Irrelevance of Past Costs and Equipment-Replacement Decisions

Learning Objective 7 Explain why book value of equipment is irrelevant to managers making equipment-replacement decisions

At several points in this chapter, we reasoned that past (historical or sunk) costs are irrelevant because a decision cannot change something that has already happened. We now apply this concept to decisions about replacing equipment. We stress the idea that book value—original cost minus accumulated depreciation—of existing equipment is a past cost that is irrelevant.

Exhibit 12-11 presents a cost comparison of the two machines. Consider why each of the following four items in Toledo’s equipment-replacement decision are 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 the company has already 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 company replaces the machine.
  3. LOSS ON DISPOSAL, $360,000. This is the difference between amounts in items 1 and 2. This amount is a meaningless combination blurring the distinction between the irrelevant book value and the relevant disposal value. Managers should consider each value 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 company purchases the machine.

Exhibit 12-11

Operating Income Comparison: Replacement of Machine, Relevant, and Irrelevant Items for Toledo Company

Table shows a cost comparison of relevant and irrelevant items related to the replacement of machine in addition to the difference between the two costs for Toledo Company.

The details of the table under three categories for two years together are as follows. The unavailable data have been marked as nil.

1. The revenues, various operating costs, and operating income of the keep category are:

a. Revenues: $2,200,000

b. Operating costs

• Cash operating costs of $800,000 per year multiplied by 2 years and $460,000 per year multiplied by 2 years: $1,600,000

• Book value of old machine

Periodic write-off as depreciation: $400,000

Lump-sum write-off: Nil

• Current disposal value of old machine: Nil

• New machine cost, written off periodically as depreciation: Nil

• Total operating costs: $2,000,000

c. Operating income: $200,000

2. The revenues, various operating costs, and operating income of the replace category are:

a. Revenues: $2,200,000

b. Operating costs

• Cash operating costs of $800,000 per year multiplied by 2 years and $460,000 per year multiplied by 2 years: $920,000

• Book value of old machine

Periodic write-off as depreciation: Nil

Lump-sum write-off: $400,000

• Current disposal value of old machine: $40,000 within parentheses

• New machine cost, written off periodically as depreciation: $600,000

• Total operating costs: $1,880,000

c. Operating income: $320,000

3. The differences in the revenues, various operating costs, and operating income of the keep and replace categories are:

a. Revenues: Nil

b. Operating costs

• Cash operating costs of $800,000 per year multiplied by 2 years and $460,000 per year multiplied by 2 years: $680,000

• Book value of old machine

Periodic write-off as depreciation or lump-sum write-off: Nil

• Current disposal value of old machine: $40,000

• New machine cost, written off periodically as depreciation: $600,000 within parentheses

• Total operating costs: $120,000

c. Operating income: $120,000 within parentheses

Exhibit 12-11 clarifies these assertions. Column 3 in Exhibit 12-11 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 2 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. Considering the cost of replacing the machine and savings in cash operating costs, Toledo’s managers should replace the machine because the operating income from replacing it is $120,000 higher for the 2 years together.

Exhibit 12-12 concentrates only on relevant items and leads to the same answer—-replacing the machine leads to lower costs and higher operating income of $120,000—even though 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, which is represented as depreciation in Exhibit 12-12.

Exhibit 12-12 

Cost Comparison: Replacement of Machine, Relevant Items Only, for Toledo Company

Table shows a cost comparison of only the relevant items related to the replacement of machine in addition to the difference between the costs for Toledo Company.

The details of the table under three categories for two years together are as follows. The unavailable data have been marked as nil.

1. The cash operating costs, disposal value of the old machine, the cost of the new machine represented as depreciation, and the total relevant costs of the keep category are:

• Cash operating costs: $1,600,000

• Current disposal value of old machine: Nil

• New machine, written off periodically as depreciation: Nil

• Total relevant costs: $1,600,000

2. The cash operating costs, disposal value of the old machine, the cost of the new machine represented as depreciation, and the total relevant costs of the replace category are:

• Cash operating costs: $920,000

• Current disposal value of old machine: $40,000 within parentheses

• New machine, written off periodically as depreciation: $600,000

• Total relevant costs: $1,480,000

3. The differences in the cash operating costs, disposal value of the old machine, the cost of the new machine represented as depreciation, and the total relevant costs of the keep and replace categories are:

• Cash operating costs: $680,000

• Current disposal value of old machine: $40,000

• New machine, written off periodically as depreciation: $600,000 within parentheses

• Total relevant costs: $120,000