I’m convinced the only way to really learn discounting cashflows math is to practice with a spreadsheet. The only way to gain intuition about how this math is used in the real world – how it can help you build wealth – is through a bit of spreadsheet practice.
In this first video I show how to build a simple calculator for determining the present value of future cashflows. This is the fundamental math used in investing in assets such as stocks and bonds. It’s also how we would value everything from annuity payments to pension payments to public liabilities.
In this second video, I show how to discount more than one cashflow. The key point is that each separate future cashflow needs it own discounting formula.
The next video shows how to discount cashflows using other-than-annual discounting rates. This is relevant because in the real world cashflows don’t just come once a year. They could be semi-annual (like a bond) or quarterly (like a stock) or monthly (like debt payments). We need to adjust our calculation by adding one extra variable – the number of compounding periods per year – as I show in this third video.
Learning how to discount cashflows can get more complex from here, especially for finance professionals, but the basic math shown here is both within the grasp of non-finance professionals as well as applicable to many important personal finance situations.
I highly recommend you open up a spreadsheet alongside this material.
For starters, we want to know how to set up a spreadsheet to calculate Future Value, if we already know Present Value, Yield, and Time.
This first video below can get you started on that journey.
COMPOUNDING MULTIPLE AMOUNTS OR WITH MULTIPLE YIELD ASSUMPTIONS
The next video adds a level of complexity. Let’s say we want to see multiple years’ worth of compounding returns. For example, we might want to contribute to a retirement account multiple years in a row, and see the results of that activity over time. Spreadsheets are ideally suited for this type of setup, as the next video shows:
The third compound interest video introduces the idea that in the real world, money can compound more frequently than annually. Bonds often compound semi-annually. Stock returns often compound quarterly (because dividends are paid quarterly.) Monthly-pay debts we owe to our mortgage company, credit card company, or auto-loan company compound 12 times a year. We need to add an additional step for compounding more frequently than once a year.
Please see related posts on Discounting Cashflows and Compound Interest:
Like many, I see education from a combination of angles. Unquestionably, education makes us broader thinkers and more sparkling conversationalists. Education makes us more actualized humans. But as a finance guy, a small evil part of me always applies the $64,000 Wall Street question to every activity – from brushing my teeth to tossing a ball with a (in my case, non-existent) dog. 1
It’s the bottom-line question: “How is this making me money, like, right now?” 2
One of the problems of education, generally, is that we have a hard time proving or quantifying its value. What is the value of holding your shoulders back and head high when you walk into a job interview, knowing you’re the best they’re going to interview that week? Or the value of the feeling, when given a work assignment, of “Boom! I got this!”
Philosophically, how can you put a value on just knowing more stuff?
The weird thing about my friend Michael Girdley – who started the computer coding school Codeup – is that he’s ambitious enough to say that the education community tradition of waving a hand at hard-to-measure fuzzy feelings is not good enough. Just because the education community finds it difficult to measure value doesn’t mean business people shouldn’t try to.
In less than two years he’s established a pattern of tracking the data on the most important finance question of education.
By that, I mean the bottom-line question: How is this making me money, like, right now?
Girdley shared with me the pre-Codeup and post-Codeup earnings of his students, along with some useful stats on entry-level and mid-career web developer salaries. Using a couple of his statistics I want to take a stab at figuring out the total value, right now, of a student’s investment in Codeup.
Statistic #1: The average Codeup graduate saw her annual salary jump $13,035 in the year after graduation from the program.
What does that really mean? What can you do with that number if you plan, say, 30 working years at this higher salary?
It would be great to say that a Codeup education is worth 30 times $13,035, or $391,050. However, money in the future is not as valuable to me as money today, so that calculation is not quite accurate.
With a salary jumped up by just $13,035, we can figure out what that amount is worth today by using a discounted cashflow formula. So let’s be sophisticated and apply our discounted cashflow formula to 30 years’ earnings, elevated by $13,035.
I have to assume a ‘discount rate’ which is some combination of taking into account inflation and future investment risks. I’m going to assume a 5% discount rate. 3
Using my 5% discount rate, I estimate the value today of my elevated salary to be $200,379.90. That’s the sum of 30 years’ worth of $13,035, but ‘discounted,’ or translated back, into today’s dollars.
That discounting allows us to more accurately compare the $16,000 tuition for Codeup with the total financial value, today, of that education.
By that measure, you pay Codeup $16K today for something worth on average, $200K, today. 4 Another way of saying that is that you are buying something today worth 12.5X that amount. Stated that way, Codeup sounds like pretty good deal.
Statistic #2 – The average web developer, nationally, earns $91,750. That’s $61,525 more than the average pre-Codeup salary of surveyed Codeup students
So that’s interesting.
We can imagine a number of reasons for that difference that don’t have to do with the value of Codeup. Maybe the average web developer is older and more experienced on the job than the average pre-Codeup student. Maybe national salaries are higher than San Antonio salaries, on average. I mean, I’m sure they are.
But still. If one of your goals is to swim in a higher-paid talent pool, it might pay to learn the butterfly stroke.
How much would 15 peak years of earning $61,525 more than you earn now be worth, like, right now?
Again, I don’t think it’s as high as 15 times $61,525, or $922,875, because of the whole discounted cashflow thing about money in the future not being worth as much as money today. Also, to be fair, you probably won’t earn the average national salary until you had a few years to ramp up your career.
But what about discounting 15 years of an additional $61,525 per year, at a 5% rate, starting 5 years from now, using the exact same formula that we used before? 5
Discounting those 15 years of earning the average industry salary gives me a value, today, of $500,366.44. Which, to state the obvious, is 31X the price of tuition. With those kind of numbers I start to feel like that salesguy from Entourage: “What if I was to tell you that you’d pay $16,000 tuition to Codeup for something worth $500K today. Is that something you might be interested in?”
Look, seriously, there’s a lot of assumptions embedded in my statement that you could pay $16K in tuition today for future salary jumps worth $500K, today. Most important of these is the assumption that by training as a programmer you can earn the national average salary for programming jobs. And we all know there’s no guarantee that happens.
But – and this is a big but 6 – it’s not a crazy assumption.
Because, really, it’s an assumption that the average happens. It’s an assumption that you could be paid what other people in your industry are generally paid. It’s an assumption that markets are somewhat efficient. It’s an assumption that if you have valuable skills you can find employers and work situations just like other people.
All of which makes me pretty confident that the financial return on a skills upgrade like Codeup can be somewhere between 12 and 31 times the upfront tuition cost.
Back to the value of an education
As I said before, education leads to more sparkling conversations as well as to living a more fully actualized life. Of that, I have no doubt. But I appreciate my friend Girdley’s business-like approach to showing that the value of his program can be somewhere between a 12 and 31 times multiple of your investment.
Just thinking like a finance guy, is that something you might be interested in?
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Notice I haven’t gotten a dog because – I ask you – where’s the profit in that? ↩
I’m still working on monetizing my teeth-brushing. Actually, a friend of mine recently posted that in today’s ‘sharing economy’ of AirBnB and Uber he wants to make his toothbrush available, when he’s not using it. Like, $5 for every two uses, for example. He’s quickly on his way to a Billion dollar valuation, Unicorn-style. ↩
How did I come up with 5%? Sorta kinda I used art in addition to science. You could call inflation 2%, so that’s a baseline for discounting the value of money in the future. Then there’s the future risk of actually earning the elevated salary, which after all is a big assumption, and also an average, and as we always say in finance ‘results may vary, past performance is no predictor of future results, etc,’ so there’s a few % points added to the inflation rate to account for that kind of risk. If you don’t like my 5% assumption, make your own, I can’t promise you I’m “right” about a 5% discount rate. You might be just as right with a different assumption. Also, remember the faux philosopher and native San Antonian Jack Handey is a good guide to these disagreements: “Instead of having ‘answers’ on a math test, they should just call them ‘impressions,’ and if you got a different ‘impression,’ so what, can’t we all be brothers?” ↩
In addition to the $16K tuition of course you have to do a lot of work to not only learn to code, but also, you know, earn a salary in the future. So there’s still that whole ‘work’ problem. But if you have to work, it’s nice for the finance part to at least make sense, no? ↩
Why did I choose 15 years and not 30 this time? Mostly because I don’t think it’s fair to assume a Codeup graduate’s salary jumps immediately to the average national salary. You work up to that. For that same reason, I calculated the value with a 5 year delay, to account for a slow ramp up. Again, Jack Handey comes to mind: “If you ever teach a yodeling class, probably the hardest thing is to keep the students from just trying to yodel right off. You see, we build to that.” ↩
I’m finishing up teaching an undergraduate course on Personal Finance this month, for which I find the assigned textbook totally useless, so I am on a quest to come up with a useful book to recommend for students as well as Bankers Anonymous readers.
The most impressive strength of Master Math: Business and Personal Finance Math by Mary Hansen is that it cuts out all the (mostly) banal ‘advice’ of a personal finance book, and concentrates instead on how to do the calculations. The math level never rises beyond algebra, which frankly is all anyone needs to know, in order to competently manage their personal or small business finances.
I find this a useful guide for a ‘Do-It-Yourselfer,’ or a person intent on learning exactly how car loan companies calculate APR vs. APY, or insurance companies quote term life insurance. A CFO for a small business or non-profit would also likely benefit from this useful introductory reference.
I’ve frequently paid but never personally calculated FICA taxes, for example, and it’s somewhat satisfying to learn how straightforward the math is. I have personally prepared business balance sheets and budgets, debt to equity ratios, and tracked profitability, but the straightforward presentation would be useful to others who have not done so before, but who need to learn.
Missing from Master Math, however, is my personal pet project: Understanding discounted cashflows and compound interest – the keys to good personal finance decisions. While the author presents a ‘compound interest’ table and defines the term (in contradistinction to simple interest), a table does not really cut it.
The limitations of print media for personal finance math
Reading the book this week has inspired a new thought, however, of which I’m increasingly convinced.
Personal finance and small business math, while not complicated, requires fluency with a spreadsheet program like Excel.
Master Math offers good, but somewhat convoluted algebraic formulas to calculate answers. In print, the author cannot show the dynamic changes in personal finance outcomes from changes in variables.
Properly set up in a spreadsheet like Excel, by contrast, a change in loan interest rate, for example, alters every monthly payment as well as the total cost of a loan. A small change in automatic monthly withholding, for example, changes everything when it comes to long-term retirement savings. Only by seeing the dynamic effects, I think, can we understand what control we can have over personal financial decisions and outcomes.
What is the right media?
I know Khan Academy has changed everything when it comes to math pedagogy. Although I enjoyed Master Math, I’m also sure personal and small business math has to be taught, and learned, through a combination of video, practice problem sets, and acquired fluency with Excel. Static text on a page isn’t enough.
This is something I’d like to work on over the next few years.