First, it useful to consider what proportion of intrinsic value is explained from our most basic simplifying assumption --- IBM grows at a normal rate of 6% in perpetuity.

You may be surprised to discover that this is usually one of the most important assumptions. For the case of IBM change the abnormal growth rate in stage I to 6%. For the current example this changes the estimate for IBM's intrinsic value to $70.06.

That is, just over 63% can be explained from normal growth assumptions or approximately 37% of IBM can be explained from abnormal growth assumptions.

Cost of equity capital. We have seen that the stage II is an important contributor to the estimate of intrinsic value. In stage 2 we made the assumption that if growth is assumed to revert to normal levels then beta is should revert to normal levels. What effect does this assumption have?

Contrast assuming CAPM (with beta equal to 1.30) versus CAPM with beta equal to 1 in stage II for IBM. You can use the drop down menu beside Stage 2 Discount rate to see this.

CAPM (beta equal to 1.30) for both stages: $97.68

CAPM (beta equal to 1.00 in stage 2, and 1.30 in stage 1): $118.85

Clearly, the Intrinsic Value is very sensitive to our assumption for beta in stage 2 when computing the cost of equity capital.

Similarly, you can test the predicted sensitivity of IBM to shifts in the long bond rate and shifts in the equity premium by changing these numbers.

Another interesting shift is the number of years assumed for stage I. For some companies 10-years may be way too high. For example, a new software start up may have an interesting product but competition may move in quickly. If they have no inherent barriers to entry then this may generate abnormal growth for 2-years and then normal thereafter. Another software company may have control of the popular operating systems which form the foundation for all applications. This control provides high barriers to entry and therefore is sufficient to protect abnormal growth for long periods of time.

For the case of IBM they have first class research and development. This generates patents that can keep them at the cutting edge for long periods of time. IBM also has demonstrated it's ability to license it's know how and generate free cash flow at the same time. As a result, some may consider 10-years to be a conservative estimate of abnormal growth and that in 10-years time IBM will still be at the cutting edge of technology and licensing "know how." In the current example if we extended 10 to 15 (keeping all other assumptions at the base case) our estimate increases from $110.37 to $127.83.

Finally, in this introduction to sensitivity analysis we may be concerned that we are using the ex post financial statements. Because we are in December the full 2001 financial statements for IBM are not currently available even though most of the year is over. As a result, analysts can make pretty good guesses at what the current year's results will look like and these guesses are likely to be superior (and evidence supports this) to using last year's numbers.

So for the case of IBM the current analyst forecasts for EPS (Earnings per share) available on the Zacks site are:

30-day consensus (based on 3 estimates) 2001 4.35 and 2002 4.79

120-day consensus (based on 21 estimates) 2001 4.36 and 2002 4.86

From the above we know that there are 1812.10 shares outstanding (000's)

As a result, the Net Income projected for IBM for 2001 is 7882.635 (using the 4.35 consensus). To get an idea of the impact that this has type it in to replace the 8093 number above. This will reduce IBM's estimate of Intrinsic value to: 106.72.

In 2002 analysts are expecting this to increase to 4.79 or 8679.96 based on current outstanding shares (which ignores potential Treasury stock transactions). Using this figure we get 120.55 for the base case which is around what IBM is currently trading at. Associated with this estimate our expected return prediction is 11.28% for IBM.

The above illustrates an interesting point. When we are estimating the value of IBM as of December 2001 we are really interested in starting with expected earnings 1-year from now i.e., December 2002 not with realized earnings from 2000. This is the difference between analysts interests in ex ante earnings versus accountant measures of ex post earnings. So from our very basic sensitivity analysis we would rate IBM as Moderate to Strong Buy depending upon our beliefs of the stage I horizon bias plus taking into account expected return forecasts relative to returns from bonds.

It should be noted that the above is merely a start to what type of questions should be considered.