Why Staples Will Increase Its Offer for Corporate Express

Imagine you go to a casino and spot a big bucket filled with 100 balls. There are 51 red balls and 49 blue balls. Next to the bucket there is a sign which informs you that you can guess the color of a randomly drawn ball for $1. If you are right, you will receive $2, but if you are wrong you will lose your bet. A rational investor will take a seat next to this bucket and will not leave anymore. By consistently betting on a red ball being drawn, he can calculate a 51% chance of achieving a return of $2 and a 49% chance of a return of $0, which gives an expected return of $1.02 for an investment of $1.

We can apply the methodology of this simple probability calculation to determine what the expected value of the acquisition by Staples (SPLS) of Corporate Express (CXP) will be. In this case, there are a couple of complications and we need to make some extra assumptions to make this calculation.

The easy part is determining the value of the bet, which is equal to the actual stock price of Corporate Express. At the time of writing, this was about 7.80 Euro, a premium of 7.5% in comparison with the offer from Staples of 7.25 Euro. Subsequently, we can calculate how much a rational investor wants to receive when the acquisition is finalized. I assume closing of the acquisition will not take place before the end of May, which means that Corporate Express shareholders will have received a dividend of 0.21 Euro before this closing. The rational investor, who is only concerned with probability calculations, will expect to receive at least an amount of approximately 7.87 Euro at the end of May, assuming an interest rate for short term deposits of 4%. At the end of April, he will already have received 0.21 Euro, which implies that the remainder of 7.66 Euro has to come from his bet on the outcome of the draw from the bucket of balls.

We still need to determine the probability of the outcomes and the values of the outcomes of the draw. Since Corporate Express was trading in a range of 5.00 - 5.50 Euro before the offer from Staples, I assume the share price could drop to 5.00 Euro again, if the acquisition fails to take place. I assign this outcome a probability of 20%. We still don’t know the value of a successful offer, but we do know that the rational investor wishes to receive at least 7.66 Euro. Knowing this, we can calculate the value of the expected offer, which has a chance of 80%. The calculation is (7.66 – (0.20 x 5)) / 0.80 = 8.33. With this offer price, an investor has a chance of 20% to receive 5 .00 Euro, and a chance of 80% to receive 8.33 Euro. This gives an expected return of 7.66 Euro, exactly his minimum requirement. Including dividend, the offer would have to be 8.54 Euro.

If we would assign a chance of 70% to a successful offer, the acquisition price would need to be 9.02 Euro, while an expected chance of 90% of success gives an acquisition price of 8.17 Euro.

The conclusion is that the rational calculating investor, who is presently considering taking a position in Corporate Express for a price of 7.80 Euro, and who assigns a 80% chance of success for the acquisition to take place, expects a final offer of 8.54 Euro, including dividend. If the offer fails, this investor will expect the share price could drop back to 5.00 Euro.

I believe that most current shareholders of Corporate Express are rational calculating investors, and that they believe a revised offer needs to be at least somewhere in the 8-9 Euro range to be successful. If Staples is serious about its intentions to acquire Corporate Express, it is hard to imagine that they would not have expected that an increased offer would be required. If this is the case, the indicated range should not come as a surprise either.

Disclosure: Author holds a long position in CXP