Luke Corporation produces a variety of products, each withintheir own division. Last year, the managers at Luke developed andbegan marketing a new chewing gum, Bubbs, to sell in vendingmachines. The product, which sells for $5.60 per case, has not hadthe market success that managers expected and the company isconsidering dropping Bubbs.
The product-line income statement for the past 12 monthsfollows:
| | | | | | |
| Revenue | | | | $ | 14,692,650 | |
| Costs | | | | | | |
| Manufacturing costs | $ | 14,443,895 | | | | |
| Allocated corporate costs (@5%) | | 734,633 | | | 15,178,528 | |
| Product-line margin | | | | $ | (485,878 | ) |
| Allowance for tax (@20%) | | | | | 97,175 | |
| Product-line profit (loss) | | | | $ | (388,703 | ) |
|
All products at Luke receive an allocation of corporate overheadcosts, which is computed as 5 percent of product revenue. The 5percent rate is computed based on the most recent year’s corporatecost as a percentage of revenue. Data on corporate costs andrevenues for the past two years follow:
| Corporate Revenue | Corporate Overhead Costs |
| Most recent year | $ | 113,750,000 | $ | 5,687,500 | |
| Previous year | $ | 76,900,000 | | 4,902,595 | |
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Roy O. Andre, the product manager for Bubbs, is concerned aboutwhether the product will be dropped by the company and has employedyou as a financial consultant to help with some analysis. Inaddition to the information given above, Mr. Andre provides youwith the following data on product costs for Bubbs:
| Month | Cases | Production Costs |
| 1 | 213,500 | $1,151,328 |
| 2 | 220,700 | 1,173,828 |
| 3 | 218,400 | 1,182,481 |
| 4 | 234,500 | 1,198,023 |
| 5 | 250,400 | 1,200,327 |
| 6 | 243,500 | 1,221,173 |
| 7 | 223,700 | 1,196,199 |
| 8 | 250,700 | 1,239,274 |
| 9 | 242,300 | 1,237,726 |
| 10 | 256,100 | 1,249,825 |
| 11 | 253,700 | 1,254,260 |
| 12 | 262,700 | 1,284,951 |
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1. Calculate the break-even for Bubbs in cases per month basedon production fixed costs and the Contribution Margin calculatedabove.
2. Write out a profit formula for Bubbs using Q, CM, and FC asin the prior question. For the desired profit note the after taxprofit is .05 P Q / (1-TX), where P is the selling price per caseand TX is the tax rate. Now solve for Q to determine the number ofcase Bubbs must produce and sell per month to earn a 5% return onrevenues
