Much of the analysis here uses the Capital Asset Pricing Model (CAPM)
and the Constant Growth Model (CGM) for cost of equity and stock
pricing. There are important limits to each ? and that, of course, is
the object of this question.
First let?s list all of the numbers that go into these calculations:
RISK-FREE RATE (Krf) = 4.24% on a 10-year T-bill
MARKET RISK PREMIUM (Km) = 7.5% (assumed)
IBM beta (?) = 1.64 (60-month)
IBM current dividend = $0.80
IBM 3-year dividend growth rate = 8.2%
Industry P/E = 23.2
IBM EPS = $4.87
The CAPM model says that the return to investors (and to the
corporation, Ks) has to be equal to:
? the risk-free rate
? PLUS a premium for stocks as a whole that is higher than the
risk-free rate. This market return premium is (Km ? Krf)
? And the market return should be multiplied by the risk factor for
the individual company, termed the ?beta of the corporation? (ßc)
Expressed as a formula, it?s:
Ks = Krf + ßc(Km - Krf)
Ks is the company's expected return on capital
Krf is the risk-free return rate, usually a long-term U.S. Treasury bill rate
Km is the expected return on the entire market of all investments.
Most measures use a common broad index, most often the S&P500 over the
past 5 or 10 years
ßc is the company's Beta, based on its covariance with the market.
IBM Ks = 4.24% + 1.64 * (7.5% ? 4.24%) = 4.24% + 5.35% = 9.59%
CONSTANT GROWTH MODEL
Also called the Dividend Valuation Model, this allows an investor to
calculate a value based on returns to the investor. It assumes that
dividends represent cash flows ? something that?s not always true (and
this problem will illustrate just that when we get to answering
The general model for stock pricing is. You don?t have worry about
which period (i) is being used, as we?ll use today?s price and today?s
dividends (it also can be used to figure a price a year from now or 5
years from now):
Pi = Di / (Ks - g)
Pi = price in period i
Di = dividends in period i
Ks = required rate of return (in decimals)
g = dividend growth rate (in decimals)
i = period, usually expressed in years
P = $0.80 / (0.0959 ? 0.082) = $0.80 / 0.0139 = $57.55
IBM?s current stock price, according to BigCharts.com, is $83.08, up
$1.88 or 2.3% by mid-day on Friday, August 19, 2005 (the DJIA is up
strongly this morning too) ?
?IBM Stock Price?
WHAT FACTORS MIGHT BE AT WORK in the difference in stock prices of
more than $25? Just about everything in your calculations can be a
factor. For example, if g (dividend growth rate) matched the IBM
5-year growth number, it could justify a stock price of $421. But
let?s deal with the most-important factors:
-- CASH FLOW: dividends indicate what?s coming back to the investor.
But in a growing corporation, managers are wise to re-invest earnings
back into new business opportunities rather than create taxable
dividends for investors. The result is higher stock valuation ? and
investors can defer taxes on those earnings.
One way to look at what?s ?really? coming back in earnings is to look
at earnings per share. Yet when you look at how analysis is done by
Wall Street analysts, they?ll go back even deeper, looking at EBIT
(earnings before interest + taxes) or even more likely EBITDA
(pronounced EBIT-DUH but representing earnings before
interest/taxes/depreciation & amortization):
?How Much is that Dotcom?? (Bacani & Shameen)
For IBM, you?ll see that earnings in the past year were $7.583 billion
? but that the company added $12.314 billion to its cash position. In
other words, there was an additional $5 billion ABOVE earnings being
generated in cash ? much more than the $1.36 billion that IBM paid its
shareholders in dividends. So, IBM could grow its dividends much
faster without even reducing its cash position.
Note, too, that the numbers we?re using from this PDF file are for
FY2003 and IBM?s in the middle of FY2005 (so complete FY2004 data
could or should be used here).
-- WHAT BUSINESS IS THIS? One of the challenges in valuation is to
estimate the future cash flows for the company. Valuations tend to
rely on past cash flows, but companies change dramatically with
periods as short as 3 years.
Consider one event in 2005 alone: IBM sold its Personal Computer
business, a unit with $9 billion in revenues, to Lenovo Group for
$1.75 billion in cash and stock. It changes the future earnings
outlook for IBM ? and eliminated about 10% of its revenues.
? WHAT IS THE BETA? Related to ?what business is this? is the issue
of what is the company?s true beta (ß):
o Some analysts prefer a 3-year beta, arguing that market co-variance
over a longer period gives too much weight to ?old? businesses that
have been discontinued or sold. This problem uses a 5-year beta,
against an unknown market model.
o Was the beta measured against the S&P500 ? or against a broader
market index like the Wilshire 5000?
? WHAT IS THE REAL Km? Just like the beta can vary over time, so too
does the market premium. Indeed many analysts argue that today?s
market, with low inflation and low interest rates, should have a lower
market premium (Km) than that of the late 1990s.
So, investors placing the bets on Friday?s trading may well be
assuming a very different Km than 7.5%. Which leads us to question #6
? what happens when the market return rate increases?
?SPX Volatility Trends,? (Hamilton, May 9, 2005)
MARKET RETURN: When the market return increases, so too does the
cost-of-capital to IBM. That means that investments will have to
increase their returns too ?
IBM Ks = 4.24% + 1.64 * (10% ? 4.24%) = 4.24% + 9.45 = 13.69%
Without even doing the CGM calculation, we know that the price of the
stock will decline. It?s like a bond ? if the interest rate goes up
INSTANTLY, the price has to go down to provide the higher returns. In
truth, the corporation will adjust its investment policies to provide
higher returns. But here?s the new price:
P = $0.80 / (0.1369 ? 0.082) = $0.80 / 0.0549 = $14.57
P/E RATIO: As mentioned above, rather than using dividends, we could
use the real earnings for the company as a way to look at what?s
coming back to shareholders. It has its own problems, especially
undercounting the significant impact that depreciation has on cash
flow ? and it will likely undercount shares that are owed to
management in stock options (or even outstanding warrants issued).
But it?s an alternate way to do valuation:
The P/E ratio model is:
P = P/E ratio * Earnings per share
P = 15.65 * $4.87 = $76.22
Value Based Management
Earnings per share (especially from the end of 2003) don?t represent
future earnings or cash flow ? though admittedly the dividends in the
CGM are even further from true cash flow since they?re only what the
board of directors have approved in the past as cash payments to
shareholders. This, of course, is the prime in trying to fix IBM?s
Note too, that P/E ratios are based on the market pricing ratio of the
stock to the earnings, so they should be closer to today?s price on
the NYSE, if only because they?re based on the NYSE price.
Again, this is why analysts often try to strip away everything that
?hides? the true cash coming into the company, resulting in their use
of EBITDA for estimates.
Google search strategy:
CAPM + CGM
Analyst + ?stock price? + ?cash flow?
?P/E ratio? model + ?stock price?