interest rate in the future. In the context of the video, future value is calculated to understand how much a present sum will be worth after a certain period, which is essential for long-term financial planning and investment analysis. The script provides an example of calculating the future value of $100 with a 10% interest rate over one year.

💡Compounding

Compounding refers to the process of calculating the interest on a principal sum at regular intervals, with each addition of interest being added to the principal, thus increasing the amount on which the next interest is calculated. The video explains compounding as the conversion of present value to future value, using the formula future value = present value * (1 + interest rate)^number of periods.

💡Discounting

Discounting is the process of finding the present value of a future cash flow. It is the reverse of compounding and is used to determine the current value of a future sum of money based on a specific discount rate. The video uses discounting to explain how to evaluate the worth of future cash flows from investments, emphasizing its importance in financial decision-making.

💡Inflation

Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, the purchasing power of currency is falling. In the video, inflation is cited as one of the reasons for the reduction in the purchasing power of money over time, which is a key factor in understanding the time value of money and the need for discounting future cash flows.

💡Risk

Risk in financial terms refers to the possibility of an investment losing value. The video mentions risk as a factor that affects the time value of money, as future cash flows are subject to uncertainties and potential losses. It is one of the reasons why future cash flows are discounted to their present value to account for the risk involved.

💡Net Present Value (NPV)

Net Present Value is a financial metric used to determine the profitability of an investment by calculating the difference between the present value of cash inflows and the present value of cash outflows over a period of time. The video introduces NPV as a technique to evaluate projects, emphasizing its role in determining the increase in shareholder wealth by comparing the present value of inflows to the initial investment.

💡Interest Rate

The interest rate is the percentage at which interest is paid by borrowers to lenders, typically expressed as an annual percentage rate (APR). In the context of the video, the interest rate is used as the discount rate to calculate the present value of future cash flows, illustrating its importance in the time value of money calculations.

💡Investment Decision

An investment decision refers to the choice made by an investor or a company regarding the allocation of funds to a financial asset or real asset. The video's theme revolves around making informed investment decisions by understanding and applying the time value of money, discounted cash flows, and NPV to evaluate the potential profitability of long-term projects.

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