My $400,000 Mistake: A Time Value of Money Lecture

Okay, great. Okay, so personal example here. So, some of you know my story, right? I went from being really broke in my early 20s to finally getting my act together, getting to college, getting a good job at Deote, and getting married. And so, when I turned 30, I was planning on my first kid. Uh my daughter, we were planning on having her and I wanted to prepare to have a house for her, right? And I was in a fortunate situation because we worked hard and applied

everything you've learned to date so far. It's a fortunate situation to have a couple hundred,000 saved up for a down payment on a house. And it was a situation that I never thought that I would have been on been in, right? Like being completely broke earlier on. And I felt very blessed to be in that situation. Um, but I wound up making a pretty bad decision in hindsight based on that decision because of some emotional things that happened when I found out that we had a kid on the way. So, first off, we were trying to buy a house. This is early 2020, late 2019.

Does anyone remember what happened in 2020? >> Co. Yeah, exactly. Co. So, my wife and I, we're trying to save up some money for this house. And Bay Area is expensive and single family homes were all a million dollars in the neighborhoods we wanted. So, we decided to go buy a condo instead, a cheap condo and a kind of a worse neighborhood. And the idea was we're never going to be home, right? We're never going to be home. We'll be in this. We'll not stay at the small condo because we'll take the kid out and we'll go to our friends houses all the time. Don't worry about buying that small house, right? Small

condo. We'll be okay because we're never home. Man, we were we were wrong, right? It was it was COVID. We were stuck in a house with an infant and my wife was working in a hospital at the time. So, we're always worried about disease and the small house. And we locked in that decision in December 2020 and we heard about CO in like February 2020. Uh December 2019 and I heard about CO in February 2020. Right. And so just a couple months later, we instantly were like, man, that was no one could have predicted that was going to happen. So it was a pretty bad spot to be in. And then we just happened to have a very energetic kid. So um so the small place

was not working out that well. So there was this having a young kid, I was emotional at the time. I had quit my job at consulting and got a job at Google on the AI deals desk. So I was starting to make some good money. And it was a scary time to be a new dad. And it was a scary time to be in the market and finally have a little bit of money because the market was going up and down a lot, right? And so I was in a fortunate situation that when I joined Google, they gave me some of their stock. And a couple years into it, that stock was worth about $200,000. Again, for me was an unprecedented amount of money. And I

was in a situation where do I pay off the condo? Like should I pay off the condo now? And I decided to sell all that Google stock in the short term to pay off the condo. The condo had a 3% interest rate on it. And that 3% interest rate this so this happened in 2022. We'll show you the math. So how much was my annual interest expense based on this condo? Anybody? 3% times 200,000.

>> There you go. Yep. Right. So I had 6,000 in annual interest expense. I felt so lucky to have this kind of cash. The market was in turmoil. The job was tough. Um layoffs were happening at my company. and I decided I'm going to pay this off and sell my Google stock even though I know I was young. I was still in my early 30s and there was a long time compounding. So like a lot of my friends were like why not hold on to the stock and keep the mortgage. But I had a lot of people who had said if you could pay off your house early, pay off the house early but the interest rates slow.

So it was 6,000. I'm going to show you something and this is depressing for me, but I'm going to show you why this is important for you all to see and everything I'm teaching you actually is relevant and will impact your lives. Let's look at the time horizon. So, these are all real numbers, real story. Um, 2020 Google stock when I sold 2022 was when I sold it. It was about $100 a share. All right. So, I was trying to save $6,000 a year in interest expense. is about a hundred uh dollars a share.

What's the price now of the shares? >> $300. Okay. So, I sold the Google stock to save $6,000 a month. Three years later, it's worth $300 a share. How much would my $200,000 have been worth? >> 600,000. Okay. So, what was my gain on my shares? If I had held the shares, what would have been my gain? Forget about taxes. 600,000US 200,000 is

I'll drop this in a second. Equals 400. Okay. In how many years of interest expense did I save? Three years of interest expense, right? What's 3 * 6? >> 18,000. Okay. This is opportunity cost, right? We've talked about opportunity cost a lot in the class. Wasn't a bad decision. I paid off the house. I was blessed enough to be able to pay off the house. I was very, very thankful. We w up selling the condo because it was too small anyways. And now we rent. We'll talk about the decision later on the rent versus buy and valuation theory. And this would have even been been

better if I didn't decide to buy the place and I decided to invest in the market. And we'll go over why that that was the case as well. But you can see just from this decision alone, I could have made an extra $380,000 in my portfolio. I didn't. And I should have known better. I should have known better at the time, but I was emotional. I had a young kid. It was a tough time in the market. And the same things will happen to you when you ignore the laws that I'm trying to teach you in the class. The laws of finance. All right? So, I'm trying to teach you everything that I'm

relevant. This number is going to get worse every year I do this lecture and it's going to be painful for me to do this, but I'm I'm exposing this so you all can learn how important these techniques are because real wealth isn't earned. Real wealth is accumulated through investments over long time horizons. And that's what I'm going to try to show you and impart on you all today. Again in a corporate finance text this also matters but I'm starting with personal finance so it's relevant to you all. Okay so another good example of this is Birkshshire Haway. So Brookshshire Haway

in 1965 was worth $19, right? This is a bit cherry-picking of an example just to illustrate the point but S&P 500 we could do something similar and it would still have a dramatic outcome. It was worth $19 in 1965. I looked at the share price in 2025 it was approximately a million. Right? So if someone had there was this story I was reading about people who were finding out they had an old stock certificate in their safe from their grandparents who worked there and now they were suddenly millionaires. All right, you would have had to save

$16,667 every single year during that time horizon to make the same amount of money. And it's easy to go well that's Birkshshire Hathaway but it's not just Birkshshire Hathaways. That's the power of compounding of leaving money alone over long time horizons. So, I'm going to show this in a more relatable example to all of you. Who read the book and read about Maya and Jordan? Some of you. Other ones, catch up on your reading. It's important. I think it's it's helpful to understand the context. I'm going to look at Maya and compare them to Jordan to show you the power of time when we're looking at compounding. And I

want you to work along the examples with me. All right? So, Maya is more like me, kind of more my style person. And I know both of them. I'm anonymizing them for you all, but these are real people that I know. Um, she was an early starter. Parents didn't give her anything. At 18, she was kicked out of the house. She got a retail job at like Starbucks or H&M. Can think of one of those places. But she knew this kind of education and she decided she was going to take a piece out of every month of paycheck and contribute to her retirement early on.

At least her parents gave her that advice and she followed it. She does it for eight years. All right? She does it for eight years and then she stops at age 26 because she just gets frustrated. She's like, "All my friends are doing better than me. They're spending on all this fun stuff. I've been hustling all this time. I'm just going to stop." And she leaves it alone until she's 42. Then we're going to talk about Jordan. All right. Jordan, opposite situation. Again, a friend I have, parents gave him money, let him stay home. He was pretty comfortable. Went to a good college. Parents paid for the college. And he

kind of slacked off a bit with his investments. Not too bad. starts at a good age at 26, but he kind of liked living luxuriously. Like I knew him and he was this guy who he moved up to the Bay Area after he graduated college and he wanted to live in a nice apartment in Menllo Park even though it was like 70% of his income cuz he liked it, right? Like it was fun for him. He liked going on big trips. He liked having a nice car and he didn't and he would always tell me like, "Devon, you're stupid for investing. You don't want to don't invest. You got to enjoy your your life." 26, he realizes,

"Hey, I don't have any investments. I should probably catch up. And he's going to invest for 15 years while Maya invests for 8 years. So he's going to invest more for longer. Who do you think will be richer at 42? Anyone have any guesses? >> Maya. >> Maya. But it's counterintuitive, right? So let's prove it out how much richer Maya will be based on this fact, these facts and circumstances. So we're going to take first. Let's do Maya. There

going to be two steps to calculating MA's future value. We're using 10% as the historic market return. We're not going to consider inflation or dividend returns or anything. We're just going to use a 10% historic average. 10 is your IY. You could just put 10. You don't need the percent there. How many years is she investing? >> Eight. And then is she investing all at one time, a lump sum, or is she investing an annuity? >> Annuity. And we're going to assume at the end of every year. So that's called an ordinary annuity. And so ordinary

annuity of what's 470 * 12? Anybody? >> 5,640. >> 5,640. Okay. 5,640. And what are we solving for? Present value or future value? >> Yeah, future value. We want to know how much she's going to be worth if she put $5,640 in every single year at the end of every

year at the end of these uh 8 years. So, how do we do this in our financial calculators? Let's throw it up on the screen. All right. 8 N 10 IY. What do we have? 5,640. We'll make that negative because it's a cash outflow. She's making an investment payment. And then we figure out the future value. We we'll round but what do you all get this calculation? Everyone's be able to do this on their

calculators. If not, raise your hand and we'll go through it again. You need to be following along. >> Yeah, we'll go through it one more time. Again. 8 N that's eight years 10 IY your annualized interest 5,640 negative here that's your payment that's your annuity and then your future value

you just press future value you able to get it this time >> great okay 65,000 is our future value. Okay. 65,000 our future value. We all agreed. So what does that mean at 8 years? From 18 to 26. At 26, how much does she have approximately? >> 65,000. So we can understand why she's frustrated, right? She's been saving money for a while. She's has a good

amount of money. That's still a meaningful amount, but it's not life-changing. So she gives up. But what happens? She leaves that money in this S&P 500 index fund. And how long does she leave it there? Well, she's got we're going to look at that calculation at 42. So what's 42 - 26? How many years does she leave it alone? 42 minus 26 is what? >> 16 years. So we need to go one step

further. n equ= 16. There's no payment now. IY is going to stay the same. What's our present value now? It's our old future value, the 65,000 outflow. And we're going to solve for future value. You all following? >> Y. >> Okay. So, let's do that.

I'll do 65,000 present value 10 IY. How many years? 16 years. That doesn't seem right. 16 years doesn't seem right, guys. You guys give me the right math. 14 years, right? 14 years. Okay. 14 years.

We'll do it again. 14 N 10 IY present value is 65,000. Okay. What's our future value? $246,000. Is am I doing all right now? That's a lot of money to have in your 40s, right? That's not a small in inconsequential amount of money, right?

So, we'll we'll summarize that. Well, let's say it's $250,000. All right, just for rounding. So, Maya has about $250,000 in her 40s. That's pretty that's sitting pretty nice. All right, let's look at Jordan now. Let's catch up with Jordan. So, Jordan starts a little later. Jordan is now, how long is he investing for? 15 years. What's his investment? What's 500 * 12?

500 * 12. Everyone do the math with me. 500 * 12 6,000, right? 6,000. Same yield on your investment, your present value. We don't have any no initial investment future value we're going to calculate. So 15

N 6,000 payment 10 IY did I get the right number? 14N. Sorry. Oh, 15N. 15. Got to make sure I did it right. 15 N 10 IY 6,000 payment. Is that what you all get?

So about 190,000. We'll round it. Who's richer? Maya. >> Maya. Who saved more? Who actually saved more money over the time? Jordan contributed $96,000 over his time horizon. $96,000. Right. How much did Mia contribute? $45,000. Ma contributed less than half of what he did. How long did Jordan do it for? 15 years. Maya did it for eight. Almost half. Who's richer?

>> Maya. Why? Why is Mia richer? her investment compounded more over time. >> Exactly. She started earlier. So, first big takeaway for all of you when you're taking this finance class. Why does this apply to you? Even if you're not in finance, it matters more than probably any of your other classes, right? You if you start now, if you any of you start now, that's going to have a huge financial impact on your later life. All right? So, make sure if you're investing, the earlier you start, the better. She just started earlier. Even though she had less and had less time to

invest, she started earlier. Let's look at what that means for retirement. All right. So Maya ended with 250,000. Let's make that the new present value. And she's in her 40s. What's a good retirement age for Maya? Maybe 62. Is that good? Still still pretty young to retire, right? It's it's not a bad time. So we'll give it her 20 more years for that to compound. She never saves another day in her life. 10 IY. Now my has almost 200 two million bucks,

right? Jordan's going to have less. We all see the power of this. Can everyone do these calculations? >> Just just pay is negative because it's the money you're using to like >> Yeah. So when we're looking at cash flows, outflows are always going to be negative. So if you're taking the money and you're investing it, I know it's complicated because you're investing in yourself. You still own those assets. You can think if you're investing it, that's your outflow. And then when you have access to it, it's your inflow. That's when it's positive.

>> Good question. Any other questions? We're all able to get these numbers. So, we can see just by Maya doing this for 8 years, she sets herself up for a comfortable retirement for the rest of her life, right? So, starting early, if you all could start early, that's going to be have a huge impact to you all. So, Maya contributes half has double the wealth because of the power of N and IY. So any of you while you're going through all of this, think of it through these levers. How long is your biggest lever to

impacting how much wealth a business or how much value a business or a person will accumulate over time? You start earlier and we're going to use some big numbers soon. Start earlier and unfathomable things become imaginable be just by using time. How much is the next piece? higher savings rates earlier and when we're gonna have a bigger impact. If you invest on day one, it's going to have a much bigger impact on your last day, which has no time for compounding. And lastly, we have our

rate of return. And we're going to have a whole class on rate of return and risk and reward and the trade-offs. But for this section, we're just going to talk about 10% average yields because that's a historical return of the marketplace. And then we're going to talk a little bit about inflation today and interest rates just so you have a baseline. But we're going to get more into uh risk and return. But that's less in your control and you have to take on risk to get greater return. So we're going to use some cooler numbers. Now let's imagine you want to retire. How

many people in this class want to retire and have a million bucks in retirement? You'd be like, I'm pretty happy with a million bucks. I'm even happy with a million bucks. A lot of money. Million bucks is a lot of money, right? How about 10? Who wants 10 million? Okay, we got our higher achievers here. You want to What are you doing with the 10 million? Maybe I live in a driving some nice cars or something. Going on first class flights. What about 100 million? Who's who's aiming for the 100 million? Mabula. I like it. Good job. Okay, we got a few hundred million um years. If we look at just what it

would take if you're going to spend 30 years to accumulate this amount of wealth without investing, we can see how challenging this might be. So $33,000 a year. We're assuming that they're just keeping this under the pillow or a checking account. No interest. All right. 33,000 a year savings to get to a million dollars if you don't invest. That's a lot of money. Okay, for anybody that's like your maximum 401k contribution limits beyond that for after tax, that's going to be a good chunk. Even if you're making 100,000 a year, that's really hard to do. You can

see the 10 million becomes nearly impossible. You'd have to save a top 2% top 1% income, all of it, in order to get 10 million, 100 million, three million a year. It's not going to happen through earnings alone. You can't earn your way to $100 million unless you're like Brad Pitt or something, right? You're like some rock star movie star and even them, they're going to really have challenges doing that, right? Um you can through we'll talk about business valuation and business exits.

That's another potential, but that's also just another style of investing that we're going to talk about through this class. But what if we were to try to look at that from a lens of investing? And so this is where the rate of return has a larger impact. If we were to look at it at $33,000 a year, but instead we're going to invest those returns, we can play around with it. So 33,000 payment 30 years. So we're maxing out our 401k or retirement 401k or

retirement accounts. 10IY. If you invest that money instead of having a million at the end, you get 5.5 million. 5.4 4 million in 30 years. Take in mind that's an early retirement. If you start in 25, start your career and can do this, that means at 55 you have you're halfway to a deca millionaire. It's a pretty big deal, right? For a $33,000 investment. I know it seems high, but that's a huge return on your life. You're going to be in the top 1%

of net worth um for people or in the top 5% for families probably. Okay. If you only keep it in a checkings account or a savings account that's getting a 4% return, you'll see a drastically different outcome. Only about 1.85 million. And we'll talk more about risk and reward, but you can see just by escalating our risk in investments can have a huge

disproportionate impact on our future outcomes. Similar to my situation, right? In the last three years, I lost out on almost $400,000 because of this logic, right? I took a 4% return instead of a 10 or 20% annualized return for the risk. Does it make sense? Yes, Jacob. >> When you're at the age of retirement, then sell all this at once when you're ready to retire as you gradually need it. >> Okay. Okay, so question was how what's

the retirement strategy for pulling this money out at that point in time, right? We're going to talk about that. That's coming up on the future slides. So, it's a good question. I'll hold off. But there's a few things we'll consider today. Perpetuity math, annuity math, and sequence of return risk. We're going to try to cover all that today if we have time. It's a good question, so hold on to it. All right. Other ways to do this is that's annuity math. What if we were to do lump sum math? So lump sum time value of money

means we're discounting that future value and instead we're going to find a rich uncle or aunt who's going to give us the gift today or we're going to hustle really hard this year to save up that money and then put that all in our retirement. This is also known as coastfi or coast retirement. You just try to work really hard to get a lump sum into your account and let it grow over time. What does that look like? If I want a million dollars in 30 years, 30 and do this along with me at a 10% return,

we need a $57,000 investment today. All right? So, if you're able to hustle really hard one year, stock away all the money for one year, you never need to save for retirement again if your million-doll retirement is your goal. Right? And again, this is caveed with volatility risk and whatnot, but still, isn't that amazing? That's a huge impact if you're able to hustle and just work really hard for one year and then you don't have to worry about saving for retirement if that's your retirement goal.

Now, let's take this one step further. Here's a game I'd like to play with you all. Who name some billionaires you know personally? No, you don't have to know them personally. If you do, introduce me, but name some billionaires that you just public billionaires that you're aware of. I want to hear a few examples and just shout them out. >> Jensen Wong. >> Jensen Wong. Okay, so that's Nvidia's CEO. Who else? >> Bezos. That's in every class, man. Say Bezos has been the most popular so far.

Who else? I want five. Come on, guys. >> Arnold Schwarzenegger. >> Oh, I wonder is Arnold Schwarzenegger a billionaire? >> Yeah, he is. >> Oh, that's pretty cool. I didn't know that. That's a new one. Thanks for the curve ball. Who else? >> You. >> Elon Musk. All right. And then let's do a fifth one. Who's the fifth famous one? No, we don't know any other billionaires. I'll say Bill Gates or Warren Buffett tend to be the common other ones that come up, right? Bill Gates or Warren Buffett. Do we know a common theme? Do

we have a common theme with all of these people other than them being old white guys? What's a common theme? There's one thing. Let's ignore the gender and the and the race for a minute. What's a common theme there? Age. I think none of them maybe Elon, how old is Elon? Maybe in his late 40s. None of them are young. The billionaires, the people have hundreds of millions of dollars. Most of them accumulate their wealth in their late 40s or post that. Many of them also had

early starts, meaning their family gave them something to start off with. All right? And that's a tough reality, but it's not something that you have to work against. It's something that can work for you by changing out your time horizon, which is tough when you're young. It was tough for me when I was young. Like someone breaks up with you and then your world's over and you're never like I remember never thinking I'm going to find get married after a breakup and then you're only 21. Right? It's like you have your whole life ahead of you. I heard someone else in my other class today being like, "Oh, I had the roughest week ever. My life's over." It's like you're 21. It's okay. There's a lot of life left to live. Your time

horizon. And as you live more life, you're going to realize that time moves faster than you'd expect and that you can tolerate longer durations of time. And you don't have to play the game with just your own retirement. Even though 50 years would all be within your own retirement age. You can play the game multigeneration. Many of the people that I've known su successful very wealthy CEOs and CFOs that I've worked with in my career have trusts either given to them or trusts given to their kids where they're planning out multigeneration. like I'm gonna give a $100,000 gift to

my unborn grandchild that they'll get access to when they're 30 or 40. So they have many many years of compounding to build up that trust so that they're succeeded for their retirement. So you can play these games on I'll fund someone's future retirement, an unborn person's future retirement, and you can imagine how compounding can work in your favor. So I'll use an example here. If you have a goal of hitting $100 million, which is an that's a we can agree that's an obscene amount of money. That's a lot

of money, right? If any of you have that, please talk to me. I need more friends. All right. 10 10 interest. We'll do 50 years. That's $850,000 today. All right. Now, that's still a lot of money, but this becomes manageable. If you think about the retirement games we played, we taught you how to get to 5 million. If you don't need that money in your retirement, you can carve that out, give it to your grandkid, and they, your family now has a chance at

multigenerational wealth. And that's what many people actually do. Benjamin Franklin was famous for this for setting up I think it was the University of Pennsylvania someone can correct me if I'm wrong setting up their entire endowment by doing something like this putting up a small initial endowment and then setting it up that they'd access it after 100 years of compounding and it's become like their largest endowment right the power of compounding is a wonder of the world we could even go further and say what if it was 70 years $und00 million

100,000 bucks. That's a much more manageable amount of money. Do we all see? I know it's hard for you to think out 70 years, but if you have the ability through this class to plan that far ahead, you can start having a drastic impact not just on your life, but the generations of lives that happen after you. Right? And if you don't if you're not thinking about kids, I know I talked about kids. I have a friend who really loves cats. They're a Deca millionaire and they have a trust set up for a cat shelter, an animal shelter. I regularly tell them like, "Hey, you

know, you could maybe we could classify my daughter as a cat or some way that she could get some access to that." But no, but that's all good. You could do it for any type of generosity to set up your future, right? So, so it doesn't have to be just if you want kids or thinking multiple generations, but you could have an impact for many generations if that's the way you're thinking. Now, we're going back to your question over here. So, so my main goal of that was to show you the power of time is can can let all your dreams come true if you just let it. If you just let it, right? All right.

And now, how do you use the money once you want to access it? Again, this is all going to go into business valuation soon, but I'm just doing this because it's a little more relatable for you all to understand time value of money. There's a concept called perpetuity and annuity. What's a perpetuity? Can anyone explain? you're taking out only the interest rate that you gain from your >> Well said. You're only taking out your gains. The idea is that you'd want to be able to do a fixed amount forever.

That's perpetuity. Annuity is you're drawing out and after a certain time horizon, you run out of money. If you're having trouble remembering that, for some of you, those are technical terms. Perpetuity, I like to think of it as perpetuity, I'm leaving something to my kids, right? I'm leaving something for the next generation. annuity. Screw the next generation. I'm It's all for me, right? We're taking all the money for myself. Okay, let's look at how that would be different for different maths. So, something we're going to teach teach about a few times in this class, do perpetuity and

annuity, per and annuity is the 4% rule. Most markets and most history, most market history, if you withdraw 4%, that's known as a safe withdrawal rate from your portfolio, your your principal balance will remain over time horizon. Oh, over any any multiple periods of historical time horizons when you back test. What does that mean? That means and it makes sense like what what's our interest rates today like between 3 and 4%. You could draw 4% forever against an

account and you'll always keep the principal balance. So that's called the rule of 4%. It changes over time, but that that idea here would be if you have 500 $5 million, you have a 4% rate, how much could you pull out? You can pull out 200,000 a year. And so 5 million, you made 4%, you pull out two,000. At the end of the year, you have still have 5 million. You can do that forever. Again, we're ignoring inflation here, but there's some inflation considerations there as well.

Well, what if we didn't want to die with $5 million because you can't take it with you. you want to use it all. We use annuity math. So, let's say someone's 65, they want to live to 95. I know that's dark, but you got to choose your death date to do this stuff, right? So, 5 million present value, we're going to say they're 65, they're going to live till 95. Um, IY is going to say the 10%. And we are going to calculate out now payment. We're going to calculate the

fixed income you can draw down in order to live off of that amount the rest of your life. So again, 5 million is your present value. 10 IY 30N payment. Oh, is that right? Let me do that again. Did I wrong? Seems high. 30 N 10 IY

5 million present value. Okay. 530,000 a year. Okay. So, you get to live a much more luxurious lifestyle over this time horizon. We all got the same number. You get to pull an extra $230,000 a year. At the end of that first year, this goes down. You you Oh, it's because I did a 10% IY. So, we did a higher

return rate here so they can live off more. Let me change this to 4%. So, we're on equal terms. So, you can see. So, we'll assume they'll just do the savings accounts. Generally, Jacob, this goes to your question earlier. Generally, when you hit retirement age, you are going to start diversifying away from high-risisk investments. Again, we'll talk about risk and reward later, like the S&P 500 or stocks. And you're going to go more towards CDs and bonds that are going to give you a steady return, which means your total return is going to drop. And

we'll explain that in sequence of return risk eventually. So 4% here go 30 years 5 million present value that sounds more right 289,000 and 150 bucks. So you get about an extra $90,000 a year

to spend at a 4% return rate. So that that you can see how the return rates have drastic changes on your modeling. What does this mean? At the end of year 1, this would reduce about $89,000 and now you have a smaller base that would grow. Eventually that's going to hit zero by the end of the 30 years. Any questions so far? >> Yes. Um, I'm kind of curious how you got the 200,000 on productivity. So, it's 5 million divided by 4% >> times 4%.

>> Multiply by 4%. >> Got it. >> Any other questions? So, you get a little more this way, but you don't leave anything at the end. All right. Cool. Last major piece to talk through here is inflation. When we're talking through inflation, we haven't built that into our returns right yet. So, we've been talking what's known as nominal returns. Nominal returns means we're not considering inflation. Story I like to say is like my my wife's my

parents-in-law, my family-in-law, my wife's parents, we go to this f place that was around when they first moved here, before my daughter was before before my wife was born, right? So, this is like 40 years ago. The f place used to sell bowls of f for $4. Now their cost $20 for the same bowl of fur. They always complain. They're like, "We'll ne we never understand why you go here. Only a good deal is $4 for the bowl of f." We're like, "Come on, guys. It's that's everything costs $20 now for a bowl of fa, right? Like that's the reasonable price to all of us. $15 to $20. What is that? That's inflation.

They are looking at their money in present value terms back then. We look at our money in present value now. What does that mean? your kids one day or the next generation 30 40 years from now, that bowl of f is probably going to be $50 to $100. It's going to be very hard for us to imagine what that feels like at that point in time until that happens. But for them, it's just going to be the regular amount of money, right? So, how do we adjust for that? Well, what you do is if you take inflation out of our return rates, so when we're using 10%, you take it to 8%,

you reduce it by 2%. Or if you're looking at 4%, you reduce it by 2%. You're going to understand what that would feel like in today's dollars. Okay? That's what doing a real return adjusted real adjusted return is going to show you what that purchasing power will feel like. It's not going to be exact. We have periods where higher inflation and lower inflation. We've been in a period of higher inflation for a while. And certain assets and certain costs change over time. Like housing's inflated more, education's inflated more, food has actually been really low inflation over the last 15, 20 years. So

things change over time, but it's just a general convention we take to make sure that we understand the math that we're using and playing on more fair terms. Does that make sense? Any question on real versus inflation? Inflation versus nominal, real versus nominal. So on a test question, I might ask you what a real return is, but I will always give you the inflation rate if I do that. All right. All right. So this is for all of you personally before we get into more technical topics. Early mistakes cost fortunes. I

hope you learned from my mistake of I should have kept the money in the market even though um it was a good decision to pay off the house. There was much better decisions to make. Time beats effort. So many of you will work the rest of your lives and then wonder why you're not as rich as a friend who didn't. We talked about May and Jordan, right? So if you invest early, that's going to have a disproportionate impact over a long time horizon. If you're making a decision, work backwards on how that's going to impact your life. Like if you're ever thinking of right now, if I was if this was a personal finance class, I'd ask

you all to make a decision on if you invested today versus waited five years to start investing, what would that look like? Start playing with those numbers so you can understand the impact they're going to have on your future. And then that know what your goals are at the end. Like having a perpetuity versus an annuity, figuring out what age you want to retire, figuring out what kind of life you want to live, it's all very important. We baseline that in other classes. And then I have an exercise here. We won't do it here, but it's just a helpful exercise if you want to do it yourself. Now, we're going to go into more technical topics. Is there any questions

on the more soft conceptual topics? In the exam, I'll just be going over present value, future value, annuities. You'll be able to you'll have to do problems like we did on the board on the exam for multiple choice or fill in the blank. All right. Okay. Next, we talked through this. There's a few technical nuances you need to understand as a finance professional. So far, we've only been talking about annuity dues. I mean, ordinary annuities.

I'm going to use an example up here. Okay. Ordinary annuities. We think about it this way. I like these little boxes when we're doing years. One, two, three, four, five years. I'm going to look at investing $30,000 a year. What have we been doing in this class so far? We're taking that 30 and we're saying we're contributing those are looking at them at the end of each year. You

following? When we are saying an ordinary annuity, we're saying it happening at the end of each year. What does that mean for this cash flow? When we're using an ordinary annuity, how many compounding periods does this cash flow get? annual compounding periods. We just count how many? One, two, >> four. That's different, right? Many students mess this up. In ordinary annuity, your first cash flow only gets four years. In a 5year

time horizon, only compounds four times. It's funky, right? That's an ordinary annuity. How many does your last cash flow get? How many does your last cash flow get? >> How many compounding periods? >> Zero. >> Zero. Thank you. Who said zero? Good job. Zero. You get it on the day that you're doing your analysis. This is your

present day. All right. So, you always want to think about in compounding periods. or discounting these flows or or ex or looking at the future value or present value of these flows based off of the amount of time periods left. Okay, that's an ordinary annuity. An annuity do is a little different. Annuity due, see, we assume they're happening at the beginning.

Still five cash flows, right? But they happen in the beginning. How much does cash flow one? How many periods does it get? 1 2 3 4 >> five. >> Five. Which balance will be bigger? Annuity due or ordinary annuity? >> Annuity due. >> Annuity due because you have more compounding periods associated with it. All right. I want you to start thinking in these terms. I use a calculator so you can get comfortable and familiar with the terms. I want you to start thinking of these terms because cash

flows will start to differ in future sections when we talk about capital budgeting where you aren't always going to have annuities. Sometimes you'll have payments that go like 30 10 15 20 and you're going to have to understand the timing of those cash payments. Is it today, at the beginning of the year, or at the end of the year? Also, in other classes, not this class, we don't necessarily compound annually. Like if you're saving for retirement out of your 401k, you're generally going to be doing that each paycheck. That's normally twice a month. So there's ways to compound

within these periods and the periods monthly, weekly, daily, but the general rule is the earlier the compounding happens, the more time or impact you'll have over those periods. All right? There's other concepts of why it might be better to diversify over time which is called dollar cost averaging which we'll go through that eventually but for but we're not going to cover that in this section. All right. So there are some advantages to investing over time rather than

investing at a point in time but they're mainly risk diversification strategies. In the workbook there are the case studies with answer sheets. There are your Google sheet examples. So make sure you use those if you want to learn the Google Sheets or the Excel versions of the spreadsheet functions. So again, we've already talked about this lump sum investing. That's investing at a point in time either in the future, looking at the future and discounting it today or looking at today

and extrapolating into the future. That's called lumpsum investing. And then we can reverse that. We've talked through that. Ordinary annuities looking at a fixed value over time. So making it a fixed payment annually or monthly or whatever it is in this class will always be ordinary annuities annually talking about nudity dues and we've talked about inflation there's two more topics I see you all

this is pretty technical a lot of you are starting to look a little dry on this one I know so I'm not going to go the full section today we'll cover we'll stop by 1:30 uh 11:30 but I have two more important important topics. So please stay with me because these are both impactful to you. First is the concept of interest rates and how they're established. If I had a full day to cover this, I would. I think it's extremely important for you to understand. But when we're looking at rates of return, it's important to understand how interest rates are established. Does anyone here know the governing governing body used to establish interest rates in the US

government? >> Who said it? What is it? >> Federal Reserve. >> Well said. Federal Reserve. The Federal Reserve helps establish interest rates in our country. What are the two mandates of the Federal Reserve? They have two mandates. Does anyone know? It's important. This this dictates the cost of money in your life and dictates inflation. They have two concepts. One is to stabilize

inflation. I believe it's at around a 2% rate. Now, first off, pause there for a second. That's a little weird. We have a government agency that's trying to dictate that things should get more expensive over time economically. Why do we do that? Your economics should have cover this. If not, why do they do that? So, you spend money. They don't want you to accumulate wealth over time. They want you to spend money. It's a consumption-based economy. All right? It's a little funky. So, recognize that's not in your best interest necessarily. The second thing that they

try to do is full employment to minimize unemployment. Now you can look at that as a benefit like yeah of course everyone wants jobs but you can also look at it as the job of this entity is to make human the the people in America as productive as possible. Right? They want to increase the cost of goods. So you have to keep working and they want to keep you working. That might necess not necessarily be aligned with you. You might not want full employment your whole life, right? You might want to get retired eventually. So you need to be aware of this. How do they establish the interest rates that are paid and how do

how does that impact the economic goals that you the government has? Well, there's a few things and it's important to know this because this is how you should establish how we establish the cost of mortgages and loans and everything else in our economy. So, first we have the risk-free rate. This is a concept of what would it be like if I had a rate that I an asset that I could buy that would pay a return that had no risk associated with it. So it'd be like,

hey, I'm going to lend you $100 and I'm going to give a guaranteed return next year. I still have an opportunity cost associated with that return. I could have invested in something else even if there's zero risk. So that opportunity cost is our risk-free rate of return at the most guaranteed rate that we're going to get it back. There's no risk associated with it. So if you think about this in government, that's like government bonds. Even though there's some risk with government bonds, like the US government might default, the US government might get attacked. So there's some risk there. There's other

ways like called tips and other things that have lower risk, but we'll we won't talk about that. So just know that there's a cost of everything even if there's no risk. Then we have an inflation premium. If I lend money to you, I want my opportunity cost, my baseline opportunity cost for no risk. Plus, I want to not lose value of my money over time from inflation. Fair, right? So, that should be my interest. Default risk. There's a risk that you don't pay me. If you have a bad credit score, your interest goes up,

right? That's what it is. If you don't pay me, there's a risk I'm taking on. I should be compensated for that. All of that is helped establish by the Federal Reserve. They help establish those that rate and the Fed rate. Then we add on to it concepts like liquidity risk, my ability to use that capital or to sell that loan, and the maturity risk. If I give you a 30-year loan, it's a long time where interest rates might go down up or down and the market might change, but I

need to be compensated for that that risk. Those five components make up your interest rate. when you're looking at buying a house or buying a mortgage or anything. So, it's important to know these. And so, on the test, I might just ask you what is an interest rate if I give you variables to all of these and I might throw some misnomers on it. Okay? The examples are on your workbooks. But you need to understand as an educated citizen how these are established and how the federal government influences these decisions. Now, why why might the

federal government want higher inflation rates or higher interest rates? If I increase interest, what happens? >> Things get more expensive. >> Things get more expensive. I buy a house, it costs 10% interest, I'm paying a million dollar home, I'm or a million dollar loan, I'm paying $100,000 in interest. Compared to a 3%, I'm only paying $30,000. Right? It's much more expensive. So, what does that do? It slows down consumption, which decreases

inflation. All right? So that's the idea there is like hey when COVID happened what did they do first the economy stopped. So what did they do? They dropped interest rates to next to zero. Why did they do that? So people borrow money and spend money. That was great, right? Like everyone got free money. Well, not so much. Because what happened a year or two afterwards? Hyperinflation. We had a bunch of inflation, right? Why did that inflation happen? Because they dropped the interest rates. They knew that was a

consequence of dropping the interest rates. How did they manage the inflation when it started going when it was up too high? They rose the interest rates. So everything got more expensive. So people bought stuff less. But what happens when they raise the interest rates? What happened to the job market? Jobs go down because companies no longer borrow to hire people. When jobs go down, it infects the prices of things again and they have to change the interest rates. So the interest rates are like a fundamental aspect of the economy and the job market. And so understanding when interest rates are

going up or down and why Trump or the administration is so impactful like so honed in on interest rates all the time is is because it has such an impact on the economy and how our purchasing behavior. All right. I remember co you could get a 0% interest loan for cars. You can't do that anymore. Right? People bought a lot of cars when it was 0% interest. Any question on interest rates? This is a fun little rule. the rule of 72. If you're having trouble with your

financial calculator, if you ever want to figure out how fast money will double, you just take 72 divided by your interest rate and you'll get your doubling rate. So, that's just a helpful hack for whenever you're trying to do your exams or figure out math in your head. Let's see, the last piece I want to talk about is sequence of return risk. Because at this point in time, a lot of you have seen how how powerful compounding is, right? Can we all agree

compounding is a real way to generate wealth other than maybe getting lucky with investments or business assets, right? >> Compounding is that's how most people get really wealthy. All right, but there's a risk there. We've been looking at 10% averages, 10% average returns. We know that the market I'll pull it up. We'll do five years. The market

doesn't just go up. There's lots of down troughs like 6,000 to 10% decreases here. There's there's huge times. And during COVID, what was it? It went was this co here. CO it went down like 50% or 40%, there's huge down troughs. So it's obviously not 10% every any given point in time. 10% is the average historical return. So what happens in real life when you

make investment decisions? Well, this is called your sequence of returns. So, I'm going to look at two people that have average 10% returns that have drastically different outcomes over a three-year time horizon. So, this goes back to your question earlier about how do we manage sequence of return risk or how do we look at retirement? We'll look at give me a boy's name. >> Ryan. >> Ryan and a girl's name.

>> Kelly. >> Okay, cool. Ryan and Kelly, thank you. Both are going to start with $5 million and ret 65. They're retired. They're going to retire for 30 years. Both of them are going to go in the same markets. Kelly's going to start one year later. All right. Plus one year. 20% downturn is the first year. 30% upturn is the next year. 40% downturn is the year after that. All

right. Both of them start with the same amount of money. Ryan's gonna start here. Kelly's going to start here. So Ryan starts in a and this would be this is counterintuitive to most of you. All right. This would be like Ryan is starting here at the top of this little market and Kelly starting at the bottom. When I ask most people when you retire, would you rather be at the top of a market or the bottom of a market?

Most of you going to say top. That's a wrong answer. You don't want to be at the top of the market when you retire. You want to be in a bottom of the market. Most of the time throughout your investing career, you want to be in the bottom of the market. You want the top of the market to be later in your retirement always. So, whenever things are bad right now, that's good for you all because you have a lot of time. Buy things when they're low. buy things when it's bad. I'll give you an example here and you see it all the time. I see it all the time where like people start bragging about I'm retiring

early when the market's at all-time highs. That happened during co a lot. A lot of people did this like I'm retiring early. All those people are back at work. All those people I knew that said that are back at work because they retired when the market was very high and then when the market dropped they got surprised by how little they actually had. So I'll walk through what that means. Ryan starts 5 million. He's at at the top of the market. It goes down. What happens to Ryan's 5 million? What's at the end of the year? Assume he's not taking out any money. How much money does Ryan have?

What's 80% of 4 million? 5 million. You all following along? What is it? >> What? >> Yeah. Four. Ryan lost a million bucks. That's a rough year for Ryan in retirement. Right. Kelly hasn't retired yet, so she still has her 5 million now. The market goes up 30%. How much does Ryan have? Five.

So, he's kind of back where he started. What does Kelly have? Okay, now they have a really bad market. What happens? 40% decline. How much does Ryan have? >> What? >> Louder.

>> Okay, so around three million bucks. That seems right. $2 million decrease. How much does Kelly have? Anybody? >> What? >> 3.9 and not checking the math here. We can see they start with the same thing. If they have a bad year in the first year after the retirement, so they start at the top, they went down. They're going

to be in a much worse position. He's almost a million dollars poorer than Kelly. And not it has nothing to do with his drawout. It's just by the time that he retired. So generally when people ask me about retirement and ages, I tell them like many people are like I want to retire at 65. My advice to them and same thing with businesses is you don't want to retire at 65. You want to hire in your 60s. You want you to sell your business in your 60s or when it's been around for 20 years because you want to

time the market a bit there. If the market's been bad for a while, then maybe it's okay because the market will likely go up over time. If you're in a very hot market and it's been a hot market for three or four years, maybe hold on and make sure or make sure that you do some stress tests. What happens if the market drops 20%. What's that going to happen to your net worth? Right? So, it's counterintuitive, but generally when markets are good, that's the time to work harder. When markets are bad, that's the time that you can actually enjoy that your accumulation. It's counterintuitive, but

that's why I teach this class. If it was intuitive, then you wouldn't need the class, right? Okay. Okay, let's do it one more year so you can see. Let's see. So 30 40 50% gain here. Can someone do it? And then we'll take the average here. We'll see that the average here is a what? 10% annualized probably. 30 that's -10. Yeah. Or 40. So we'll do 40. 40% here. Sorry. We'll do a 40% increase again. What does this get to? What?

What's 1.4* 3.12? Someone give me the math. >> What? 4.368. >> Okay. And then how about this one? 3.9 times 1.4. Anybody make sure you can do the math? >> Does everyone get 5460?

Another important lesson here. It's an elevator down. It's a staircase up. All right. They went 40% down from the 6.5 million. Then he went back the 40%. Right? This is a 10% annualized return annually over the 3 years. I could show you a lot of different 10% annualized returns that have drastically different outcomes depending on what time the declines and inclines happened.

Okay, but you can see they have a million dollar difference from this and then she Kelly doesn't get back up to 6.5 million even though the return stabilized because she had the drop. It's an elevator down a staircase up. All right. So, even though we're talking about annualized returns throughout this class, it's just important to realize that there's a sequence of return risk. So, what's this called? Sequence of return. All right. Can you all remember that? Okay. Let's see.

So, again, with the class, make sure we've already gone through this is a section of clarifying goals. Like we've already talked about where you are now as accounting, understanding your budgeting, your basics, understanding financial statement analysis and ratio analysis. Then we're moving to now to setting goals. And so once you've set your goals using the marks framework, you work backwards after you've chosen your assumptions to make sure that your plan of action is going to meet that goal. And this is a very helpful tool to make sure that you meet the goals in your life. All right.

So are there any questions about the lecture today? This is a lot. I normally would go over workbook problems, but I don't want to kill all your brains after so much math, but any questions about the content today. Was that helpful? Interesting. All right. So, for next class, please work on your workbooks and the case studies. We're going to practice this in detail. It's going to ramp quickly because the next lecture is going to be going over valuation theory, how this applies to stocks, bonds, and businesses. All right. Okay. I

appreciate you all. You all have an excellent day. Thanks for being in class. Bye-bye.