Time Value of Money: Basic Concept【Dr. Deric】

Summary

In this educational video, Deric introduces the fundamental concept of the time value of money, emphasizing why receiving money today is preferable to receiving it in the future due to its potential to generate earnings. He explains the importance of this concept for comparing cash flows across different periods and discusses future value (FV) and present value (PV), along with the methods for calculating them, including equations, financial tables, calculators, and spreadsheets. Deric also touches on the significance of timelines, cash flow patterns, and the difference between simple and compound interest, all crucial for making informed investment decisions.

Takeaways

• 🕒 The concept of time value of money is based on the principle that money available now is worth more than the same amount in the future due to its potential to earn returns.
• 💰 People generally prefer to receive money today rather than in the future because of its present earning capacity and the ability to invest and grow wealth immediately.
• 📈 The decision to choose between receiving money now or in the future depends on the interest rate one could potentially earn on the money if received today.
• 🔢 Future Value (FV) is the concept that translates the value of money today into its equivalent value in the future, involving the process of compounding.
• 💼 Present Value (PV) is the concept that translates the value of future money into its equivalent value today, involving the process of discounting.
• 📊 There are four computational aids for time value of money calculations: equations, financial tables, financial calculators, and electronic spreadsheets like Microsoft Excel.
• 🗓 A timeline is a crucial tool for solving time value of money problems, helping to visualize cash flows over time and understand the sequence of events.
• 💹 Cash flow patterns can be categorized into three basic types: a single amount, an annuity, or a mixed stream, each with different implications for investment decisions.
• 🏦 Investment decisions should consider the time value of money, comparing cash flows at a single point in time to determine if an investment is wise.
• 📈 Simple interest is calculated based on the original principal amount, without earning interest on interest.
• 🌐 Compound interest is calculated on the total balance, including previous interest earned, leading to an increasing amount of interest over time.
• 👋 The video concludes with a reminder that all time value of money questions will apply compound interest for calculations.

Q & A

What is the basic concept of time value of money?

The time value of money is the concept that a sum of money available at the present time is worth more than the same amount in the future due to its potential earning capacity. Essentially, $1 today is worth more than $1 in the future because of the interest or investment returns it could generate.

Why would someone prefer to receive $10,000 today rather than in five years?

Someone would prefer to receive $10,000 today because the money can be invested and potentially earn returns, making it grow in value over time. Receiving the money now allows for immediate use and the opportunity to benefit from its earning potential, rather than waiting for it in the future.

How does the concept of time value of money allow for the comparison of cash flows from different periods?

The time value of money allows for the comparison of cash flows from different periods by converting future cash flows to their present value or present cash flows to their future value. This makes it possible to evaluate and compare the worth of cash flows at a single point in time, regardless of when they occur.

What is the significance of knowing the interest rate when choosing between receiving $1,000 today or $1,100 one year from now?

Knowing the interest rate is crucial because it helps determine whether it's more beneficial to receive the money now or later. If the potential interest rate is higher than the implied rate of 10% in the example, it would be better to receive $1,000 today and invest it to earn more than the $100 difference. Conversely, if the interest rate is lower, it would be more advantageous to wait for the $1,100.

What is meant by the future value (FV) in the context of time value of money?

Future value (FV) refers to the amount of money that a given sum of money will grow to in the future, taking into account the interest it will earn. It translates the value of $1 today into its equivalent value at a later time, through the process of compounding.

What is present value (PV) and how does it differ from future value?

Present value (PV) is the current worth of a future sum of money, given a specific interest rate. Unlike future value, which calculates the amount money will grow to, present value calculates the amount of money that, if invested today, would accumulate to a future sum. It involves discounting future cash flows back to their value today.

What are the four computational aids mentioned for calculating time value of money questions?

The four computational aids for calculating time value of money questions are: using equations, financial tables, financial calculators, and electronic spreadsheets such as Microsoft Excel. These aids help in performing the necessary calculations to understand the time value of money.

Why is drawing a timeline important when solving time value of money problems?

Drawing a timeline is important because it visually represents the sequence and timing of cash flows. It helps in organizing the information and understanding the time periods involved, which is crucial for accurately calculating the time value of money.

What are the three basic patterns of cash flow mentioned in the script?

The three basic patterns of cash flow are a single amount, an annuity, and a mixed stream. A single amount refers to a one-time cash flow, an annuity involves equal cash flows over a series of periods, and a mixed stream has varying cash flows over time.

How does the concept of compounding differ from simple interest in the context of time value of money?

Compounding involves interest being calculated on the initial principal as well as on the accumulated interest of previous periods, leading to interest on interest. In contrast, simple interest is calculated only on the original principal, without any interest being earned on previously earned interest.

What is the decision-making process when evaluating an investment that will produce cash flows over multiple years?

When evaluating an investment with cash flows spread over multiple years, it's important to compare the cash flows at a single point in time. This can be done by either converting all cash flows to their future value at the end of the investment period or by discounting all cash flows back to their present value at the beginning of the period. This allows for an accurate comparison of the investment's profitability.

Outlines

00:00

💰 Time Value of Money: Present vs. Future

Deric introduces the fundamental concept of the time value of money, emphasizing that money available now is worth more than the same amount in the future due to its potential to generate earnings. He illustrates this with a hypothetical choice between receiving $10,000 today or in five years, highlighting the preference for immediate payment. The video explains the importance of this concept for comparing cash flows across different time periods and introduces the decision-making process based on interest rates. Deric also covers the basic principles of future value (FV) and present value (PV), the processes of compounding and discounting, and the tools used for calculating time value of money, such as equations, financial tables, calculators, and spreadsheets. The importance of timelines in solving time value problems is also discussed, along with assumptions made in these calculations.

05:00

📈 Analyzing Investments: Future vs. Present Value

This paragraph delves into the decision-making process for investments, using a scenario where a firm must choose between spending $15,000 now for a series of cash flows over five years or not investing at all. The concept of converting cash flows to a single point in time, either as future value at the end of the period or present value at the beginning, is explained to facilitate comparison. The paragraph also contrasts simple and compound interest, with a focus on the latter for time value of money calculations. The video concludes by summarizing the key points and thanking viewers for their attention, promising more information in the next video.

Keywords

💡Time Value of Money

The time value of money is the concept that a sum of money is worth more the sooner it is received. This is due to its potential earning capacity, which is a fundamental principle in finance. In the video, Deric explains that receiving $10,000 today is preferred over the same amount in five years, illustrating the concept with a direct comparison that highlights its importance in financial decision-making.

💡Present Value (PV)

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 used to determine the value of money today of a future sum, which is essential for comparing different investment opportunities. In the script, Deric discusses how PV translates a future amount of money into its equivalent today, using the concept to evaluate investment decisions.

💡Future Value (FV)

Future value is the amount of money that a sum of money will grow to in the future, given a specific rate of interest. It is calculated by compounding the initial amount over time. The video script uses FV to explain how money today can be projected into its value at a future date, which is crucial for planning and forecasting financial outcomes.

💡Compounding

Compounding is the process where interest is calculated on the initial principal as well as on the accumulated interest of previous periods of a deposit or investment. This concept is fundamental to understanding how money grows over time. In the video, Deric explains compounding as the process that translates today's money into its future value, emphasizing its role in investment growth.

💡Discounting

Discounting is the process of finding the present value of a future cash flow, which is the opposite of compounding. It is used to determine how much a future sum of money is worth today. The script mentions discounting in the context of translating a future sum into its present value, which is key for evaluating investments and making financial comparisons.

💡Interest Rate

An interest rate is the percentage at which interest is paid by borrowers to lenders, or paid by lenders to borrowers on investments. It is a critical factor in determining the growth of an investment. In the video, Deric uses the interest rate to illustrate how the decision between receiving money now or in the future depends on the potential earnings from that money.

💡Cash Flow

Cash flow refers to the movement of money into and out of a business or investment. Positive cash flow indicates inflow, while negative cash flow indicates outflow. In the script, Deric discusses cash flows in the context of different investment patterns and their impact on the time value of money calculations.

💡Timeline

A timeline is a graphical representation of cash flows over time, which is a crucial tool for visualizing and solving financial problems involving the time value of money. The script emphasizes the importance of drawing a timeline to understand and compare cash flows at different time intervals.

💡Compound Interest

Compound interest is interest on a loan or investment where the interest is added to the principal, so that the total amount on which interest is paid grows over time. This is contrasted with simple interest in the script, where Deric explains that with compound interest, you earn interest on interest, leading to exponential growth.

💡Simple Interest

Simple interest is calculated only on the principal amount, without any addition of interest to the principal balance. It is a straightforward calculation compared to compound interest. In the video, Deric contrasts simple interest with compound interest to clarify how interest is calculated differently and affects the growth of an investment.

💡Investment Decision

An investment decision involves choosing between different options for allocating funds with the goal of earning a return. The script uses the example of choosing between receiving $1,000 today or $1,100 in a year to illustrate how the time value of money and potential interest rates influence such decisions.

Highlights

Introduction to the basic concept of time value of money, emphasizing that money available now is more valuable due to its potential earning capacity.

Discussion on why individuals would prefer to receive $10,000 today rather than in five years, illustrating the preference for present value.

Explanation of how the time value of money allows for the comparison of cash flows from different periods.

A hypothetical scenario where viewers are asked to choose between $1,000 today or $1,100 in a year, highlighting the decision-making process based on potential interest rates.

Clarification that the choice between receiving money now or later depends on the interest rate one could earn on the money.

Definition and explanation of future value (FV) as the process of translating present money into its equivalent in the future through compounding.

Definition and explanation of present value (PV) as the process of translating future money into its equivalent today through discounting.

Introduction of four computational aids for time value of money calculations: equations, financial tables, calculators, and electronic spreadsheets.

Importance of drawing a timeline for solving time value of money problems, with an explanation of cash flow (CF), time (T), and interest rate (i).

Assumptions made in time value of money calculations, such as the decision point being today and cash flows occurring at the end of a time interval.

Description of the three basic cash flow patterns: single amount, annuity, and mixed stream, with examples for each.

Analysis of an investment scenario where a firm must decide if spending $15,000 today for $17,000 spread over five years is wise, emphasizing the need for time value comparison.

Explanation of how to compare cash flows at a single point in time, either by converting to future value or present value.

Differentiation between simple interest, where interest is calculated only on the principal, and compound interest, where interest is calculated on both principal and previous interest.

Emphasis on the use of compound interest for all time value of money questions in the video.

Conclusion of the video with a reminder to stay tuned for the next one, highlighting the educational value of the channel.

Transcripts

Hey guys, I am Deric, welcome to my channel.

In this video, I’m gonna talk about the basic concept of time value of money.

As we know, time has value.

Like 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.

Alright, 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.

What is future value, FV?

FV translates $1 today into its equivalent in the future.

This process is called compounding.

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.

First, use the equations.

Second, use the financial tables.

Third, use financial calculators.

Fourth, use electronic spreadsheets, such as Microsoft Excel.

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.

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.

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.

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.

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.

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.

As shown in the table, every year the interest is calculated based on the previous year total

balance, that’s why the interest payment is getting higher and higher.

So, you earn interest on interest.

For all the questions of time value of money, we will only apply compound interest.

Alright, that’s all for this video, thanks for watching, see you in the next one, bye!