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Differential revenue is a key concept in decision-making processes, especially when comparing two business scenarios. To better understand this, let's look at how the Daniels Lumber Company calculates differential revenue when choosing between selling rough-cut versus finished-cut lumber.

• The rough-cut sells for \(615 per hundred board feet.
• The finished-cut sells for \)820 per hundred board feet.

The differential revenue is the extra amount earned by choosing one option over the other. Here, it is the difference between the revenue from finished-cut and rough-cut lumber. This can be calculated as:\[ \text{Differential Revenue} = \text{Revenue from Finished-Cut} - \text{Revenue from Rough-Cut} \]Plugging in the values, we have: \[ \text{Differential Revenue} = 820 - 615 = 205 \]Hence, the differential revenue is $205 per hundred board feet, indicating the extra income from selling finished-cut lumber over its rough-cut counterpart.

Differential cost helps businesses evaluate the additional expenses incurred when opting for one option over another. For Daniels Lumber Company, this involves assessing the costs of producing rough-cut versus finished-cut lumber.

• The cost of rough-cut is \(445 per hundred board feet.
• The cost of finished-cut is \)560 per hundred board feet.

To find the differential cost, calculate the difference in processing costs between these two options. The formula is: \[ \text{Differential Cost} = \text{Cost of Finished-Cut} - \text{Cost of Rough-Cut} \]Substitute the given values: \[ \text{Differential Cost} = 560 - 445 = 115 \]Thus, the differential cost is $115 per hundred board feet. This amount reflects the additional cost of processing finished-cut lumber compared to rough-cut.

Differential income represents the net benefit of choosing one business alternative over another by considering both revenues and costs. In Daniels Lumber Company's case, differential income informs the decision of opting for finished-cut lumber.
The differential income can be calculated by finding the difference between differential revenue and differential cost: \[ \text{Differential Income} = \text{Differential Revenue} - \text{Differential Cost} \]From the earlier calculations:

• Differential Revenue is \(205.
• Differential Cost is \)115.

Substituting these values gives: \[ \text{Differential Income} = 205 - 115 = 90 \]Hence, the differential income is $90 per hundred board feet. This reflects the additional profit generated per hundred board feet when choosing the finished-cut lumber over rough-cut, considering both increased sales revenue and higher processing costs.