Please see earlier posts Part I – Why don’t they teach this maths 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 maths 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 $35,467.98

The following year’s pension payment I’d calculate as $36,000/(1+0.02)2, or $34,943.82

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 $26,728.94

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 maths teachers. And the Financial Infotainment Industrial Complex.

Please see earlier posts

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

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

And subsequent posts:

Part V – Discounted cash flows – example of an annuity

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

[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 maths technique, not debate the proper discount rate for GM pensions.

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