A company is considering replacing an old piece of machinery, which cost $400,000 and has $175,000 of accumulated depreciation to date, with a new machine that has a purchase price of $550,000. The old machine could be sold for $250,000. The annual variable production costs associated with the old machine are estimated to be $72,500 per year for eight years. The annual variable production costs for the new machine are estimated to be $24,000 per year for eight years. Required:
a. Prepare a differential analysis dated May 29 to determine whether to continue with (Alternative 1) or replace (Alternative 2) the old machine.
b. What is the sunk cost in this situation?

Company A

a. Differential Analysis dated May 29

                                              Alternative 1           Alternative 2

Opportunity cost                       $250,000            $550,000

Variable production costs          580,000                192,000

Total cost                                  $830,000             $742,000

b. Sunk cost in this situation is: $225,000 ($400,000 - $175,000) cost of the old machine.

Explanation:

Company A's relevant cost for the old machine is the opportunity cost that it will lose if it continues with Alternative 1 or continued use of the old machine and the additional cost for the new machine for Alternative 2.  Also relevant is the variable production costs that would be incurred if the old or new machine is used.

Company A's sunk cost is the cost of the old machine minus accumulated depreciation.  Sunk cost is not relevant for decision making under differential analysis.

Company A's differential analysis is a managerial tool that is used to differentiate one decision alternative from another.  In this analysis, only relevant costs are considered.  A relevant cost in this case is cost that its inclusion or elimination makes a difference in the decision outcome.

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