Learn To Be A Discounting Cashflow Wizard Part 3 – With Book Excerpt


Editor’s Note: This post first appeared in Make Change magazine, an online personal finance site with a social conscience.


I don’t believe it’s an actual conspiracy of silence to keep us in the dark about our finances, but sometimes it feels that way to me. That’s partly why I wrote The Financial Rules For New College Graduates, because I’m convinced that learning how to do some not-too-sophisticated math in a spreadsheet could go a long way toward demystifying finance for the non-finance professional.

The skill of discounting cashflows is the fundamental tool of all investing. It answers important questions like:

You may not want to always do the math on these questions, but if you learn how it works you have a much better shot at pulling back the curtain on supposedly complex financial mysteries.

Watch this first video, for example, to see how we would build a discounting cashflow calculator in a spreadsheet.

Learning the math

It’s not hard, and if you’ve learned compound interest, then it’s kind of a snap. See for example earlier posts on Be a Compound Interest Wizard Part I, and Be a Compound Interest Wizard Part 2.

But it does involve math and poking around with a spreadsheet.

[Begin Book Excerpt]

So what is it?

Discounting cash flows – in the simplest mathematical sense – is just the opposite action to compound interest.

Specifically, the discounting cash flows formula tells us how a certain known amount of money in the future (FV) can be ‘discounted’ back to a certain known amount in the present (FV) through the intervention of an interest rate (Y) and multiple compounding periods (N).

Notice that we use the exact same variables in both formulas. Notice, also, that the only difference mathematically is that we’re solving for a different number.

The discounted cashflow formula simply reverses the algebra of the compound interest formula.

The discounted cashflow formula solves for Present Value, so that:

PV = FV / (1+Y)^N

So why do we care about discounting cashflow?

A simplified example should help to get us started.

A builder’s insurance company offers you a $25,000 lump sum payment to compensate you for the pain and hardship of an injured pet hit by an errant beam that fell from his construction site.

Picture a big piece of wood, it hurt the dog’s paw, the dog will likely make a full recovery, but the developer/builder offered you this settlement to avoid a costly lawsuit with bad public-relations potential.

Importantly, however, the settlement will be paid out 10 years from now. Note, by the way, that this is common practice in injury-settlement cases. Lump sums get offered far into the future. This is partly because such agreements incentivize the victim/beneficiary to comply with the terms of the settlement for the longest period of time. But also importantly, as we will see, it’s much cheaper for the insurance company to make payments deep into the future.

Now, back to the math.

Let’s assume the insurance company is a very safe, stable, company, and we expect moderate inflation, so the proper Y, or discount rate for the next 10 years, is around 3%.

How much is that settlement worth to us today?

Let’s go to the spreadsheet.

We set up our formula in a spreadsheet that the value today, or Present Value (PV) is equal to FV/ (1+Y)^N.

We know the future payout, FV, is $25,000.

We know how many years we have to wait, so N is 10.

We’ve assumed a Y of 3%.

The present value will be equal to $25,000/ (1+3%)^10.

This is easy-peasy math for your spreadsheet, which tells us the present value is $18,602.

What does this mean in practice? We’re not going to ‘invest’ $18,602 in this future $25,000 insurance payout, but it can be very helpful for us to understand that the future $25,000 payment really only costs the insurance company about 75% of what it first appears to cost

By the way, how did I come up with 3%?

Frankly and honestly, I made up the 3% for the example.

I don’t just say ‘I made it up’ to be flippant. I mean to emphasize that ‘I made it up’ because ‘making up’ Y, or the proper yield or discount rate (remember, those mean the same thing!) is a key to effectively using the discounted cash flows formula.

In fact, any time you discount cash flows, you have to “make up,” or assume, a certain Y or discount rate, and the Y assumption you use is as much art as science.

Is that 3% Y I assumed “correct?”

I don’t know, but it’s reasonable, and that’s usually the most we can say about any assumed Y. How do we come up with a reasonable Y number?

Y as an interest rate or discount rate (remember: same thing!) reflects a combination of

  1. a) the market cost of money, which is often called an ‘interest rate,’
  2. b) the expectation of inflation in the future, and
  3. c) the risk of the payment actually being made in the future.

Only some of these things can be known at any time, so only some of our Y is scientifically knowable. The rest has to be assumed according to best estimates. That’s why we can reasonably say that sometimes this Y assumption is as much art as science.

[End book excerpt]

If you want to take it to the next level of how discounting cashflows is used in practice among investment professionals, you could set up your spreadsheet to discount a series of cashflows. Setting up formulas to discount a whole series of cashflows is how we build a model for valuing bonds, for example, or fundamental pricing of stocks.

This video explains the basics for setting up a series of discounting cashflows.

If you decide later become a complete discounting cashflows ninja, you’d then want to layer in one more additional level of complexity, by discounting cashflows that happen more than once a year. A simple video introducing how to deal with that is here:

The last thing I would say about this is that while you don’t have to learn this math in order to manage your money right, I think its useful to know what the Wizards of Wall Street are up to. If you understand their tools, you’re more likely to ask a financial guru a hard question, like:

“Um, why do charge so much, when this doesn’t seem that complex?”


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  1.  Important personal finance PSA: Never Play The Lottery!

Learn To Be a Compound Interest Wizard Part 2 – Including Book Excerpt

The_Financial_Rules_For_New_College_GraduatesEditor’s Note:  A version of this post ran in the finance blog Make Change. Also, embedded in this post is an excerpt from Chapter 4 of my book The Financial Rules For New College Graduates: Invest Before Paying Off Debt And Other Tips Your Professors Didn’t Teach You.


Can I tell you what makes me mad? Finance gurus.

Everybody from Wall Street analysts, to supposed investment-advisory wizards, to pretty talking heads on your TV, sounding smart but spouting nonsense. The Financial-Infotainment-Industrial-Complex is what I call it, and collectively it’s keeping you poor, and charging you too much in fees.

Can I tell you what makes me happy? Teaching compound interest.

wu_tang_financeLearning compound interest math is Kryptonite against finance gurus. Being able to calculate compound interest for oneself exposes the wizards as very ordinary people. As Dorothy, Tin Man, Cowardly Lion, and Scarecrow realized, once you’ve seen there’s no magic trick to growing money, you can get on with it. Learning compound interest math can allow you to be, to paraphrase my favorite Twitter account Wu_Tang_Finance, “A gentleman or lady in the streets, but a freak in the spreadsheets.”

How mad does the Financial Infotainment Industrial Complex make me? Mad enough to spend a few years writing a book to help break through the BS, “The Financial Rules For New College Graduates.” College graduates do not need gurus, they need a few simple rules, and a bit of math so that you can gain intuition into why those rules will work. I mean, you shouldn’t do a lot of math to manage your personal finances, but I see it as a key way of pulling back the curtain on those finance gurus.

So what does learning compound interest math do for you? It tells you:

  • How much a $5,000 IRA invested at age 25 grows to by age 75, if you achieve a 6% return. (Answer: $92,101)
  • How much your rent will cost fifteen years from now, if your rent starts at $1,000 and increases by 10% each year. (Answer: $4,177.25)
  • How much federal government debt will grow to 15 years from now, if it starts at $15 trillion and compound grows by 8% each year. (Answer: $47.5 trillion)
  • How much money your credit card lender can make off of your $7,000 balance, if your bank charges you 22%, you pay only monthly interest, and they continuously reinvest your interest payments every month for 10 years (Answer: $61,929)

You can calculate all this stuff yourself, free yourself of gurus, and build a better relationship to your own money. My frustration with all the other personal finance books I’ve ever read is that they don’t teach this math. They just show a “compound interest” table, or some other impractical nonsense that doesn’t teach people how to do it for themselves. So…are you ready to become a freak in the spreadsheets?

[The following is an excerpt from Chapter 4 of my book]

For best results, I recommend opening a spreadsheet—like right now—for calculating the following algebraic formula.

For a simple demonstration, let’s assume we have three variables, and one unknown variable.

The unknown variable we want to solve for is “how big will our money become at some point in the future?”

Let’s call this variable Future Value, or FV for short.

The three known variables are

  • How much do we have now? Let’s call this Present Value, or PV for short.
  • At what annual % return does our money grow? Let’s call this Annual Yield, or for short.
  • How many years does our money grow? Let’s call this Number of Compounding Periods, or for short.

I’ll skip all the math proofs, but if we know the last three variables, we can calculate the original unknown variable Future Value, FV, through the following formula.

FV = PV * (1+Y)^N


Look at that! That’s it! If you’re comfortable already with algebra, you may be able to begin to work from my explanation above to apply that formula.

But especially if you’re not comfortable, let’s do some examples below that use the variables. Also, I think watching the embedded video above can help you see how you would use a spreadsheet to solve this math.


Let’s say I have 4 feral kittens terrorizing my back yard. And let’s say that on an annual basis, the population of kittens in my backyard grows by 50%. After 10 years, how many kittens will I have?

With that information we can use the compound interest formula to give us a precise answer.

The number of kittens we have today, 4, is the present value (PV).

The growth rate of kittens, 50%, is the Rate of Return, or Yield (Y).

The number of compounding periods in years,10, is our (N).

We plug those three variables into the formula

FV = PV * (1 + Y)^N

to find out the future number of kittens (FV).

Future number of kittens = 4 * (1+0.5)^10

In my spreadsheet I calculate the answer of the future number of kittens (FV) = 230 kittens (plus some fractional amount of kittens, which I interpret as kittens still in utero). Talk about a loud feline ROAWR!

I am so glad I got those backyard kittens fixed.

Inflation over time

Just as our money grows over time, inflation works in a compounding way to erode the value of our currency. We can use the compound interest formula to understand the change in prices due to inflation.

Let’s say we need to know the future price of monthly rent in an apartment in our city, which currently rents for $1,000 per month. Every year the landlord raises the rent by 10%. What will the apartment cost us in the future, say, 15 years from now?

The inflation in our monthly rent can be calculated because we know the present rent (PV) of $1,000, we know the annual growth (Y) of 10%, and we know the number of compounding periods (N) from now that we need to calculate is 15. The future rent (FV) is calculated as PV * (1+Y)^N.

So, the future rent is $1,000 * (1+0.10)^15.

My spreadsheet solves this to tell me my rent in 15 years will be $4,177

Good to know.

[END Book Excerpt]


Finally, setting up a compound interest formula in a spreadsheet works extremely well for calculating how small investments made over time – like in our 20s – can inevitably become large investments in our later years. This second video below shows how it’s relatively easy, once you know how to set up a compound interest calculator, to take charge of planning your own wealthy future.

To really master compound interest, go ahead and purchase my book – hardcover or Kindle! – at your favorite bookstore or your favorite online bookseller.


For more on the magical power of compound interest, search through the search window in the upper right hand of this blog for “compound interest,” or try previous articles on Bankers-Anonymous.com

Also, see earlier introduction to compound interest and discounting cashflows, Part I

and Discounting Like a Wizard, Part 3 (forthcoming)





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Learn To Be A Compounding and Discounting Cashflow Wizard – Including Book Excerpt

Editor’s note: This post first appeared in Make Change magazine, an online personal finance site.
Interest rates don’t seem like a crucial thing to learn about in your 20s or 30s. And learning the seemingly-complicated math of interest rates – specifically compound interest and discounting cashflows – might not seem like an accessible or important skill. Oh…but they are. One reason why I insisted on teaching this math in the early chapters of The Financial Rules For New College Graduates: Invest Before Paying Off Debt And Other Tips Your Professor Didn’t Teach You is that we need to demystify finance. I mean, it’s not a magic trick. Financial professionals are not wizards. They really don’t deserve to be paid as much as we pay them. You can learn this by opening up a spreadsheet and watching a few embedded videos here. With a little effort you should end up knowing it better than 99% of people. Better than most financial professionals, for that matter.

wealth_monorailIt starts with understanding simple interest, and we build from there. You probably know that if you borrow $1,000 from a buddy for a year at 8% that you will have to pay back $1,080 at the end of the year. In that sense, interest on money that you’ve borrowed means you have to work extra hard to earn enough every year to pay off your debts. The higher the interest rate, the harder it becomes. Like owing $1,000 on a credit card charging 22% in interest creates an even harder headwind, costing you something like $220 on the $1,000 debt. That interest rate is like a backwards moving monorail, against which is it hard to get ahead, when you’re in debt.

But interest rates, as I explain in my book, can work in your favor as well:


But here’s an optimistic thought: The monorail also moves the other way. Interest rates on your money—also broadly understood as Yield and Return—can move you forward. When interest rates work in your favor— specifically when you are a lender or an investor— your money today grows into larger amounts in the future without you hardly even trying.

For wealthy people, money they have today for investment simply grows into larger amounts of money tomorrow. They can choose a slow-moving and safe monorail, historically earning 1 to 3% annual return, or they can choose a more volatile but ultimately faster monorail, earning above 5% per year. Done correctly, this wealth-building requires little skill or effort.

I use the monorail metaphor to understand this phenomenon because wealthy people with the right approach to investing cannot prevent themselves from having more money in the future. Just by standing still. Just by doing absolutely nothing. Money just grows on money, pretty much all by itself, if we can get ourselves out of the way and let it.

I hope to inspire you to examine whether the monorail you are currently on— the interest rates that affect you and your money— moves you forward or whether it moves you backward. I hope you embrace the optimistic thought that even if right now you find yourself working twice as hard just to stay in one place on a backward-moving monorail, you can flip that switch. In the future, you could let yourself be propelled forward by the same monorail.


The mathematical power of flipping that switch is captured in the concepts of compound interest and discounting cashflows, which I’ll introduce and explain further in subsequent posts. As a preview though, I think the following two ideas we gain from compound interest and discounting cashflows are worth thinking about:

Compound Interest: If we managed to scrape together a nest egg amount of $5,000 to invest in an IRA at, let’s say, age 25, we could invest that for the long term, let’s say for 40 years until retirement age, at 65. If that $5,000 earned a compound return for 40 years at the reasonable rate of 6%, it would be worth $51,429, rounded to the nearest dollar. If it compounded for 50 years until age 75, at the high (but historically plausible) rate of 10% annually, it would be worth $586,954. That’s potentially life-changing. And it’s not magic or wizardry. It’s math. It’s demonstrable when you learn compound interest math such as in this embedded video:

Discounting Cashflows: If we knew we wanted to have a retirement portfolio of $1,000,000 at age 65, and thought we could achieve a 6% return between now (age 25) and then, this math concept tells us we’d need a nest egg today of $97,222 rounded to the nearest dollar. If we could achieve an 8% return, we’d only need a starting amount of $46,031. That’s a solid but not outrageous amount of money to gather together in one’s 20s. The math required to do that calculation is introduced in this embedded video:

This is really what understanding interest rates, and interest rate math, helps us do.

Please see related posts:

Introduction to Compound Interest with Book Excerpt – part 2

Introduction to Discounting Cashflows with Book Excerpt – part 3 (forthcoming)

And buy my book here: The Financial Rules For New College Graduates

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Discounting Cashflows – A Deeper Dive

Welcome! This post is meant to accompany Chapter 5 and Appendix to Chapter 5 “On Discounting Cashflows” in my book “The Financial Rules For New College Graduates – Invest Before Paying Off Debt And Other Tips Your Professors Did Not Teach You.” (Praeger, April 2018.)

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.




Please see related posts:

On Compound Interest – A Deeper Dive

Book Review: The Intelligent Investor by Benjamin Graham


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