When one happens to casually scroll through IBM's (NYSE:IBM) key statistics on financial websites like Yahoo Finance the number that pops out immediately is its stellar Return on Equity. For 2011, IBM's RoE stood at 73%, which is mind boggling at first sight. When a company like IBM posts a RoE number that is so high it warrants a deeper dive into understanding how exactly has the company been able to achieve this growth. After all, a Return on Equity is considered by many as the ultimate measure of a company's profitability.

In this article we are going to find out IBM's real RoE and then use a valuation technique to estimate the actual value of the stock.

IBM had a Return on Common Equity of 15% in 2002 which has increased almost every single year to 73% in 2011. The chart below tells the story better:

Return on Equity is defined as follows:

Return on Equity = Net Income earned in a single year/Shareholder's Equity

By simple arithmetic we know that if the company keeps reducing its shareholder's equity, the RoE will increase even if net income remains constant. This is one way in which companies can increase the RoE.

So let's see what the shareholders equity is made up of;

Shareholder's Equity = Share capital issued + Retained Earnings - Treasury Shares

If the increase in Treasury shares held by the company is more than the increase in share capital issued plus retained earnings then the shareholder's equity decreases leading to an increase in the RoE. The total value of IBM's treasury stock in 2002 was $20.2 billion. Since then the stock price has increased and the company has purchased additional shares each year increasing the value of its holdings. At the end of 2011, the value of IBM's treasury stock stood at $110.9 billion, an increase of 450%. In contrast, the value of share capital + RE has increased only 200%. These two numbers clearly tell us that a major component of the increase in RoE is due to the increase in the holdings of treasury stock.

To calculate IBM's realistic RoE, we must adjust for its holdings of treasury stock by making an assumption that the company sells all its treasury stock and receives cash equal to the amount recorded on the balance sheet. After making this adjustment IBM's RoE falls down to 12.08%.

Now that we have cleared some froth it might make sense to estimate IBM's stock price using a valuation model like the discounted cash flow.

In one of my earlier posts I applied the Discounted Cash flow analysis to Microsoft and explained the detailed mechanism here.

In applying the discounted cash flow analysis we need to estimate the following variables:

**Required rate of return:** The required rate of return should be a little more than the weighted average cost of capital for the company. As of 2012 the WACC for IBM stands at 8.5%, so we use a 10% required rate of return.

**Free Cash Flow Growth Rate:** We assume that the free cash flow will grow at this rate for the next three years. For a reasonable estimate I calculate the average FCF growth rate for the past ten years which is 7%. So, here we are going to build two scenarios:

- Assuming the growth rate for the next three years is 7%.
- For investors who want more margin of safety, we assume that the cash flow for the next three years is 3.5%.

**Perpetual Growth rate**: This is the rate at which the cash flow grows into perpetuity after the three years. It is generally a good idea to assume that this rate will be much lower than the three year growth rate or the rate at which the company has grown in the past. Again, I shall build three scenarios:

- Assuming the growth rate is 2.5% (for optimistic investors)
- Assuming the growth rate is 1% (for medium risk investors)
- Assuming the growth rate is 0.1% (for cautious investors)

We have six different prices in the output from which we construct six different scenarios for investors with different risk profiles.

Estimated price when the three year growth rate is 7% and,

- The perpetual growth is 2.5% is : 221 - scenario 1
- The perpetual growth is 1% is : 186 - scenario 2
- The perpetual growth is 0.1% is : 170 - scenario 3

Estimated price when the three year growth rate is 3.5% and,

- The perpetual growth is 2.5% is : 200 - scenario 4
- The perpetual growth is 1% is : 168 - scenario 5
- The perpetual growth is 0.1% is : 153 - scenario 6

Scenario 1 is for an investor who is optimistic about the prospects of IBM both in the short term and long term and does not mind taking a higher degree of risk. For such an investor, IBM is currently trading at a discount to its intrinsic value.

Scenarios 2 and 3 are for investors who are optimistic about the next three years but not as optimistic about the long term prospects. For them, the stock is trading at some premium to its intrinsic value.

Scenario 4 is for investors who have a cautious outlook for the next three years but are positive about the longer term prospects. The stock is trading close to its intrinsic value for such investors.

Scenarios 5 and 6 are for investors who are cautious about both the short term and long term and do not prefer taking a lot of risk. For such investors the stock is trading at a significant premium to its intrinsic value.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.