GB519 Unit 3 Break-Even Analysis Example

What an Eight-Dollar Cut Must Win: A Unit 3 Break-Even Analysis of a Lab's Foot Orthosis Price

[Student Name]

Purdue University Global

GB519: Measurement and Decision Making

Unit 3 Break-Even Analysis

[Instructor Name]

[Date]

The lab, its clinics and every figure are composite and illustrative; the sources cited are real.

The Proposal

Fernhill Orthotic Lab sells custom foot orthoses to podiatry and orthotic clinics at $88 a pair. An online fabrication lab has begun quoting $79, and two of Fernhill's larger clinic accounts, together about 1,400 pairs a year, have asked for a match. A podiatry group that does not yet use Fernhill has said it would send about 1,800 pairs a year at $80. The sales director proposes cutting the price to $80 for every clinic.

The Inputs, Stated Once

Price: $88 now; $80 proposed.

Variable cost per pair: $46, made up of $9.40 of shell and top-cover materials, $27.20 of technician time and $9.40 of variable overhead such as oven power and mill tooling.

Fixed cost traceable to the foot orthosis line: $504,000 a year, covering its technicians' base hours, the scanning software, a share of the mill lease and the line's quality staff.

Current volume: 16,000 pairs a year.

Fixed costs shared with the other lines, such as the building lease and the billing office, are left out because the price decision does not change them. Datar and Rajan (2021) recommend this treatment when a cost-volume-profit analysis is run for one product line.

Exhibit 1: Base Against Proposal

Contribution per pair: $42 at $88; $34 at $80, a fall of 19.0 percent.

Contribution margin ratio: 47.7 percent at $88; 42.5 percent at $80.

Break-even volume: 504,000 divided by 42, or 12,000 pairs, at $88; 504,000 divided by 34, or about 14,824 pairs, at $80.

Profit at current volume: 16,000 times 42, less 504,000, or $168,000, at $88; 16,000 times 34, less 504,000, or $40,000, at $80.

Volume needed to hold $168,000 of profit at $80: 504,000 plus 168,000, divided by 34, or about 19,765 pairs.

Increase required: about 3,765 pairs, or 23.5 percent.

Margin of safety: 25.0 percent at $88; about 7.4 percent at $80 if volume stays at 16,000.

An eight-dollar cut, a little over 9 percent of the price, takes nearly a fifth of the contribution and requires almost a quarter more volume just to stand still.

Exhibit 2: The Requirement Against the Offers

The cut must win about 3,765 new pairs. What is actually on offer is smaller:

The podiatry group: about 1,800 new pairs a year.

The two accounts at risk: about 1,400 pairs, which the cut would keep rather than add.

Single-shift capacity: about 20,500 pairs a year, so the requirement could be produced but not without nearly filling the line.

With the cut and the podiatry group's volume, Fernhill would sell about 17,800 pairs at $34 of contribution, earning $101,200, or $66,800 less than today. Even if the two at-risk accounts were lost at $88, profit would be $109,200, still higher than with the across-the-board cut.

Exhibit 3: The Profit Lines

On a graph with pairs on the horizontal axis and profit on the vertical, both lines start at a loss of $504,000 at zero volume. The $88 line rises at $42 a pair and crosses zero at 12,000; the $80 line rises more slowly at $34 and crosses at 14,824. At 16,000 pairs the gap between them is $128,000. The lines never meet, so at every volume the cut earns less unless it wins new volume.

The Alternative: A Volume Tier

A tiered price offers $80 only to clinics that send more than 1,200 pairs a year, which today means the two at-risk accounts and the podiatry group. Everyone else stays at $88.

Under that tier, 14,600 pairs at $42 contribute $613,200; the at-risk accounts' 1,400 pairs at $34 contribute $47,600; and the podiatry group's 1,800 pairs at $34 contribute $61,200. Less $504,000 of fixed cost, profit is about $218,000, about $50,000 more than today and $116,800 more than under the across-the-board cut.

Marn and Rosiello (1992) found that small changes in realized price move operating profit far more than equal changes in volume, which is why discounts should be granted where they buy volume and withheld where they do not. Nagle et al. (2023) add that a tier tied to a clear rule, such as annual volume, is easier to defend to other customers than a private discount.

Recommendation

Decline the across-the-board cut. Introduce an $80 tier for clinics sending more than 1,200 pairs a year, offer it to the two accounts and the podiatry group now, and review the threshold each year.

Risks

The tier's main risk is that smaller clinics learn of it and demand the same price; a published volume rule answers that better than a private discount. The online lab could cut again, and some clinics value turnaround and fit more than price, which Fernhill should measure through its remake rate before matching further. The analysis also assumes variable cost holds at $46; a rise in shell material prices would narrow every margin above. Garrison et al. (2021) note that cost-volume-profit analysis holds price, cost and mix constant, so it should be rerun if any of them change.

References

Datar, S. M., & Rajan, M. V. (2021). Horngren's cost accounting: A managerial emphasis (17th ed.). Pearson.

Garrison, R. H., Noreen, E. W., & Brewer, P. C. (2021). Managerial accounting (17th ed.). McGraw Hill.

Marn, M. V., & Rosiello, R. L. (1992). Managing price, gaining profit. Harvard Business Review, 70(5), 84-94.

Nagle, T. T., Müller, G., & Gruyaert, E. (2023). The strategy and tactics of pricing: A guide to growing more profitably (7th ed.). Routledge.