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

Answer In this problem supervisor’s fixed salary and allocated general fixed overhead are not relevant to calculate indifferent price of gold crown. Only variable cost has taken in consideration for this purpose.

Indifferent point between in-house production of gold and porcelain crowns- Net in-house total production cost= net purchase cost of crowns form local laboratory

1800 crowns*$81 per crowns+ 1200 crowns*$115 per crowns=1800 crowns*$100+1200 crowns*Purchase price of gold crown- $16000 annual rent income

$145,800+$138,000=$180,000+ 1200*Purchase price of gold crown-$16000

$283800=$164,000+1200* purchase price of gold crown

$119,800=1200* purchase price of gold crown

Purchase price of gold crown=$11980/1200

=$99.83 or $100 approx.

Hence local laboratory should charged $100 for a gold crown for indifferent between in-house cost of production and purchase cost of crowns from local laboratory by Lift Dentistry Services.