Jan Van Voorhis is a florist in Boulder, Colorado. Dividing his clients into two major categories, he provides you with the following income statement. He stresses that, for most florists (including himself), each segment accounts for 50% of total revenues.
Required:
a. Suppose Jan allocates common fixed costs equally between the two segments. Treating each segment as a separate business, determine the breakeven revenue for institutional revenues and for retail revenues. Does Jan’s shop, as a whole, break even with these revenues?
b. Assume Jan does not allocate any fixed costs between the two segments (including the traceable fixed costs). Compute Jan’s Weighted Contribution Margin Ratio using the product mix provided in the problem text. What is Jan’s breakeven revenue?
c. Why do the answers for parts (a) and (b) differ? What key feature of Jan’s business is not captured in the answer to part (a)? What do you conclude about the wisdom of allocating common costs and performing breakeven analysis separately by segment?
d. When would a firm perform breakeven analysis for a segment?
SOLUTION
a. The following table provides the required computations.
| Retail | Institutional |
|---|
| Traceable fixed costs | 175,000 | 80,000 |
| Allocated fixed cost | 100,000 | 100,000 |
| Total | 275,000 | 180,000 |
| Contribution margin ratio | 66.67% | 40% |
| Breakeven revenue | $412,500 | $450,000 |
At this volume, Jan breaks even for the entire company as well. After all, his total fixed costs are $175,000 + $80,000 + $200,000 = $455,000. Then, at the computed volumes, he generates a contribution of $412,500 × 0.6667 + $450,000 × 0.4 = $455,000. The firm also breaks even at the total level of $862,500.
b. Jan’s weighted contribution margin ratio is $480,000/$900,000 = 53.33%. With this estimate, we can calculate breakeven revenue as
$455,000 / 0.53333 = $853,125 Or, $426,562.50 each in retail and institutional sales.
c. The answers in parts a and b differ because we “fix” different items. In part (b), we fixed the sales mix to be 50% from each segment. With this assumption, the breakeven sales are $853,125. However, sales mix is not fixed in part (a). Rather, we have “fixed” the allocation to be $100,000 to each segment. Thus, the final answer has a sales mix that is not 50-50 across the segments. Moreover, the fixed cost also is not allocated in proportion to the sales mix at breakeven. In general, it makes more sense to fix the sales mix as in part (b) in multi-product CVP analysis.
d. In general, we perform multi-product CVP for the entire firm. This is particularly appropriate when the products are similar (e.g., car dealership), are substitutes and share considerable fixed cost. However, we also encounter situations in which products are distinct with few common fixed costs. In this case (e.g., divisions of General Electric or John Deere), it makes sense to compute a division level break even.