Stay Rational: Speculating On Dell

| About: Dell Inc. (DELL)

The article titled, "Why I'm Buying Dell, (NASDAQ:DELL), at $14" proposed an interesting recommendation on Dell; Buy Dell at its current price of about $14, above the current buyout-deal price of $13.65 a share. Many strong points were made about why this is a good idea. Southeastern Asset Management owns 8.5% of Dell and is vehemently against a deal being done at $13.65 a share because it believes the intrinsic value of the company is much higher (It believes Dell is worth closer to $23 a share). It is reasonable to think that Southeastern's influence could force the proposed buyout price to increase.

A second strong point that was made is that even if the buyout price doesn't change, there is very limited downside at a current market price of about $13.90 a share. If you were to buy a position at the current price and the proposed deal goes unchanged, only a 1.8% loss would be incurred. This is not that bad considering there is a much greater potential upside if Southeastern can get the terms of the deal to change in its favor.

After reading through some of the comments, however, it was concerning to hear that some people were going to go "head-first" in on this expectation. I am in no way objecting to the idea of buying Dell at $14 because in many ways it makes sense, but what concerned me was that the quantitative method of determining if this idea makes sense was not mentioned (which I will address later).

It's important to discuss the nature of buying Dell above what is the current buyout-price of $13.65 a share. This idea falls under the speculative category of investments. Speculation is often thought of as a dirty word as investing jargon goes, but I'm not using it in that context. Speculative situations in some cases actually make more sense than "investing" in the defensive-minded sense of the word. To determine this, let's consider the details of this situation.

As we all know, on February 5, Dell Inc. announced that it had signed a definitive merger agreement under which Michael Dell, Dell's founder, chairman and CEO would acquire the company in partnership with the investment firm Silver Lake. Shares surged on the news and they now sit around $14 a share above the buyout-price of $13.65 a share.

Based on the above, to speculate successfully with a long position at $14 a share, the terms of the deal must be renegotiated. If nothing happens though, you will lose money. So that is the first uncertainty that must be dealt with.

The second thing that must be considered is that even if Dell is worth more than $24.4 billion that the deal values it at, what is the probability that the spread is large enough that action is taken? Even if Southeastern is right that Dell is worth substantially more than $13.65 a share, are they (along with other like-minded shareholders) powerful enough to get the terms renegotiated?

A third factor to consider is how much is Michael Dell and Silver Lake willing to pay for the company. Since there is no "white knight" and no other bids, Michael Dell and Silver Lake must be willing to pay more for this idea (buying in at $14 a share) to pay off. As the only group with an offer, they have substantial leverage in the deal because there is nobody to compete with.

A fourth factor to consider is the potential upside if Southeastern and the like get their way. Some have thrown around rumors that the deal could get renegotiated to $20 a share. This seems unlikely as Dell is currently struggling, with the fourth quarter FY 2013 earnings falling 30% below what they were during the year-ago quarter.

Now with these points in mind I will provide a method for you to determine if buying Dell at $14 makes sense. This will be achieved using legendary investor Ben Graham's method of determining "risk-adjusted projected rate of return." The first part of the equation requires that you figure out what your potential return is. To do this, assign what you believe the buyout-price will be changed to assuming Southeastern gets its way. I believe that if the buyout-price were to change, it would be revised upwards to $15.50 a share. This means that my projected rate of return is 10.7% (($15.50-$14.00)/$14.00).

Step two is to figure out the likelihood that the event will occur. Does it have a 60% chance? Or a 85% chance? There is no calculation for this; it's more of an art than science. You should consider how much influence Southeastern and company have in changing the current buyout price of $13.65. As an example, I'm going to assign my likelihood at 75%, meaning I feel there is a 75% chance the deal price will be renegotiated up to $15.50 a share.

Step three is to determine the adjusted projected profit. To do this, multiply the likelihood of the deal happening (step 2) by the projected profit (calculated in step 1). In my case it is 0.75 * $1.50= $1.125. Therefore $1.125 is my adjusted projected profit.

Step four is to calculate your adjusted projected rate of return. To do this, divide your new adjusted projected profit (step 3) by our investment (which is $14.00 a share for everyone). In my case it is $1.125/$14.00= 0.08

My adjusted projected rate of return is 8%.

Step five we have to determine our projected loss, if the deal falls through. There is two parts to this. Part A is that the deal falls through, Michael Dell and Silver Lake back out and shares likely fall back to what they were trading at before the buyout was announced (approximately $11 a share). Part B is that the deal doesn't fall through, but doesn't get changed and the buyout happens at $13.65 a share. Part A seems very unlikely and as an example I'll assign a low 5% probability to this happening. If this does occur, however, we would lose $3 a share. Now to adjust it to your probability, multiply the 5% chance by the $3 to get an adjusted loss of $0.15. Our loss if Part B occurs is the complement probability to that which I assigned in step two 100%-75% = 25% so 0.25 * ($14-$13.65) = loss of $0.0875.

Finally let's determine our risk-adjusted projected profit/return, which is what we're really after. There will be two risk-adjusted projected profits/returns depending on whether Part A or Part B occurs.

Part A risk-adjusted projected profit: Take the adjusted potential profit, which is $1.125 in my case and subtract from it the adjusted projected loss ($0.15)=> 1.125-0.15= $0.975. I'll call this $0.975 the risk-adjusted projected profit. Now divide this figure ($0.975) by the original investment of $14 a share ($0.975/$14) to finally get the Part A risk-adjusted projected rate of return of 6.9%.

For Part B do the same, except subtract ($0.0875): $1.125-$0.0875= $1.0375. Divide this ($1.0375) by the original investment of $14 a share to get a Part B risk-adjusted projected rate of return of 7.4%.

So now the real question becomes are these risk-adjusted returns attractive enough to buy Dell at $14 a share? This depends on whether or not you can invest your capital elsewhere and get a higher return within the same time period. Part A is expected to close by end of second quarter FY 2014 (if it occurs). In my case it would be worth my while if I could not get a return of greater than 6.9% by the end of Q2 FY 2014. If Part B occurs then some guesswork on the time frame must be made on your part. In my case the question is, "can I get a better return than 7.4% elsewhere?"

Conclusion: The idea of buying Dell now (at $14.00 a share) is a matter of determining your risk-adjusted rate of return and comparing it to your next best investment idea. As discussed earlier, this is speculation because certain events must occur to profit with the way conditions currently exist. The method is certainly not foolproof, but it provides a helpful guide in determining if Dell is right for you at its current price.

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.