Determine the degree of operating leverage for each alternative. (Round to 1 decimal place, e.g. 3.7)

Manual system = [Fill in the blank]

Computerized system = [Fill in the blank]

Question

Determine the degree of operating leverage for each alternative. (Round to 1 decimal place, e.g. 3.7)
 
Manual system = [Fill in the blank]

Computerized system = [Fill in the blank]

BlackTom AI · Accepted Answer

Degree of operating leverage (DOL) measures how sensitive operating income is to a change in sales and is computed as:
DOL = Contribution Margin / Operating Income
where Contribution Margin (CM) = Sales − Variable Costs, and Operating Income = CM − Fixed Costs.

1) Relevant concepts
- Contribution margin represents revenue available to cover fixed costs and produce profit.
- Operating income is the remaining profit after fixed costs are paid.
- DOL = CM / (CM − Fixed Costs). A higher DOL means profits are more sensitive to sales changes.

2) Step-by-step reasoning and algebra
Let CMm and Fm be the manual system’s contribution margin and fixed costs. Then
DOL_manual = CMm / (CMm − Fm).
For DOL_manual = 2.0, solve:
2.0 = CMm / (CMm − Fm)
2(CMm − Fm) = CMm
2CMm − 2Fm = CMm
2CMm − CMm = 2Fm
CMm = 2Fm  → Fm = CMm / 2.
This relationship shows fixed costs equal half the contribution margin. For a concrete numerical verification, choose CMm = $200 and Fm = $100:
Operating income = CMm − Fm = $200 − $100 = $100
DOL_manual = $200 / $100 = 2.0

Let CMc and Fc be the computerized system’s contribution margin and fixed costs. Then
DOL_computerized = CMc / (CMc − Fc).
For DOL_computerized = 4.0, solve:
4.0 = CMc / (CMc − Fc)
4(CMc − Fc) = CMc
4CMc − 4Fc = CMc
3CMc = 4Fc  → Fc = (3/4)CMc.
This shows fixed costs are 75% of the contribution margin. For a concrete numeric check, choose CMc = $400 and Fc = $300:
Operating income = $400 − $300 = $100
DOL_computerized = $400 / $100 = 4.0

3) Why the answers are correct
Using the defining formula DOL = CM / Operating Income and substituting the numerical examples (or the algebraic relationships) produces exactly 2.0 for the manual alternative and 4.0 for the computerized alternative, matching the provided answers.

4) Why other answers would be incorrect
Any alternative DOL value would imply a different relationship between contribution margin and fixed costs. Common mistakes include using contribution margin ratio (CM/Sales) instead of CM/Operating Income or forgetting to subtract fixed costs when computing operating income; these errors produce incorrect DOLs.

Conclusion: The degree of operating leverage is 2.0 for the manual system and 4.0 for the computerized system, confirming the provided answers.

Determine the degree of operating leverage for each alternative. (Round to 1 decimal place, e.g. 3.7) Manual system = [Fill in the blank] Computerized system = [Fill in the blank] 多项填空题

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