Something about things automotive and financial entices men and women -- OK, especially men -- to pretend to know more than they do. Seldom outright fraud, the human equivalent of this behavior usually takes the form of glossing over details as a given when they aren't.
If this describes your relationship with the math behind present value, don't worry -- the basics of present value, as you're about to see, are embarrassingly simple. No need to pretend anymore, friend. After this series, you'll be able to look at a company's cash flows just like our Motley Fool analysts -- er, at the very least, you'll be able to understand how cash flows form the basis for a company's value and inform your future reading.
Choices, choices
You'd rather have a hundred bucks today than my promise to give you a hundred bones in a year, right? Of course.
But how much more than $100 could I promise to give you in one year to make it hard to decide between that Benjamin now and my promised $100-plus a year later?
If you're an investor, you might intuitively think of the return on dull-but-risk-free U.S. Treasuries as an absolute floor. If Uncle Sam offers 3% a year, a sketchy freelance writer will have to do better than $103 -- a lot better.
Whatever extra return you demand from me over that risk-free rate is termed a risk premium, and is more an estimate than a precise calculation.
So your telephone psychic thinks you'd better demand the 3% Treasury rate plus an extra 10% from me, totaling an unlucky 13%. If you agree with her, the value of $100 to you now and that of my promise of $113 in a year should be pretty similar (i.e., you'd have a hard time deciding between the two).
Now I'm going to go out on a limb and predict that if you're equally happy with a dollar from me now and a promised $113 from me in a year, you'll be similarly content to get a promise from me of $128 in two years. How did I know?
I just took 13% of $113 and added that $15 to (year one's) $113 to get year two's $128. Remember, to you, either promise -- $113 in one year or $128 in two -- is worth the same $100 today: The present value of either is $100.
Multiplication compounds, division "uncompounds"
What if we had to do a lot of these calculations? We'd skip the rigmarole above and just multiply any given year's figure by 1.13 to get the next year's equivalent value.
To get to $128 this way, we could either multiply year one's $113 by 1.13, or we could multiply our original (year zero) $100 by 1.13 times 1.13. Actually, we'd be doing the same thing. So if I wanted to promise you something three years hence that equates to $100 today, I'd have to give you $100 times 1.13^3. See the pattern?
Let's see if you do. And let's depart from this easy-to-work-with $100 figure: After four years, I'll give you a sum equal to $262 times 1.13^4. What's its present value, assuming the same 13% "discount" rate we've been using?
It's $262.
"My kid could do this," you're thinking. I won't argue. But do notice that you divided by 1.13^4, or the intimidating-looking formula (1 plus discount rate)^# of periods, to undo the multiplication.
So what's the present value of a promised $1,000,000 in 60 years if your discount rate is 15%?
Divide your million by 1.15^60 to get $228. In other words, if you're 16 and working a summer job at McDonald's
Multiple cash flows
Now let's say you've won the lottery and will get $1 at the publicity ceremony tomorrow, plus $1,000,000 per year for five years, starting a year from now. In present-value terms, the $1 is worth its full value, but everything else, less.
Since it wasn't the Washington, D.C., lottery, we can reduce the risk premium and use a conservative 6% discount rate this time on account of municipal reliability. Divide the first million by 1.06^1 to get $943,396. Divide the second by 1.06^2 to get $889,996, and so forth, noticing that you'd require more and more in the future to "equal" $1,000,000 now, but since you're not getting any extra, that same amount is "equaling" less and less now the further into the future it's promised. For closure, $5 million over five years has a total present value of $4,212,364 at a 6% discount rate. Oh, add your buck, too.
The mighty, yet fickle, discount rate
Up until now, I've ducked and dodged the topic of discount rates. Surely, investment professionals -- people who know what they're doing -- must have some obtusely brilliant way of divining actual discount rates, not the sloppy estimates we're spitting out.
Well, they don't, but they try.
First, though, pretend you've got an imaginary financial instrument similar in all respects to U.S. Treasuries. A discount rate already exits -- the yield on a comparable-term Treasury.
In reality, comparisons are not straightforward, so the financial community turns either to straight approximations like we've used (8% to 16% is a common range for U.S. equities) or to more "precise" methods like the famous capital asset pricing model (CAPM).
Leapfrogging its complexities and criticisms, I'll tell you that CAPM basically derives a stock's above-Treasuries risk premium (remember the extra 10% from me the psychic wanted?) by first estimating a general risk premium for the S&P 500 (5.5% or 6% above Treasuries is typical), then multiplying that "market" risk premium by a given stock's "beta," a number you can get from financial websites like Yahoo!
To understand beta, think of fashion. The "norm" -- what the masses are wearing, and comparable to the S&P 500 financially -- in any given trend has a beta of one by definition. Those taking trends to the extreme have fashion betas above one (two or higher is possible), while trend-opposite rebellious teenagers and oblivious retirees would have negative fashion betas. People like me, whose insipid wardrobes show minimal awareness of trends, have fashion betas near zero.
Beta's contribution is measuring the additional "risk" (really just historical volatility) -- or the diversification benefit -- of adding a stock to your market-resembling diversified portfolio. Held alone, a low-beta stock may be risky, but its addition to your portfolio should reduce your overall volatility -- the volatility you're concerned about. Still, beta's not without its faults, an obvious one being that the future might differ from the past.
The moral of the story here isn't that the financial community is misguided in its discount rate approximations. The moral is that discount rates are approximations, and one would be misguided to assume otherwise.
And one last thing about discount rates -- present value models are very sensitive to changes in them, especially over long time periods. Remember our 16-year-old burger flipper? If he earns 10% returns instead of 15%, his $228 will be $69,453 in 60 years instead of $1,000,000. Still not bad, but what a difference!
All dressed up and nowhere to go... for now.
Sure, it's nice to be familiar with the foundation of finance for its own sake, but we'll have to wait till next time to work on finding the next Starbucks
Fool contributor James Early is a former Cadillac mechanic and hedge fund analyst. While he won't disclose his own pretensions, he will disclose that he owns none of the stocks mentioned in this article. The Fool has a disclosure policy.
