EV Problem

[Gabe]

You represent Company A (the acquirer) which is currently considering acquiring Company T (the target) by means of a tender offer. You plan to tender in cash for 100% of Company T's shares but are unsure how high a price to offer. The main complication is this: the value of the company depends directly on the outcome of a major oil exploration project it is currently undertaking.

The very viability of Company T depends on the exploration outcome. In the worst case (if the exploration fails completely), the company under current management will be worth nothing-$0/share. In the best case (a complete success), the value under current management could be as high as $100/share. Given the range of exploration outcomes, all share values between $0 and $100 per share are considered equally likely. By all estimates the company will be worth considerably more in the hands of Company A than under current management. In fact, whatever the value under current management, the company will be worth 50% more under the management of Company A than Company T.

The board of directors of Company A has asked you to determine the price they should offer for Company T's shares. This offer must be made now, before the outcome of the drilling project is known.

Thus, you (Company A) will not know the results of the exploration project when submitting your offer, but Company T will know the results when deciding whether or not to accept your offer. In addition, Company T is expected to accept any offer by Company A that is greater or equal to the (per share) value of the company under its current management.

As the representative of Company A, you are deliberating over the price offers in the range $0/share to $150/share. What offer per share would you tender?

[BruceZ]

I have computed the optimal price to offer to the penny using the methods of calculus. If this is a real offer, and if you do not know the optimal answer, then I want to profit from this information. If you do not know how to calculate the answer, it is unlikely that you could optimize your profit to within 1%. This would represent a loss to you.

There are others here who are also capable of giving you the correct answer. We could all undercut each other until the price of this information is minimal, but we would recognize that we all profit the most if each correct answerer agrees to split 1% of the profit equally.

If you agree to this, post an anonymous email through which all parties can identify themselves and exchange addresses and phone numbers with you for verification. Then you will mail each of us a contract agreeing to send each participant who sends you a correct answer with explanation by a certain time an equal share of 1% of the profit. The contract will specify the name of the company to be purchased. Our individual contracts will be binding when you purchase the company for the amount which is within 1% of the answer, which will be a matter of public record.

You might respond that this is a made up problem in order to receive free answers. All potential respondents are urged not to answer in this case.

[BruceZ]

I can't really make the above offer because you should not offer to buy the company for any price.

Let x be the value you offer, and let t be the true value of the company to the current owner. If t > x, then the ev is 0 since the company will refuse the offer. So the ev will only be non-zero if t is between 0 and x. The amount you gain is equal to 1.5t-x. This is the value of the company to you minus the cost. So the ev is:

ev = integral[0 to x](1.5t-x)*1/100dt

ev = -.0025x^2.

So your ev is always negative for any offer.

[brad]

'Thus, you (Company A) will not know the results of the exploration project when submitting your offer, but Company T will know the results when deciding whether or not to accept your offer.'

well obviously this is a sellers market, heh.

brad

[lorinda]

Heh, I was just coming to that conclusion myself, and it's kept me up way past my bedtime [img]/forums/images/icons/frown.gif[/img]
My reasoning, as ever is wordy.

Whenever you have aquired the company, you spend $x
Since all prices are equally likely, the actual worth of the company is going to be x/2 on average.
we know that this increases by 50%, so the worth becomes 3/2 *x/2 =3x/4
So on the occasions we purchase the company we lose x/4 or .25x on the deal.
The occasions we purchase it happen to be x% of the time, so we lose the .25x a grand total of x% of the times we bid.
which thankfully gives us x/100 * x/4 = (x^2)/400
which thankfully gives us .0025x^2 loss without me having to remember how to integrate [img]/forums/images/icons/laugh.gif[/img]

I'm sorry I keep posting these weird solutions, but I like to give hope to the less mathematically gifted (like myself)and show that , although logic has to be even more rigorous than usual, it IS possible to solve a lot (though I concede not all) of these problems without real training in the subject.

[BruceZ]

I think Sklansky would like your solution. Nice job.