Question 7:

Attention Industries has two divisions. Division 1 makes cleaning products and the net worth of this

division (present value of cash flows) is $1,000. Division 2 makes a chemical product. The net worth of

division 2 is $600, absent any potential liability. There is a chance that division 2 could have $880

liability for pollution damage. The potential victims have no contractual relationship with the firm. The

probability of such a loss is 0.55

(1+ss) , where s is the amount the firm spends on safety. The firm must

choose the level of s. (Note that the derivative of aa

(1+ss) with respect to "s" is equal to aa

(1+ss)2)

i) First, calculate the total value of the firm, including both divisions at the same time, as an

equation of "s". Second, take derivative with respect to s to find the "s" that maximizes the

total value. Third, plug in the value of "s" you found into total value equation to find the

maximum total value. [5]

ii) Division 1 is riskless and has a stand-alone value of $1,000. Since all the risk comes from

division 2, we must consider the chosen level of safety "s" of this unit as a stand-alone entity.

First, calculate the stand-alone value of division 2 as an equation of "s". Second, take

derivative with respect to s to find the "s" that maximizes the stand-alone value of division 2.

Third, plug in the value of "s" you found into the equation of stand-alone value of division 2

to find the maximum stand-alone value of division 2. [5] (Hint: the value of division 2 is

$600 if no liability arises. However, if a loss of $880 occurs it cannot pay more than the

original $600 stand-alone value due to limited liability.)

iii) What is the maximum value of the firm if we treat division 2 as a separate entity? Note that

we are splitting the two divisions assuming that separated division 2 as a stand-alone firm is

protected by limited liability. (Hint: Add your answer to part ii) to the net worth of division

1.) [2]

iv) What is the gain from splitting the firm up? [2] (Hint: It is the difference between the

maximum total value without split up that you found in i) and the maximum total value with

split up that you found in iii).)