Problem 10 - Accounting

Question

Bunyon Lumber Company incurs a cost of \(\$ 490\) per hundred board feet in processing certain "rough-cut" lumber, which it sells for \(\$ 635\) per hundred board feet. An alternative is to produce a "finished cut" at a total processing cost of \(\$ 565\) per hundred board feet, which can be sold for \(\$ 840\) per hundred board feet. What is the amount of (a) the differential revenue, (b) differential cost, and (c) differential income for processing rough-cut lumber into finished cut?

Step-by-Step Solution

Answer

(a) \$205, (b) \$75, (c) \$130 per hundred board feet

Step 1: Understanding Differential Revenue

Differential revenue is the difference in revenue between two options. For the rough-cut lumber, the selling price is \\(635 per hundred board feet. For finished cut lumber, the selling price is \\)840 per hundred board feet. So, the differential revenue is calculated as \(840 - 635 = \$205 \) per hundred board feet.

Step 2: Calculating Differential Cost

Differential cost is the difference in processing costs between two options. The cost of processing rough-cut lumber is \\(490 per hundred board feet, while the cost for finished cut lumber is \\)565 per hundred board feet. Thus, the differential cost is \(565 - 490 = \$75 \) per hundred board feet.

Step 3: Determining Differential Income

Differential income is the differential revenue minus the differential cost. From the previous steps, the differential revenue is \\(205 and the differential cost is \\)75. Therefore, the differential income is \(205 - 75 = \$130 \) per hundred board feet.

Key Concepts

Differential Revenue

Differential revenue is a key concept in decision-making when comparing two business alternatives. Essentially, it's the additional income generated when switching from one option to another. In the context of our lumber example, the differential revenue refers to the extra money Bunyon Lumber Company earns by choosing to produce finished cut lumber instead of sticking with rough-cut lumber. Think of it as the added boost in revenue from upgrading the product.

Calculating differential revenue involves a simple subtraction of the selling prices. For the rough-cut lumber, the selling price is $635 per hundred board feet. On the other hand, the finished cut lumber brings in $840 per hundred board feet. So, the calculation goes:

• Differential Revenue = Selling price of finished cut - Selling price of rough-cut
• Differential Revenue = $840 - $635
• Differential Revenue = $205 per hundred board feet

This means Bunyon earns an extra $205 for every hundred board feet by selling finished cuts instead of rough cuts.

Differential Cost

When deciding between two options, understanding the differential cost is crucial. The differential cost is the difference in expenses required to handle each option. For Bunyon Lumber Company, this means calculating the added cost associated with processing lumber into finished products rather than stopping at the rough-cut stage.

To determine the differential cost, you subtract the cost of processing for rough-cut products from the cost for finished cuts. In our lumber scenario:

• Cost for rough-cut = $490 per hundred board feet
• Cost for finished cut = $565 per hundred board feet
• Differential Cost = Cost of finished cut - Cost of rough-cut
• Differential Cost = $565 - $490
• Differential Cost = $75 per hundred board feet

Thus, it costs Bunyon an extra $75 per hundred board feet to turn rough-cut lumber into finished lumber. This concept helps in evaluating whether the additional cost is justified by the extra revenue.

Differential Income

Differential income gives an overall picture of the financial impact of switching from one business option to another. It combines both the additional revenue and the extra costs associated with a decision. For Bunyon Lumber Company, differential income determines how profitable it is to refine their product by processing rough-cut lumber into finished cuts.

The differential income is calculated by taking the differential revenue and subtracting the differential costs. From our previous calculations, we have:

• Differential Revenue = $205 per hundred board feet
• Differential Cost = $75 per hundred board feet
• Differential Income = Differential Revenue - Differential Cost
• Differential Income = $205 - $75
• Differential Income = $130 per hundred board feet

This means that every hundred board feet of lumber that Bunyon processes into finished cuts yields an additional profit of $130 compared to producing only rough cuts. Understanding this helps make informed business decisions by analyzing whether the extra effort and cost are worth the additional profit gained.