 Hello and welcome to the session. This is Professor Farhad in which we would look at the topic of inflation and real interest rate. Those topics are covered on the CPA as well as the CFA exam and in essentials or principles of investment, graduate or undergraduate. As always, I'm going to remind you to connect with me on LinkedIn if you haven't done so. YouTube where you would need to subscribe. I have 1,700 plus accounting, auditing, tax, finance, as well as Excel tutorial. If you like my lectures, please like them, share them, put them in playlists. If they benefit you, it means they might benefit other people. Connect with me on Instagram. On my website, farhadlectures.com, you will find additional resources to complement and supplement your accounting, your finance courses, as well as this course. So let's assume you have $100 today and the bank is offering you a 10% return on it. So if you deposit this money, a year from now, you will earn 10%. So simply put, a year from now, you're going to get your $100 plus $10. That's your rate of return, 10%. It's going to give you $110. Let's also assume today, this basket of food, it will cost you to buy it $100. This is what you will need for your food, milk, meat, eggs, banana, fruit, vegetables, all sorts of things. A year from now to buy the same exact food basket, it will cost you $106. So what really happened? Here's what happened. You deposited this money in your bank account, this $100 that you had today. You could have bought the basket of fruit or the basket of food. And a year later, you got $110. Here's what happened. This $110, now to buy this basket of food, you will need $106. What does that mean? It means you lost some of your purchasing power. Why? Because the same basket of food that used to cost you $100. Now it's costing you $106. What does that mean? It means your purchasing power went down, although it's the same basket, but you have to pay more for it. How much more? $6 more. And in the bank account, you only earned an additional $10. What does that mean? That means you earned $10. Of that $10, $6 went to inflation, Arap would inflation. What's left is $4. So the $4 is your real interest rate. So here we're going to call the $10, the $6, and the $4 something, they have specific names. And simply put, to approximate the inflation, you can take the real rate. It's approximately equal to the nominal rate minus inflation. Well, we did not define those. Let's define them in a moment. So what is the nominal rate? The nominal rate is what the bank gave you. The nominal rate, for our example, is 10%. The interest rate in term of the nominal, not adjusting for purchasing power. For our example, was 10%. The real interest rate, the growth rate of purchasing power derived from the investment. Well, although you earned $10, $6 was eating by inflation because the basket of fruit went up by $6, 6%. What's left is 4% or $4. What is the inflation rate? The rate at which prices are rising measure as the rate of increase of the CPI, Consumer Price Index. Usually it's a basket of food. And for our purposes, CPI went up 6%. So you have to know the nominal rate, 10%. Real rate is 4 and inflation rate is 6. And let's go back to this formula. So if we take the nominal rate minus the inflation will give us approximately, this is a dirty and quick shortcut to find the real rate, 4%. But this is not the real formula. We're going to look at the real formula in a moment. It's just, it's a dirty, quick and dirty shortcut. Okay, part of your interest earning, which is the $10 had been offset by the reduction in the purchasing power of the dollar you would receive at the end of the year. And this is what happened with the 10% rate. We net out only 6 after you net out the 6% reduction. What's left is 4%. So basically this is the real rate. So your purchasing power increase in proportion to the growth of invested fund, but falls with the growth of prices. So that's fine. Your rate, your purchasing power increase with the growth rate, the 10%, but as the prices of the goods rises, your purchasing power falls down. So when you earn 10% or $10 from your bank deposit, but the food basket increased by $6, the number of items you can buy increased by a multiplication of 1 plus the nominal rate divided by 1 plus the nominal rate. So simply put, if we take 1.031 minus 1, so really the real rate is approximately not 4, not approximately, it's 3.8. So there's a formula to compute the real rate. So to compute the real rate, we're going to take the nominal rate, which happens to be 10% minus 6%, the inflation rate we set 6%, 1 plus 0.6, the inflation rate. And by doing so, we can find basically what it boils down to, basically to find the real rate, this is one way to do it, the nominal minus the inflation, which is 0.04 divided by 1.06. Let's get the calculator and find the formula, 0.04 divided by 1.06. And that's going to give us 3.78 rounding. It's going to give us 3.8 rounding, 3.8%, which is what we thought it was when we said, so that's 10 minus 6, it's 4, that was the approximate rate, but the real rate is 3.8. So this is the formula. So let's assume if the interest rate on a year CD is 8%, this is the nominal and you expect inflation to be 5% in the coming year. How do you compute the real rate? Well, I'm going to take the nominal rate 0.05, subtract inflation 0.08 minus 0.05, then divide this by 1 plus the inflation 0.05. So if I compute this formula, I should come up with 2.86%. Now on the exam, 8 minus 5, it should be around 3%. So 2.86 is close to 2.3%, is approximately close to 2.86. So if you have to approximate, at least you should know, it's a little bit less than 3%. Okay, so this is the answer. Irvin Fischer is an economist. Irvin Fischer argued that the nominal rate ought to increase 1.41 with the increase in inflation. Such an increase would be needed to preserve the investor's real rate of return. So what does that mean? It means the nominal rate should increase in parallel with inflation. If inflation goes up, your nominal rate goes up. So using expected inflation to donate the current expected inflation over the coming period, the Fischer, basically the Fischer formula is the nominal rate should equal to the real rate plus some rate of inflation. So suppose the real rate of interest rate is 2% and the expected inflation rate is 4%, the nominal rate is 6%. This is basically the Fischer formula. So if the expected inflation rises to 5, if this becomes 5, now you need to quote me 7%. So the nominal rate should approximately be 7%. So the increase in the nominal rate offsets the increase in the expected inflation, given the investor an unchanged growth rate of purchasing power of 2%. So you still maintain your 2% purchasing power as long as inflation goes up, the bank will give you more money and the nominal rate will go up as well. Suppose the real interest rate is 3% per year and the expected inflation is 8%. Can you find the nominal rate? Now we know the real rate. So basically the formula is real equal to nominal minus inflation divided by 1 plus inflation. So let's fill in the formula 3%, this is the rate 3% equal to n is the nominal, which is we don't know minus 0.08 divided by 1 plus 0.08. Now if we cross multiply and find n, we'll find out that the nominal rate 11.24. Now again, 3 plus 8 equal to 11, it should be approximately 11, 11.24, this sounds right. Suppose the inflation rate rises to 10%, but the real rate unchanged, what should be the nominal rate? Basically change the 8 to 0.1 and what you will find out, this should go up, it should go up to 13.3%. Again, 10 plus 3, so 10 plus 3 equal to 13, it should be approximately 13, 13.3%. Now in the US, what is the closest thing to measuring inflation? Basically, one month T-bill, one month T-bill government, is close, it works in tandem close enough to inflation. For example, from 1926 to 1951, the average annual rate of return on the T-bill, which is one month treasury bill, if you lend your money to the government, was 1.04, inflation was 1.68. So simply put, the real T-bill, it was giving you a negative return. So if you put your money with the government, what's happening is the inflation is eaten up your return. Between 1952 to 2016, the T-bill earning on average 4.38 and inflation is 3.51. So here the T-bill is covering your inflation and giving you a real rate of less than 1%. This is all on average. And if we see from this graph, interest rate and inflation, T-bills and inflation, T-bills and inflation, you will see that they work hand in hand. Now here we have the depression, obviously they did not work hand in hand. And here we have World War II. Also it's a special time. Otherwise, they go notice hand in hand together. So T-bill is close enough to inflation. That's the point. Now why is this important? We'll see later on that the T-bill is going to represent for us a risk-free measure. Risk-free measure. We'll talk about this in the next, well, starting in the next few sessions. But it's very important to know how the T-bill and inflation rate works hand in hand. In the next session, we're going to start an important topic and that's risk and risk premium. How to measure risk and how to measure risk premium. As always, I'm going to remind you to like my recording, share it, put it in playlist. And I am going to ask you to visit my website forhatlectures.com to compliment to compliment and supplement your accounting and finance education. Study hard and stay safe.