Question

Lift Dentistry Services operates in a large metropolitan area. Lift
has its own dental laboratory used to produce porcelain and gold
crowns. The per unit variable costs to produce these crowns are:

   porcelain  .......  $81 per crown
   gold  ............  $115 per crown

Fixed overhead includes the following:

                                   porcelain         gold
   supervisor's salary             $15,000         $20,000
   allocated general overhead      $ 6,000         $ 6,000

A local dental laboratory has offered to supply Lift all the crowns
it needs. Its price is $100 per porcelain crown and $136 per gold
crown; however, the offer is conditional on supplying both types of
crowns (i.e., the local laboratory will not supply just one type of
crown for the price indicated). If the offer is accepted, Lift could
rent the space now being used to make the crowns to another company
for $16,000 per year. Lift uses 1,800 porcelain crowns and 1,200 gold
crown per year.

Assume the local laboratory will charge $100 per porcelain crown, but
is willing to negotiate on the price of the gold crowns. Calculate the
selling price per unit charged by the local laboratory for the gold
crowns that would make Lift Dentistry Services economically indifferent
between making the crowns themselves and purchasing the crowns from the
local laboratory.

Answer 1

Solution:

Relevant cost of making porcelain = (1800*$81) + $15,000 = $160,800

Relvant cost of making gold = (1200*$115) + 20000 = $158,000

Total relevant cost of making porcelain and gold = Relevant cost of making poecelian + Relevant cost of making gold + Opportunity cost of renting the space = $160,800 + $158,000 + $16,000 = $334,800

Buying cost of laboratory = 1800*$100 = $180,000

Now to be indifferent in both situation of making and buying the crown, the cost under both option will be same, let selling price per unit charged by local laboratory for the gold crown in $x per unit that make both option indifferent

Now buying cost of gold crown = 1200 X

Now

1200 X + $180,000 = $334,800

X = $129 per unit

Therefore selling price to be charged by local laboratroy for the gold crown = $129 per unit