$1)$ Kodrox

Kodrox has two divisions. Division A produces plastic bottles. Division B produces proprietary Kodrox Elixir, then bottles and markets it$.$ Kodrox owns three buildings, each with a

book value of $$12$ million and annual depreciation of $$1\mathrm{.}2$ million. The resale value of the

entire property is $$25$ million, but individual buildings cannot be sold $($or leased$)$ individually because of possible infringement on company security. The first building is currently

occupied by Division A$,$ the second building is currently occupied by Division B$,$ and the

third building is currently sitting empty. Either division can occupy the third building if

they are willing to pay headquarters a fee of $$0\mathrm{.}6$ million per year. Disregard maintenance

expenses and assume that at any given time only one division can occupy the third building.

Here are some essential facts about Division A:

$$ The marginal cost of producing plastic bottles is $$10$ per bottle.

$$ Each building has a capacity of $10,000$ bottles per month.

$$ Division A is currently at capacity in the first building.

$$ The equipment required to produce each batch of $1,000$ bottles in the third building can

be leased at a cost of $$10,000$ per month. For example, to produce between $1,001$ and

$2,000$ bottles per month in the third building, the equipment costs would be $$20,000.$

$$ Any number of bottles can be sold to outside clients at a market price of $$30$ per bottle.

Here are some essential facts about Division B:

$$ Division B can buy bottles either from Division A$,$ or from an outside supplier who

charges $$35$ per bottle. The Elixir ingredients are then added and the product is sold

at a price of $$105$ per bottle. The variable cost of the ingredients is $$40$ per bottle.

$$ Each building has a capacity of $10,000$ bottles per month.

$$ Division B is currently at capacity in the second building.

$$ All bottles are currently purchased from Division A at a cost of $$30$ per bottle.

Division B is considering lowering the price of its Elixir to $$95$ per bottle and expanding

production by moving into the third building. In addition to paying the headquarters fee,

this would require purchasing a production line, the monthly payment for which is $$25,000.$

a$)$ Present a break$-$even analysis from the perspective of Division B$$s management. As the

manager of Division B$,$ your goal is to maximize Division B$$s profits. Under what conditions,

if any, should you want Division B to move into the empty building?

b$)$ Present a break$-$even analysis from the perspective of the firm. Your goal is to maximize

total firm profit. Under what conditions, if any, should you keep the third building empty?

Under what conditions, if any, should you expand Division A into the empty building? Under what conditions, if any, should you expand Division B into the empty building?

c$)$ Compare your answers in $($a$)$ and $($b$).$ Be sure to discuss decision rights and firm profits.