Small-Caps Stagger
...and a discounted cash flow primer, part 1
By Greg Markus
(TMF Boring)
ANN ARBOR, Mich. (July 27, 1998) -- The major market averages staged an afternoon reversal, turning deep Monday morning losses into solid gains for the Dow and S&P 500 and at least a small positive advance for the Nasdaq, which was off as much as 40 points in the early going.
The Boring Portfolio, alas, continued southward Monday, falling 1.23% as six of eight holdings closed lower.
As much as the Borefolio's lackluster performance disappoints me, it's not as if it is without company. The Borefolio has always been heavily oriented toward stocks of small- and mid-capitalization companies, because that is where valuations have been most attractive, for the most part.
Cash flowing into mutual funds has increasingly sought not the best value for money, however, but the places where it can surge in -- and ebb out -- while creating the least disturbance in share prices. In a word, funds prefer liquidity; and that means large-cap stocks, and the larger the better.
Consider that the Russell 2000 index of small-cap stocks has now lost 6.6% of its value in the past seven sessions and is now in minus territory for the year-to-date!
I suppose that the Borefolio could sell off its small-cap holdings, regardless of their attractive valuations, and load up on everybody's nifty fifty... or fifteen, more like it. Changing disciplines in mid-stream can be a dangerous business, though. Chances are that just as the Borefolio tossed in its value orientation and joined the big-cap party, they'd turn off the music and run out of beer.
Ironically, the one really big-cap stock in the Borefolio has been its saving grace this year. I speak, of course, of Cisco Systems (Nasdaq: CSCO). Cisco's stock eased $1/4 today, but it is still only a few dollars back of its recently-established all-time high and up handsomely for the year.
Not surprisingly, at such prices CSCO has attracted a few souls who are pondering whether the share price has gotten a bit ahead of itself. In that regard, in Friday's recap I mentioned that I had executed my own bit of back-of-the-spreadsheet valuing of CSCO and judged it fairly priced: no table-pounding bargain, to be sure, but no screaming short, either.
I pointed out that my valuation focuses on projected future free cash flows, discounted by to present value using a plausible discount rate. Different folks will have different notions of those future cash flows and their own preferred rates of discount. That, as they say, is what makes a market.
In any event, the model I used projected Cisco's free cash flows to increase by 25% per year for the next three years, 20% annually for four years after that, and 8% "forever" thereafter. I considered that to be a reasonable trajectory, although certainly not one beyond argument. I also employed a discount rate of 12.5% -- that is, more or less equivalent to the long-run rate of return for the S&P 500.
That model yielded a "fair value" for CSCO of $103.
In my recap, I offered that I'd say more this week about the mechanics of this approach to valuation -- a method that is second-nature to students of finance (of which I am decidedly not one) and employed by, among others, one reasonably successful investor by the name of Warren Buffett.
Believe it or not, I actually received a few emails over the weekend encouraging me to proceed.
So here goes... and in bite-sized pieces: some today, some tomorrow, the rest later this week.
Question: Suppose you invested $1000 in a "risk-free" bond (say, a note issued by the U.S. government) that paid 6% simple interest when held for one year. How much would you receive at the end of a year?
Answer: $1060, because 6% of $1000 = $60, or $1000 x 1.06 = $1060.
Now let's make it a little more difficult. Suppose you wanted to receive $1000 at the end of one year. How much would you need to invest at that same 6% rate?
To answer this, we need to figure out the present value of the $1000 you'd receive at the end of a year, with a discount rate of 6%. Let V stand for the amount you'd need to invest. Then
V (1 + 6%) = $1000
V = $1000/ (1 + .06)
V = $943.40
Invest $943.40, and at the end of the year collect a thousand bucks.
That's still pretty easy. Let's kick it up a notch.
Suppose you want to invest a sum of money that will provide you (and your heirs) with a $1000 annuity, starting one year from now. That is, you want to receive $1000 a year from now, another $1000 a year after that, another $1000 a year after that, and so on. Forever. Such things are called perpetual annuities.
As before, let's assume a constant 6% annual return on the invested money.
So how much do you need to invest?
We already know that at 6% you'd need to invest $943.40 today in order to get $1000 a year from now. But what about the $1000 you want to receive two years from now?
Well, with an annual interest rate of 6%, the present value of $1000 received two years from now (assuming compound annual interest) is:
V (1+ 6%)(1 + 6%) = $1000
V = $1000/ (1+ .06)**2
V = $1000/ 1.1236
V = $890.00
And for the $1000 you'll want to receive three years from now, you'll need to invest today
V = $1000/ (1 + .06)**3 = $839.62
See how it works? The present value, V, of $1000 received t years from now, at a discount rate of 6%, is
V = $1000/ (1+ .06)**t
Notice that the longer you're willing to wait in order to receive your $1000, the less you need invest today. That's the magic of compound interest. It also means that once we get out fairly far into the future, the present value of $1000 becomes quite small, approaching zero as the time horizon stretches to infinity.
For example, to receive $1000 fifty years from now at 6% annual interest, you'd need only to invest today
V = $1000/ (1 + .06) **50 = $1000/ 18.420 = $54.29
As you move even farther into the future, the net present value of $1000 becomes but a few dollars, and even mere pennies. For example, to provide $1000 for your heirs 100 years from now at a 6% compounded rate of annual interest, you'd need to invest only $2.95 today. And if you stretch it to 120 years, the required investment drops to less than a dollar ($0.92, to be precise).
Back to our annuity problem. To figure out how much you'd need to invest today in order to receive $1000 next year, two years from now, three years from now, and so forth, you could calculate each of the (very large number of) present-value terms and add them all up. Or, you could make use of a neat mathematical rule that states that the value of the sum of all those terms, V*, is equal to:
V* = $1000 / r
where r = the discount rate.
So for your annuity, you'd need to invest up front
V* = $1000 /.06 = $16,666.67
That is, $943.40 + $890.00 + $839.62 + ... + $54.29 + ... + $2.95 + ... = $16,667.67
You don't need to take this on faith if you don't want to. In fact, it would be a great if you didn't. If you're even a little bit handy with a spreadsheet application, it will take you maybe five minutes to compute the values of, say, the first 150 terms of this series and add them all up. If you do that properly, you'll come within a few bucks of $16,667.67. Guaranteed.
(In Excel, use FILL to make a column with values of t running from 1 to 150. Then in the next column use the POWER function to compute successive values of 1.06 to the t-th power; and then in the third column divide $1000 by each of those values. SUM up the 150 resulting values, and you're done.)
Neat. But what does this have to do with arriving at a fair value for Cisco stock?
As it turns out, quite a lot. More about that tomorrow.
Stock Change Bid ANDW --- 17.75 CGO + 3/4 36.50 BGP -1 1/4 32.88 CSL - 11/16 45.63 CSCO - 1/4 97.50 FCH - 13/16 29.06 PNR - 9/16 39.50 TBY - 1/16 8.25 |
Day Month Year History
BORING -1.23% -1.66% 2.55% 29.03%
S&P: +0.57% 1.18% 18.22% 84.56%
NASDAQ: +0.11% 2.03% 23.11% 85.72%
Rec'd # Security In At Now Change
2/28/96 400 Borders Gr 11.26 32.88 192.06%
6/26/96 150 Cisco Syst 35.93 97.50 171.34%
8/13/96 200 Carlisle C 26.32 45.63 73.31%
3/5/97 150 Atlas Air 23.06 36.50 58.29%
4/14/98 100 Pentair 43.74 39.50 -9.70%
5/20/98 400 TCBY Enter 10.05 8.25 -17.87%
11/6/97 200 FelCor Sui 37.59 29.06 -22.69%
1/21/98 200 Andrew Cor 26.09 17.75 -31.97%
Rec'd # Security In At Value Change
6/26/96 150 Cisco Syst 5389.99 14625.00 $9235.01
2/28/96 400 Borders Gr 4502.49 13150.00 $8647.51
8/13/96 200 Carlisle C 5264.99 9125.00 $3860.01
3/5/97 150 Atlas Air 3458.74 5475.00 $2016.26
4/14/98 100 Pentair 4374.25 3950.00 -$424.25
5/20/98 400 TCBY Enter 4018.00 3300.00 -$718.00
1/21/98 200 Andrew Cor 5218.00 3550.00 -$1668.00
11/6/97 200 FelCor Sui 7518.00 5812.50 -$1705.50
CASH $5528.69
TOTAL $64516.19
