Please see earlier posts Part I – Why don’t they teach this math in school?

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

**Preamble**

In the last two posts I wrote about how, using the compound interest formula, you can compute precisely how large your money will grow over time, using compound interest. If you assume a particular growth rate (aka yield, or rate of return) and you know how frequently your money compounds (monthly, quarterly, yearly) you can model into the future what your money will become.

This post is about the reverse process, called discounted cash flows, and is – in my humble opinion – the most important piece of math for investing in anything. The discounted cash flows formula is what you need to know in order to decide to invest in something today that will have some future value.

Despite what the Financial Infotainment Industrial Complex wants you to believe about the reasons to buy something, evaluating the true value of an investment depends on you knowing how to discount future cash flows. The rest is just hype, spin, sales and marketing.

And all our yesterdays have lighted fools

The way to dusty death. Out, out, brief candle!

**What about discounted cash flows?**

First, let’s say what the formula is as, again, the Financial Infotainment Industrial Complex does not want you to know this stuff.

The discounted cash flows formula uses the exact same variables as compound interest, but ‘in reverse,’ solving for “Present Value” instead of “Future Value”

Present Value = Future Value/ (1+Yield)^{N}

Where:

Future Value is the known amount coming to you at some point in the future.

Yield is the growth rate of money, also known as the discount rate.

N is the number of times money gets compounded.

Present Value is generally what you’re solving for when you use this formula.

Most importantly when you figure out how to discount cash flows, a whole series of financial and macroeconomic questions become clearer.

**An example of a pension buyout showing the value of discounting cash flows**

The discounted cash flow formula is what you’d need to use, for example, if your company offered you a lump sum buyout instead of a life-time pension, as GM did to many workers in 2012, and as many companies frequently do to get rid of their future pension obligations. Let’s say they offer you a $500,000 buyout. Sounds like a big enough number to induce many people to take a buyout.

Is the lump sum offer a good deal? How would you know?

If you could set up a spreadsheet to discount cash flows, you’d know precisely what kind of deal it is.

You could add up the value of all of your future monthly pension payments, properly discounted by the formula above, and you could compare that to the amount GM’s pension department offered you.

Let’s say you would normally receive a $36,000 per year pension for the rest of your life, and you expect to live for another 20 years, here’s what you would do.

You might want to know the Discount rate, or Yield, on GM bonds to gauge the risk of the future pension, or you might want to just assume the government guarantees your pension, so you’d input a lower yield. Let’s assume low, government guaranteed risk for this example and use a 2% yield to reflect government risk and moderate inflation.[1]

Next year’s payment I’d calculate by the formula Present Value = $36,000 / (1+0.02)^{1}, or $35,294.12

The following year’s pension payment I’d calculate as $36,000/(1+0.02)^{2}, or $34,602.08

I can calculate all of these values easily in a spreadsheet, until I added up the 20th year’s amount, which is calculated as $36,000/(1+0.02)^{20}, or $24,226.97

When I add up all 20 years the result is $588,651.60

Which one is bigger?

Of course you can input different assumptions about your remaining life, and the discount rate, and even the pension amount, but all of this is to show that you need this tool to level the playing field and make good decisions.

I guarantee you that GM’s financial officers know how to discount cash flows, and they’re negotiating from a position of extraordinary advantage against their retired workers who cannot discount cash flows.

So, again, blame the math teachers. And the Financial Infotainment Industrial Complex.

Please see related posts

Part I – Why don’t they teach this in school?,

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part V – Discounted cash flows – example of an annuity

Part VI – Conclusion and why everyone needs to know this math for the good of society

and Video Posts

Video Post: Compound Interest Metaphor – The Rainbow Bridge

Video Post: Time Value of Money Explained

[1] Really you can input whatever assumptions you want to derive a discounted cash flow. Please don’t start a fight with me about whether 2% is the right assumption. I’m just trying to show a math technique, not debate the proper discount rate for GM pensions.

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Tags: compound interest, discounted cash flows, financial infotainment industrial complex, Pension buyout

Hey Mike, Can you recommend something over the internet that I could access that would give me simple, clearly worded instructions as to how to make these and other calculations using my HP12C. When you answer think of person with only the most basic math skills and no more and one who gets more confused, the more words there are (me). I would really like to understand these important computations and am motivated but unfortunately am extremely math challenged and averse. I feel that if I could understand then I could eventually help my family to understand it as they are in the reality of the financial pressure cooker now. Thanks for any effort you may make with me.

Richard,

I would strongly encourage you to do these compound interest and discounted cash flows not on a calculator, but on an Excel spreadsheet. Its so much more powerful and flexible than the old financial calculators. Let me think about your question more and figure out whether I could do a webinar type deal for people who want to learn this stuff.

There are some great tutorials on the web. Here is a shortened URL with search results for ‘HP12C Tutorials’ By the way, once you are familiar with the RPN method of calculating you will most likely never want to go back to conventional calculators. I hope HP brings back their RPN HP17BII as it was in the late 1980′s

http://tinyurl.com/aleo4qo

lump sum from GM today = $500m, ok

v.

PV = FV 36m * 20y/ (1+0.02) raised 20 = $485m

v. your computation of $588m???????

each of the separate $36Ks needs to be calculated and discounted according to the number of years you discount it. You can’t just multiply $36K * 20

& db, i’m using an HP 17B II set to RPN., which is light years ahead of a 12C, which i could never understand why anyone would not have ditched & replaced. if u can explain that riddle…….?

Thanks You make DCF so easy I always thought you need to be genius like warren buffett to understand this but no even a school kid can understand this THANKS

You’re welcome. Glad it was clear enough to get started.

Great example of compounded interest. If I save $1,000 a year for my newborn son for college at a reasonable 5% interest, when he is 18 he will have $29,539. The cost of tuition, room and board at The Ohio State University is $21,000 a year in todays costs. Your equation answers the question on the difficulty saving for college. Throw in four more kids and your screwed.

See? Compound interest is not only good for finances but might serve as birth control as well!

I have read all your comments about DCF and enjoyed them all. I took a finance class and wanted to reconcile what I thought I read with your experience. In the textbook I was taught that if you calculate the sums of all the cash flows after discount, if the sum is greater than zero, it is a good investment. Is this correct or incorrect?

If you sum all of the discounted future cash flows, you know what the ‘present value’ of all those cashflows is, at the assumed discount rate. For example, you could apply a 7% discount rate to some set of future cash flows, and lets say the number adds up to $50,000. With that information you could compare the $50,000 present value with the current cost of that investment. If the investment only costs you $40,000 you could reasonably say the investment is “cheap,” by $10,000. If the investment costs $50,000 then you could say it is fairly valued. If the investment costs you $60,000, then you could reasonably say the investment is too expensive. Again, by how much? $10,000.

An alternative way to use all that same information is to apply a different ‘discount rate,’ a term which could otherwise be understood as ‘yield’ or ‘expected return’ on an investment. If that same investment with the same future cashflows is offered to you at $40,000, an equally reasonable and important use of the discounted cash flow math is to understand that you need a higher % discount rate to make those cash flows equal to $40,000. You may find the right ‘discount rate’ is 7.5% or 8.5% or 9% (rather than 7%) in order for them to all add up to $40,000. (it depends on the specific terms of the cash flows of course.) But in this way you use the math formula to discover that in fact your expected return may be 7.5% or 8.5% or 9% (or whatever). This is how banks, bond investors, insurance companies figure out their expected return on cash flows. It’s also the fundamentally correct way for individual investors to approach stock or bond or business investing, even if few of us bother to do this.

I’ve come to believe that time is the asset I have to build something for my family using compound interest. I see that as the wealth builder I can use in the same way people in my community use the mineral rights on their land to pay royalties to the past and future generations. I’m a little discouraged though knowing that to achieve substantially significant results the compounding time required will be something I’m likely not to live to see.

Chris,

Thanks for reading and commenting. Anyone who can consistently achieve a monthly surplus will have savings. Anyone who has savings can take advantage of compounding. If you have time on your side, even a modest compounding return will start to build significantly. If you don’t have time on your side, even impressive returns won’t be enough to build something big. If you have to theoretically choose between “lots of time” or “high returns,” a good case could be made for ‘lots of time.’ Good luck!