Finance Fundamentals : Time Value of Money

1. Time Value of Money (Introduction): Hi everyone. Welcome to our time value of money class of Finance fundamental scores. In this class, we will understand very key concept, which is time value of money, and we will try to understand why money is worth more now than in future. We will take a look into some key concepts such as future value, present value, net present value, also known as NPV, IRR, also known as internal return rate. We will try to understand the change over the time, how impacts the value of the money, and this will be also linked very much to our previous understanding of inflation. Also, please note that this course is designed to help you to make calculated decisions in your daily life via understanding finance or economics. It doesn't provide any investment tax, or financial planning advice. 2. 100$ Today or 100$ Next Year?: Hello, everyone. Today, we will unlock a very important concept with a simple question. Let me ask you. If I tell you that I will pay you $100 today, or I will give you $100.01 year later, which one would you prefer? Most of you would prefer to receive that $100 as of today. But why we want to have the money today instead of one year later? Because there is something called time value. Money has different value today than it will have at future date due to its potential earning capacity. Let's imagine that I give you $100 today. And forget about the other investment options and focus on only depositing that money to the bank. Banks have some saving interests that they provide to their customers on yearly basis. And this can change based on the country's money politics or inflation rates. But let's assume a bank will provide you 5% interest rate per year. If you deposit your $100 today and wait for one year with 5% interest, you will receive your money at the end of that one year as $105. Receiving $100 today has potential earning capacity that you can receive it as $105 in one year, based on this imaginary example of 5% interest rate. So receiving it today is better than receiving the same amount next year. Although $5 seems low due to 5% interest rate assumed, imagine you deposit $1,000,000. So 5% of $1,000,000 will be significant value around $50,000. Or imagine that you will keep your hundred dollar, not only one year, but for ten years. So you will continue to receive 5% every upcoming year as well, and your money will continue to grow. This is compounding. In our next section, we will see more understanding in terms of the power of compounding, and we will see how much our money would look like in ten years if we deposit $100 today. Stay tuned. Thanks so much. See you in the next session. 3. Future Value of Money : Everyone, in our previous session, we have asked a very simple question. Would you prefer receiving 100 taller today or would you prefer receiving 100 Teller one year later? And we said that most of the people prefer to receive that 100 tar as of today, and they can deposit that money to a bank, which gives them x percent interest rate, and we assume the interest rate as 5%. Let's see that over the time period, not only one year, but let's imagine that person deposit that $100 to a bank and waited for ten years. What would be the amount of money in the end of ten years? Let's say that you deposit $100 here and interest rate is 5%. In the end of one year, you will have $100, which is your main money plus 5% interest rate applied to this $100, and it will be $105. Second year, this interest rate will apply to $105 because your money now is $105 with the interest rate of the past period. So you will have $105 plus 5% applied on $105, 110.25. And for third year, it will be same. You will have 110 plus $25, will be having 5% interest rate on it, and it will become 115 point $7. As you see here, 0-1 year, your money has increased by $5. From first to second year, it increased more than $5, 5.25. From second to third year, it increased 5.5 dollar. So the increased amount of your money is also growing. This also known as the compound impact of the interest rate. However, let's explore, do we have an easier way to calculate? Future value equals to present value multiplied with one plus interest rate over the years. How we can implement it to our calculation. Let's say that for the first year, your future value of the money will be $100 multiplied with one plus 5% over one year period. It will be $105. In the end of second year, it will be $100 is your initial amount of the money, which is the present value of your money, multiplied with one plus 5%, which is the interest rate over two years. So that interest rate will apply twice to your money and your money will grow to 110.25. This will continue in this way, and let's see in the end of ten year, your hundredtar will be applied by 5% interest rate, which is one plus 5% over ten years, and this will equal to 162 point $8. As you see here, you may have expected my money should increase by $50 because 5% of 100 is $5 over the ten years, it should be $50. However, your actual increase is more than $50. It is 62 point $8. This is the reason of your main money is also growing and interest rate is applying in that growth amount, and this is the power of compounding. Thank you so much. In our next session, we will explore the other way around. What is the present value of the money that you are going to receive in future, and we will apply something called discount rate. See you there. 4. Present value of Future Money: Everyone. In our previous session, we have discovered the future value of present money. Now we will discover the present value of future money. We will look for the answer of, I I pay you $100.10 years later, what does it mean compared to receiving some amount today? When we are trying to do this, it is the other way around calculation, which we covered as the future value of the present money. Let's unlock it. If you are going to receive on the tenti, you need to move the money ten years back. So how we're going to do that is present value equals to future value divided by one plus discount rate over years. Which is basically if you are going to receive $100 in the end of ten years, which is the future value divided by one plus 5%, we are assuming 5% is discount rate. This count rate depends on different parameters, such as inflation, central bank policies, which is interest rate, which we assumed 5% for bank as well. Risk profile of your company or you, et cetera. However, for the sake of simplicity, we are assuming 5% is the inflation rate, and also banks provide 5% interest rate, which we applied in our previous exercise. So discount rate for the more accrued calculation, we will unlock in following session, and we will see some details. But for now, let's stick on the 5% discount rate for this time period. If we apply the formula, we receive the amount of 61.30 $3 worth of money today. So receiving $100 in ten years with an economy which has 5% inflation rate, means that receiving 61.40 $3 today is the same scenario. Because remember that inflation makes your money lose some value. If you have 5% inflation, means that if you're able to buy this phone for $100 this year, then next year, phone price will be $105. The following year, it will be 110.25, et cetera. The price will be increasing. So on the other way around, to be able to buy this phone, you need to pay more amount of money. So if you take it back by the inflation rate or discount rate, you will receive the amount of money, which is to divert. So you can do the other way around calculation as well. If I give you 61.40 $3 today, then you can apply 5% interest rate, which we assume same with inflation rate, you will receive $100 in ten years by the bank based on 5% interest rate. So we are discounting money instead of compounding the value. However, you can double check with the other way around as well. Let's see this discount rate depends on different parameters. What are those? As we explained, inflation is one of the main criteria when it comes to discounting the money. Higher inflation typically leads to higher rates, means that if you have very high inflation, such as 50% or 100%, et cetera, which means that your money will lose value much more over the time period. So you need to discount your future money to today's value and more rates. Or central bank policies, which is policies set by institutions like the Federal Reserve influenced the interest rates. Companies risk profile. The risk associated with a company or individual affects the rate offered. So you may receive a different interest rate than I receive. This depends on our risk profile. This also applies on company level as well. For simplicity, as we have done in our exercise, you can focus on the inflation rate because also interest rates in an ideal world impacted by the inflation rate of a country. If you want more accurate calculation, especially on the company level, you can use WACC, also known as weighted average cost of capital. You will understand how to calculate this WACC in our following session. Thanks so much. See you there. 5. Exercise 1 : Calculate WACC for a company: Hello, everyone. In our previous session, we mentioned a very important thing called this WACC, which is the more accurate version of the discount rate for companies. Now, we are going to calculate the weighted average of cost of capital for a company. We mentioned in our previous classes such as exploring balance sheet or financial ratios, we said that a company can make capital two ways. This can be either debt receiving some money from bank or using equity, which is the amount of money that investors put. Cost of debt is the effective rate a company pays as interest to the bank. Let's say that I received $100,000 from bank to invest into my operations, then I need to pay interest rate such as 5% to this bank in the following years. Or let's say that investors put $100,000 to this company as equity, and I'm planning to use this 100,000 to my operations, then I need to be careful about to pay back this 100,000 in higher amounts because these investors put this money with an expectation of their money will grow. So the minimum return that potential stakeholders demand before investing, I need to cover if I'm going to use the equity for my operations. Let's assume that a company A is using 80% of its capital as debt, borrowing money from bank, and cost of debt is 5%, which is the interest rate. Other 20% of their investments are covered by the equity part. And cost of equity is, let's say, 15%. Investors are expecting that their money will grow by 15% in yearly basis. So if I'm using that money, I need to be careful that I will pay that 15% as potential increase to these equity owners, which are the stakeholders. So what is the net present value of $1,000 to be received in three years? Let's calculate it. First, we are going to calculate the WACC, which is the weighted average. Very basic calculation, weight of debt, multiplied with cost of debt plus weight of equity, multiplied with cost of equity. If this company is using 80% of their capital through debt, we are putting 80% here, multiply it with the cost of debt, which is 5% plus 20% of their capital used through the equity, multiplied with the 15%, which is the cost of equity, reaching up to 7% as discount rate as WACC for this company, which means that the amount that we need to discount in every year is 7%. If we are looking for the net present value of $1,000 to be received in three years, then we need to discount this amount for three times one plus 7% over three years, and we are reaching up to 816 point $3, which means that for this company, receiving $1,000 in three years means that receiving 816 point $3 today. As you can see, this calculation gives us more accurate way based on the company profile in terms of the discount rate that we need to apply to find the net present value of a money that the company will receive in certain amount of years. We will discover more in our following session on a person level and company level, so stay tuned. Thank you so much. See you there. 6. Exercise 2 : Calculate Jack’s Future Wealth : Hello, everyone. Today, we will calculate Jack's future health. If we are going to unlock the future amount of the money that he's putting today or in the following years, then we need to use the interest rate version, which is compounding the money, increasing the money over the time period. Let's assume that every year, Jake invests $10,000 to stock market with average expected return of annual 10% for ten years. Each year he expects that his money will grow by 10%. And please note that this 10% is an imaginary rate, and this is not a financial advice. We're trying to see that in the end of ten years how much money Jack expects to have? Let's do it together. Let's say that he invests in the end of one year, $10,000 to the stock market. And every year he expected to increase by 10%. If he deposit 10,000 stock market, then this will grow by 10% every year over nine years, which means that 10,000 multiplied with one plus 10% over nine years, this will give us 23.6 thousand almost. In the end of second year, he invest another $10,000, and this $10,000 will grow over eight years by 10% each year. So we need to multiply 10,000 with one plus 10% over eight years. This will apply for every year. In the end of third year, if you put $10,000, this will grow over seven years and his money will become 19,000 from the amount that he deposit in the end of third year. Let's see the last year example, if he deposits $10,000 in the end of ten years for that year of the money, then he will see the amount will be 10,000 because there will be no interest rate applied in the end of ten years because we're trying to see what will be the total amount in the end of ten years, whatever he deposit, without applying any increase on that amount, you will see that as 10,000. If you sum this up, you will see 159.374 thousand. Instead of his money stay as $100,000, due to the 10% impact over each year, his money will grow to almost $160,000 levels. And as we mentioned, this 10% is just an example. If you want to calculate as investing to a bank which will give you 5% interest rate each year, then this money will be less, but concept is same. That 5% will apply every year to the money that you deposit in the end of that year. Thanks so much. In our next session, we will discover for a company how it looks like from net present value perspective. See you there. 7. Exercise 3: Which Project “Company A” Should Select?: Hello, everyone. Today, we are going to understand which project Company A should invest in. Imagine that company A has two projects in front of them to choose and invest in. We will help them to decide which one is the better option. The first investment option, which is the A, requires initial investment of $9,613 to be put to start or kick off the project. And company A expects to receive $4,000 per year over four years. So they will receive in the end of first year 4,000 in the end of second year, another 4,000 in the end of third year, another 4,000, et cetera. And discount rate for company A assumed as 10%. As you know, this discount rate is calculated to be more accurate as weighted average cost of capital. It depends on the company profile and the existing inflation rates in the country. Investment B requires an initial investment of $10,000 and Company A expects $3,000 to be received over six years. The end of first year, they expect to receive $3,000 in the end of second year, another 3,000, et cetera, and discount rate is 10% because it's the same company. We want to understand which is the better option, and there is a hint that we will also apply in our calculations. The company needs to invest whichever project has the higher net present value. Before any calculation, if you do something from top of your mind, you may say that $4,000 over four years, which is $16,000, initial investment was 9.6 thousand, so a company should make around 6.4 thousand dollar. And this one, 3000/6 years, so $18,000 -10,000, so they should make 8,000. So while you are making 6.4 here, you are making 8,000 here. So a company should invest in Project B. But is this right? Because we are not taking into account that they will receive this amount over a time period. The money that they are going to receive in the end of six year is not worth of 3,000 when you try to look from today's perspective. You need to discount that money over the time period, and you need to see what is the worth of that earning after one year, two year, or six years as of today, and we will calculate our net present value. Let's remember it. What is the net present value? So net present value is the present value of future cash flows minus the initial investment. Actually, nothing is new. We will calculate the future cash flows. What does it work as of today, and we will subtract the initial investment. Don't let this formula complicate the understanding. This is basically your future cash flows divided by one plus discount rate over the year period minus initial investment. This is exactly the same calculation of if you are receiving $100 next year, then you need to divide it by one plus discount rate over one year period, and you will see what is today's value. So from the very simple perspective, if you are asked to invest $100 to a project, as of today, and if I tell you that, you will be paid $105 next year with a discount rate of 5%. Would you invest or not? So what you need to do is you need to see the present value of $105 that you are going to receive in one year. So you need to divide $105, which is future value in the end of one year, divided by one plus discount rate, which was 5% in this example, one plus 5%, and you will see $100 as present value of the money that you're going to receive in one year as $105. If I'm asking you to pay 100 teller to receive something equivalent of 100 taller as of today, then you're making actually nothing. Your 100 teller that you're going to receive minus today investment of 100 Teller will equal to zero. So there is no winning for you in this kind of simple example. But let's see how does it apply for investment A and B? So for investment A, we have a calendar of a 10% discount rate, value of $9,613 should be investment at 0.0 point is today. And company will receive in the end of one year 4,000, in the end of second year, another 4,000, another 4,000, another 4,000 by the fourth year. So now we will go to Excel and we will calculate what is today's value of the money that they are going to receive in the following years? And we will do the same for company B. So let's go to Excel. So this was the option A. We said that company needs to make an investment of $9,613, and they will continue to receive 4,000 over the four year period. So now we need to calculate what is the net present value of this $4,000 that they're going to receive in one year. How we are calculating 4,000, which is the future value divided by one plus discount rate over time period of one year. So now we need to fix the formula and we will see how will be the turnout today's value of that future 4,000. So receiving 4,000 in the end of one year means that receiving three point, $6,000 as of today. If we do the same for second one, which means that you are receiving $4,000 in the end of second year. However, this is equivalent of 3.3 thousand. What we have done here basically is 4000/1 plus interest rate over the time period of two years. So this I copy paste the formula, so it is capturing from the year's value here. So if we continue to do the same, you're seeing $4,000 that you're going to receive in the end of third year equals to $3,000 this year, and the amount that you're going to receive 4,000 in the end of fourth year equals to 2.7. And the initial payment was 9,000. If we bring this as well, you are seeing that the money that you're going to make as net present value is $3,066. Let's see and calculate for the other option. This is the present value of future earnings. Let's do the same for the option B. Present value of the 10,000 initial investment as of today is $10,000. There is no change. So $3,000 that you're going to receive in the end of one year should be divided by one plus interest rate over the time period, which is one. I'm fixing this one, and I will copy paste the formula over the year periods. And if you don't want to do it in the copy paste of formula way, then you can see, for example, 3,000 that you're going to receive in the end of six year, divided by one plus interest or discount rate over the time period of six years, or you can write six basically, so you will see the same amount here. Now, let's sum this up as well, and what is the value that we are seeing is same, actually. There are other ways to do that. There is a net present value function that you can use in Excel directly. Net present value, you will use the interest rate as you can see here Excel suggests, which is 10% in our example. Then starting from the first year over the four year time period, this is the cash flow that you are going to make. You made initial investment of 9.6 thousand, so amount will be this apply the same formula for the option B. Let's do that net present value of 10% discount rate over the cash flow of six years, then you will plus 10,000, which is the initial investment, and you will see that these are almost same values. As we see that, we reach up to net present value, which is $3,066. So now how we will decide. Now we are with presentation again. So you see this calculation on Exle and we reached to the same level of net present value. Now, what's going to happen? Because we are saying that both investment A and investment B is going to give the same amount of money in the end of the year period that the project will pay us. Now, if two projects are giving the same amount of net present value, we need to check IRR. IRR also known as internal return rate. This is the discount rate which makes net present value zero. You can use Exl. We will see the IRR function over there, and let's calculate, but you need to understand the concept fully. If the discount rate is increasing for a company, this means that you need to discount more your future cash flows to see today's value. If discount rate is increasing, the today's value of future payment will be less because you will be discounting it more. It can increase to a certain level, which will make your net present value zero and this known as IRR. Let's go to Exl. So we said that we will try to see what is the IRR for the project A. For IRR, we are putting the IRR function, and we need to put the values that we are expecting from cash flow perspective. The initial payout company needs to invest 9,613 and they will continue to make 4,000 over the years. If you select all of these cash flow for the company over the time period, it will return the IRR for us. Let's do the same for the option B, if you select the initial investment and the future cash flows, you can see that the IRR, which is 20%. This means that if I make the discount rate, 24%. So if I copy this and paste here, which is my discount rate, then I will see this sum should go to around zero. If I paste this, it is value wise, as you can see, my value in terms of the net present goes to zero. The money that I invest in the initial year doesn't change. It is 9,600. In the second year, the money that I make dropped because I increased the discount rate. Or if we do the same and make discount rate 20% for the option B, as you can see, my total amount goes to zero. If the discount rate increases to 20% level, and if I need to discount my future earnings by 20%, the total money that I will make will go to zero. Go back to presentation. As you see over there for investment A, IRR was 24%, which means that if discount rate increases up to 24%, company will make zero net present value. For investment B, it was 20%, which means if this county rate increases to 20%, company will make no value. In this kind of a case, you need to go for the option which has higher internal return rate, which means that it will give you more space, even if this count rate increases to 24% levels due to inflation or company profile or money politics that government decides in terms of the interest rates, et cetera. Even if it increases 24%, I still have room. However, if this count rate increases to 24% for investment B, if it goes to 24% for option B, let's put this as same to this value. You will see that net present value will become negative. If it becomes negative with the discount rate of 24%, and this is zero, then you should go with the option A. So whichever project has higher internal return rate, then you need to go with that option. In this example, we will say that investment A is the better option compared to investment B from net present value and internal return rate perspectives. Thanks so much. See you in the 8. Summary: Everyone. Welcome to our summary session for time value of the money. Time value of the money is a concept states that the money today is worth more than the same amount in future. We gave the example of if I give you $100 today, and if I tell you that I will give you $100 in one year, which one you would select. And most of the people prefer to receive that money today as $100 because money has some earning potential. That $100, if you deposit to bank, maybe it would become $105 in one year. And this change accounts for inflation, opportunity cost, and risks. What are the key components that we have covered? We said that present value is a very important thing to understand what is the current value of the money that you will receive in future. Future value, what is the value of money after growing over time period? If I give you $100 today and you invested in to a bank and grows by 5% every year, then that money will be increasing over the time period. Discount rate, we said that this rate used to calculate the present value of the future cash flow. This reflect risks and opportunity costs. Even we have discovered something called weighted average of cost of capital for companies, and they apply this as discount rate to see what is today's value of the future earnings. We also discovered two key concepts, which is compounding and discounting. If you are calculating the future value of today money, we used compounding because your money will grow or discounting. We use discounting to calculate what is today's value? What is the present value of future received money. If you're going to receive 100 taller next year, we need to discount it. How much does it worth as of today? We also discovered net present value. We said that this is a method to evaluate the investments by subtracting the initial investment from the present value of future cash flows. We also showed the formula and we simplified it with some examples. Net present value formula was the future cash flows divided by one plus discount rate over year of the time. If you are going to receive $200 in the end of two years with a discount rate of 10%, you need to divide it by one plus 10% over two years. And we subtracted the initial investment amount because this is happening today. The net present value equals to the money that you are making as of today. And we said that if net present value is higher than zero, this means that investment is profitable. If net present value is lower than zero, it is not profitable, you shouldn't invest in. Between two projects, if they have same net present value, we said that you need to check something called IRR, which is internal return which is the percentage. If your discount rate increases to that level, your net present value will drop to zero. And we said that always go with the higher IRR option if you have the same net present value between two options because this gives you more flexibility, more room in case of discount rate increases over the time period. This concept will be very helpful in terms of understanding the investment options and their future money that they're going to bring. What is the word as of today, and you should go for it or you shouldn't. Thanks so much for being with me in this class, seeing the next one. Bye.