By walking you through a set of real-time financial data for IBM, this
assignment will help you better understand how theoretical stock
prices are calculated; and how prices may react to market forces such
as risk and interest rates. You will use both the CAPM and the
Constant Growth Model (CGM) to arrive at IBM's stock price. To get
started, complete the following steps.

First, find an estimate of the risk-free rate of interest, krf. To
calcuate this rate, first go to Bloomberg.com: Market Data
[http://www.bloomberg.com/markets/index.html], to find the 10-year
Treasury bond rate. Use this interest rate as the risk-free rate. In
addition, you also need a value for the market risk premium. Use an
assumed market risk premium of 7.0%.


Download this IBM Stock Information document (.doc file). This
document was generated from recent financial data for IBM. Using this
document, find an estimate of:
a) IBM's beta (?)
b) IBM's current annual dividend
c) IBM's 3-year dividend growth rate (g)
d) Industry P/E
e) IBM's EPS. 
Also find IBM's current annual dividend and its 3-year growth rate, or g. 
With the information you now have, use the CAPM to calculate IBM's
required rate of return or ks.


Use the CGM to find the current stock price for IBM. We will call this
the theoretical price or Po.


Now use appropriate Web resources to find IBM's current stock quote,
or P. Compare Po and P. Do you see any differences? Can you explain
what factors may be at work for such a difference in the two prices?
This section is especially important?with more weight in grading?so
you may want to do some study before answering such a question.
Explain your thoughts clearly.


Now assume the market risk premium has increased from 7.0% to 10%; and
this increase is due only to the increased risk in the market. In
other words, assume krf and stock's beta remains the same for this
exercise. What will the new price be? Explain what happened?


Recalculate IBM's stock using the P/E ratio model (pp. 350-1) and the
needed info found on the Web. Explain why the present stock price is
different from the price arrived at using CGM.

Please show all work, including formulae and calculations used to
arrive at financial values. Submit your work to your instructor via
the drop box.

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)