Problem 8 - Accounting

Question

A company is considering replacing an old piece of machinery, which cost \(\$ 600,000\) and has \(\$ 350,000\) of accumulated depreciation to date, with a new machine that costs \(\$ 450,000\). The old equipment could be sold for \(\$ 72,000\). The annual variable production costs associated with the old machine are estimated to be \(\$ 165,000\) for eight years. The annual variable production costs for the new machine are estimated to be \(\$ 112,750\) for eight years. a. Determine the total and annualized differential income or loss anticipated from replacing the old machine. b. What is the sunk cost in this situation?

Step-by-Step Solution

Answer

a. Total differential income: \( \$40,000 \). Annualized: \( \$5,000 \) per year. b. Sunk cost: \( \$250,000 \).

Step 1: Identify Initial Costs of the Old Machine

The old machine originally cost \( \\(600,000 \). The accumulated depreciation on the old machine is \( \\)350,000 \).

Step 2: Determine Sunk Costs

Sunk costs are costs that have already been incurred and cannot be recovered. Here, the sunk cost is the original purchase cost minus the accumulated depreciation: \( \\(600,000 - \\)350,000 = \$250,000 \).

Step 3: Calculate Cost Savings per Year With the New Machine

Annual variable production costs with the old machine are \( \\(165,000 \), and with the new machine, they are \( \\)112,750 \). The annual cost saving is \( \\(165,000 - \\)112,750 = \$52,250 \).

Step 4: Calculate the Revenue From Selling the Old Machine

The old machine can be sold for \( \$72,000 \). This is revenue that will offset the cost of the new machine.

Step 5: Determine Initial Investment for the New Machine

The cost of the new machine is \( \\(450,000 \). Taking into account the revenue from selling the old machine, the net investment becomes \( \\)450,000 - \\(72,000 = \\)378,000 \).

Step 6: Calculate Total Differential Income Over Eight Years

The total cost saving over eight years is \( \\(52,250 \times 8 = \\)418,000 \). The differential income over eight years is total savings minus initial investment: \( \\(418,000 - \\)378,000 = \$40,000 \).

Step 7: Calculate Annualized Differential Income or Loss

The annualized differential income is the total differential income divided by the number of years: \( \\(40,000 / 8 = \\)5,000 \) per year.

Key Concepts

Understanding Sunk Costs

Sunk costs are expenditures that have already been incurred and cannot be recovered. In the context of machinery replacement, the sunk cost of the old machine is the original purchase price minus any accumulated depreciation. For the old equipment, the original cost was \(\\(600,000\), with accumulated depreciation of \(\\)350,000\). Thus, the sunk cost here is \(\$250,000\) — the amount that has been expended and isn't recoverable. Sunk costs are important because they should not influence the decision to replace machinery. Decisions should focus on future costs and benefits, ignoring money already spent.

Machinery Replacement Considerations

When considering machinery replacement, it is essential to evaluate both cost savings and future expenses. The company must compare the variable production costs of keeping the old machine versus buying a new one. Alongside identifying the sunk costs, consider the potential sales revenue from disposing of the old machinery. In this exercise, the old machine can be sold for \(\$72,000\), which partially finances the new machine's purchase. Evaluate the costs of the new machine against these revenues to determine the net investment required. This facilitates a more comprehensive understanding of whether or not to replace the existing machinery.

Exploring Variable Production Costs

Variable production costs are expenses that change depending on the level of output. In the machinery replacement scenario, the company must assess the yearly variable costs associated with both machines. For the old machine, these costs are \(\\(165,000\) annually, compared to \(\\)112,750\) for the new machine. This results in annual savings of \(\$52,250\) if the new machine is purchased. Evaluating variable costs is crucial as they directly affect the ongoing profitability and efficiency of the company's operations. Lower variable production costs with the new machine highlight potential for increased profitability.

Maximizing Cost Savings Through Differential Income Analysis

Differential income analysis serves to highlight the financial benefits of alternative choices. For machinery replacement, the relevant cost savings are derived by comparing operation costs and calculating the difference. This analysis in the exercise predicts total cost savings of \(\\(418,000\) over eight years by replacing the machine, with \(\\)40,000\) as differential income when subtracting initial investments. Annually, this results in an additional \(\$5,000\) of savings. Such analysis enables informed decision-making, ensuring that replacement enhances the company's financial health by focusing on future financial impacts rather than past expenditures.