solution

CareLess Industries has two divisions. Division 1 makes cleaning products,

and the net worth of this division (PV of cash flows) is 500. Division 2 makes

a chemical product. The net worth of division 2 is 300, absent any potential

liability. However, there is a chance that division 2 could have a 700 liability for

pollution damage. The potential victims have no contractual relationship with

the fi rm. The probability of such a loss is 0.2>(1 + s), where s is the amount

the firm spends on safety. The firm must choose the level of s. If you could sell

off division 2, would you do so? What is the gain from splitting the firm in

this way? Assume a separated division 2 (as a stand-alone firm) is protected by

limited liability. Note also that the derivative of a>(1 + s) with respect to s is

-a>(1 + s)2; that is, [a>(1 + s)]>s = -a>(1 + s)2.