Cost Accounting (14th Edition)

IRRELEVANCE OF PAST COSTS AND EQUIPMENT-REPLACEMENT DECISIONS 411
Toledo Corporation uses straight-line depreciation. To focus on relevance, we
ignore the time value of money and income taxes. 2 Should Toledo replace its
old machine?
Exhibit 11-11 presents a cost comparison of the two machines. Consider why each of the
four items in Toledo’s equipment-replacement decision is relevant or irrelevant:
1. Book value of old machine, $400,000. Irrelevant, because it is a past or sunk cost. All
past costs are “down the drain.” Nothing can change what has already been spent or
what has already happened.
2. Current disposal value of old machine, $40,000. Relevant, because it is an expected
future benefit that will only occur if the machine is replaced.
3. Loss on disposal, $360,000. This is the difference between amounts in items 1 and 2.
It is a meaningless combination blurring the distinction between the irrelevant book
value and the relevant disposal value. Each should be considered separately, as was
done in items 1 and 2.
4. Cost of new machine, $600,000. Relevant, because it is an expected future cost that will
only occur if the machine is purchased.
Exhibit 11-11 should clarify these four assertions. Column 3 in Exhibit 11-11 shows that
the book value of the old machine does not differ between the alternatives and could be
ignored for decision-making purposes. No matter what the timing of the write-off—
whether a lump-sum charge in the current year or depreciation charges over the next two
years—the total amount is still $400,000 because it is a past (historical) cost. In contrast,
the $600,000 cost of the new machine and the current disposal value of $40,000 for the
old machine are relevant because they would not arise if Toledo’s managers decided not to
replace the machine. Note that the operating income from replacing is $120,000 higher
for the two years together.
To provide focus, Exhibit 11-12 concentrates only on relevant items. Note that the
same answer—higher operating income as a result of lower costs of $120,000 by
replacing the machine—is obtained even though the book value is omitted from the
calculations. The only relevant items are the cash operating costs, the disposal value of
the old machine, and the cost of the new machine that is represented as depreciation in
Exhibit 11-12.
Decision
Point
Is book value of
existing equipment
relevant in equipment
replacement
decisions?
Two Years Together
Keep Replace Difference
(1) (2) (3) = (1) – (2)
Revenues $2,200,000 $2,200,000 —
Operating costs
Cash operating costs
($800,000/yr. 2 years;
$460,000/yr. 2 years) 1,600,000 920,000 $ 680,000
Book value of old machine
Periodic write-off as depreciation or 400,000 — —
Lump-sum write-off — 400,000 a
Current disposal value of old machine — (40,000) a 40,000
New machine cost, written off periodically
as depreciation — 600,000 (600,000)
Total operating costs 2,000,000 1,880,000 120,000
Operating income $ 200,000 $ 320,000 $(120,000)
Exhibit 11-11
Operating Income
Comparison:
Replacement of
Machine, Relevant, and
Irrelevant Items for
Toledo Company
a In a formal income statement, these two items would be combined as “loss on disposal of machine” of $360,000.
2 See Chapter 21 for a discussion of time-value-of-money and income-tax considerations in capital investment decisions.