I do not have access to the document to which you referred, so I have
sought data from other sources.
I obtained Kf from the Bloomberg website you provided. Today
(April 15, 2005) the 10 year Treasury yield is 4.24%.
From Yahoo Finance ("International Business Machines Corp"
http://finance.yahoo.com/q/ks?s=IBM), I obtained the current annual
dividend of IBM of $0.72/sh. and its Beta of 1.638. Beta is typically
calculated by taking the slope of the line that best fits a plot of
the returns of IBM stock versus the market's returns for a set of
periods. A discussion of this is found, along with examples, on pages
183-185 of Brealey & Myers. Presumably appropriate data detailing the
performance of IBM stock versus the market is found in the document
referenced in your question.
From the IBM website ("Stock Information"
http://www.ibm.com/investor/stock/index.phtml), I obtained details
regarding its annual dividend for the last three years.
Using the Compound Annual Growth Rate formula from Investorwords.com
("CAGR" http://www.investorwords.com/666/CAGR.html), I calculated the
CAGR of IBM's dividend: (0.72/0.60)^(1/3) - 1 = 6.27%.
Using the CAPM model: Ks = Beta(Km - Kf) + Kf, I obtained Ks =
1.638(7 - 4.24) + 4.24 = 8.76 (page 162 of Brealey & Myers)
The Constant Growth Model: Po = DIV1/r-g = $0.72/(8.76% - 6.27%) =
$28.91 (page 62 of Brealey & Myers). From the Yahoo Finance source
above, IBM's current stock price is $76.70. Possible reasons for the
difference: The market risk premium is currently lower than the
estimate we used. Another possibility is that investors expect IBM's
growth rate to increase in the future, making the estimate of its
future growth rate from its previous history inaccurate.
With the new Km of 10%, Ks = 1.638(10-4.24)+4.24 = 13.67. Po =
$0.72/(13.67%-6.27%) = $9.73.
A riskier stock (increase stock market risk makes each individual
stock riskier) with the same growth prospects results in the share
price being reduced.
The P/E ratio model is Po = P/E ratio * EPS. From the Yahoo Finance
source above, IBM has a current P/E ratio of 15.74 and an EPS of
$4.873. Therefore, the share price is $76.70. Source: "P/E Ratio -
Price to Earnings" http://www.valuebasedmanagement.net/methods_PEratio.html.
If IBM has had a significantly different PE ratio in the past that is
more representative of its expected future prospects, then of course
use of this PE ratio would result in a different Po. You will want to
consult the document that you have been provided to ensure that you
are not to use a different PE ratio for this calculation, such as the industry one.
It is important to note that "[t]here is no reliable association
between a stock's price-earnings ratio and the capitalization rate
[Ks]. The ratio of EPS to Po measures [Ks] only if [the present value
of growth opportunities] = 0 and only of reported EPS is the average
future earnings the firm could generate under a no-growth policy."
(Page 61 of Brealey & Myers).
Sincerely,
Wonko
Source: "Principles of Corporate Finance" Fourth Edition by Brealey &
Myers, McGraw-Hill Inc. (1991) |