1.
At the current
price of $6.95, what is the $ contribution margin per unit sold (say in March)?
[The contribution margin per unit sold is equal to Price less Variable Cost]
2.
At the same
price of $6.95, is the extra facility justified, i.e., is there a higher total
contribution margin with the additional facility vs without?
3.
What is the
total contribution margin (across all units sold) in July with and without the
extra facility? [Note that in this exercise profit means contribution margin]
4.
Katja sells
17,000 loaves in July. Of those, 10,000 loaves can be produced in the old
facilities and the new facility satisfies demand for the other 7,000. This new
facility is only needed for this extra demand and it costs $21,000. Does the
total contribution margin on the 7,000 loaves cover this $21,000?
5.
Look at the
table showing the Price-Demand schedule for March. This shows Katja's best
estimates about what sales would be in the month of March at different prices.
What price would you charge (assume that any additional facility for March is
for March alone but needed to be procured for the quarter January to March)?
6.
Look at the
table showing the Price-Demand schedule for August. Work out the optimal price
for August (assuming the demand schedule holds) and remembering Katja already
has the addiitonal facility for July which can be used in August. If she didn't
have the extra facility in July, how much should she charge and how many should
she sell?
7.
Look at the
table showing the Price-Demand schedule for July. What price should Katja
charge (assume the additional facility is needed for July alone if demand is
more than 10,000)?
8.
Why should
Katja not charge $7.15 but sell only 10,000 units (i.e., not expand capacity)?
9.
If the
incremental facility cost decision is across two months, what price will you
charge for July and August?
10.
How should
Katja allocate the $21,000 across July and August?
Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Aradhna Krishna Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Published by WDI Publishing, a division of the William Davidson Institute (WDI) at the University of Michigan. ©2017 Aradhna Krishna. This exercise was developed by Aradhna Krishna (Dwight F. Benton Professor of Marketing) at the University of Michigan’s Ross School of Business. This exercise was prepared exclusively as the basis for class discussion and is not intended to illustrate either effective or ineffective handling of a situation. The exercise should not be considered criticism or endorsement and should not be used as a source of primary data. This exercise series is presented in five short parts (Katja’s Danish Bread exercises A-E). Students are expected to come prepared to class with Exercise A. Exercises B-F are read by students in class and done sequentially during class. Through this series of increasingly more sophisticated exercises, students gain a deep understanding of the connection between price, demand, variable cost, and capacity. Exercise A: Current Pricing Model Katja Jorgenson came from Copenhagen, Denmark to San Francisco as an exchange student while in college. She fell in love with the city and decided to stay on, supporting herself by opening a Danish bread bakery. Danish bread or rugbrød is a very dense bread. It is also a very healthy bread because it is made with rye flour, rye berries (the actual rye grain), oats, and sunflower seeds. Rugbrød is difficult to make, and Katja found a ready market with restaurants and delis. (See Exhibit 1 for a photograph of rugbrød.) Exhibit 1 Rugbrød Source: http://spisogskrid.dk/2012/03/rugbrod/. Accessed 27 Feb. 2017. exercise W80A05 June 1, 2017 revised: January 28, 2022 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 2 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Table 1 shows Katja’s Danish Bread’s revenues, costs and sales from her rugbrød for a recent fiscal year. Although Katja was happy with her success, she wondered if she was doing things right. In particular, she was concerned about pricing—was her price too low? Or, was her price too high? She charged her customers $6.95 for a loaf of rugbrød. Table 1 Revenues, Costs and Sales Total Unit sales 105,000 Revenue $729,750 Rye flour $52,500 Cracked rye berries $26,250 Whole rye berries $26,250 Sunflower seeds $31,500 Sea salt $2,100 Yeasty beer $25,200 Rolled oats $15,750 Kefir $10,500 Labor $134,600 Electricity and water $122,850 Rent for facility with industrial oven $21,000 Overhead allocation $94,500 Total Contribution Margin $166,750 To see how these ingredients are used, a basic recipe for Rugbrød is provided in Appendix A. Information on Demand Katja’s sales each month were 8,000 loaves, except for July when sales were 17,000 loaves.i To calculate total contribution margin, Katja simply took all the costs and divided them by the number of units (bread loaves) sold, as shown in Table 2. i These are slightly simplified numbers. W80A05 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 3 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Table 2 Total Dollar Contribution Margin per Unit Sold Per Rugbrød Unit sales 1 Revenue $6.95 Rye flour $0.50 Cracked rye berries $0.25 Whole rye berries $0.25 Sunflower seeds $0.30 Sea salt $0.02 Yeasty beer $0.24 Rolled oats $0.15 Kefir $0.10 Labor $1.28 Electricity and water $1.17 Rent for facility with industrial oven $0.20 Overhead allocation $0.90 Total Dollar Contribution Margin $1.59 But, Katja began to wonder whether this was the right way to calculate total contribution margin and prices. She had heard that fixed costs should not affect pricing decisions. “Should they?”, she wondered. Information on Cost Katja supposed that rye flour, cracked rye berries, whole rye berries, sunflower seeds, salt, yeasty beer, rolled oats and kefir could be bought in any quantity, and hence they were variable costs—they could vary per the number of loaves produced. However, overhead cost was a fixed cost and did not vary based on the number of loaves produced. She had some uncertainty regarding the categories of labor, electricity and water, and the rent of an additional facility with an industrial oven. In terms of labor, some of her workers were very well trained now in making rugbrød, and she needed to keep them on contract. Thus, Katja felt that $80,000 of labor cost was fixed. The remaining $54,600 (or $0.52 per unit) was variable cost. She felt that electricity and water could also be treated as variable costs. Additional Information on Cost of Facilities Rugbrød, similar to other good quality bread, could not be stored — it was perishable. Katja’s company, called Katja’s Danish Bread, owned some facilities and equipment that were paid off and had little retail value (i.e., Katja had paid off the loans on these facilities and equipment). But, these assets would also be very difficult for her to sell — the equipment was old and likely to break if transported. What’s more, the facility also doubled as her living space. In short, she considered these assets to have zero cost and zero retail value. Nonetheless, these old facilities together could satisfy demand for 10,000 loaves a month. W80A05 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 4 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Recently, however, Katja’s Danish Bread had rented an additional facility with an industrial oven to satisfy the extra demand that took place in July. This rented facility was close in proximity to the original one and had to be rented for a minimum of three months or quarterly. Katja asked herself: should the price of a loaf of rugbrød reflect the rent of this additional facility? The rent of the additional facility was $21,000 for July, August, September and the facility could produce 7,000 loaves every month — yielding a capital cost of $1.00 per loaf if the facility was fully utilized. But, the additional facility was filled to capacity only in July and was not needed for August and September. Katja wondered what to do with this information. W80A05 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 5 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Exercise B: Price in March Katja deliberated whether she should charge lower prices in some months. She also wondered whether she should charge higher prices in July when she had strong demand for her bread. Looking over the calendar year, Katja felt that sales could be increased quite a lot in the month of March if she lowered her prices (Table 3 shows her best guess for the price-demand relationship). This price- demand relationship was the “expected” demand curve—what Katja expected sales to be at different price points. This type of data was very tough to get—one needed to do surveys or field studies, and even then the data was still prone to error. Alternatively, she could just make a best guess, but that could have an even higher margin of error. Nonetheless, that was what she had to work with. Reviewing all her data, Katja wondered what price she should charge. To simplify her calculations, she decided to assume that any additional facility for March was for March alone but needed to be procured for the quarter of January-February-March. The facility cost $21,000 to rent. She also assumed that the price in January and February would remain $6.95 with sales of 8,000 loaves. Table 3 Price - Demand Schedule for March Price Volume $6.95 8,000 $6.75 10,000 $6.55 12,000 $6.45 12,500 $6.00 15,000 $5.85 15,300 $5.70 15,500 For her calculations, she remembered that: • demand in each month was 8,000 (at $6.95) except for July, when it was 17,000 (also at $6.95). • the old facility produced 10,000 loaves per month. • the rented facility produced 7,000 more loaves in July, August, September, and cost an additional $21,000. Katja began running the numbers to determine what price she should charge in March. A different thought also occurred to Katja. What if the same numbers held for August—would she make the same decision? (Remember that Katja already has the new facility for July which can be used for August, as well.) W80A05 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 6 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Exercise C: Price in July Next, Katja stepped back to determine if producing 17,000 loaves in July and selling them at $6.95 was the best decision to make; and whether she should be renting the additional facility for July at all. She made some estimates for what sales would be in the month of July at different price points (see Table 4). What price would be the best price for her to charge? (For simplicity, assume that Katja would need an additional rental facility for July alone if demand was greater than 10,000 loaves; and that she would not need this for August and September). Table 4 Price - Demand Schedule for July Price Volume $7.55 8,500 $7.45 10,000 $7.35 10,500 $7.25 12,000 $7.15 13,500 $7.05 15,000 $6.95 17,000 W80A05 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 7 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Exercise D: Pricing Decision over July and August Having calculated the numbers for July, Katja started thinking that she should not rent the additional facility for July alone. So, next Katja decided to look at both July and August together (see Table 5). (She could have also considered September since the additional facility was also rented for September, but she decided to ignore that for now because the computation for three months would be similar to that for two months, and she wanted to keep it simple). What prices should she charge in July and August if the incremental fixed cost (i.e., the rent for the additional facility) is borne across these two months? Table 5 Price-Demand Schedule for July and August August July Price Volume Price Volume $6.95 8,000 $7.55 8,500 $6.75 10,000 $7.45 10,000 $6.55 12,000 $7.35 10,500 $6.45 12,500 $7.25 12,000 $6.00 15,000 $7.15 13,500 $5.85 15,300 $7.05 15,000 $5.70 15,500 $6.95 17,000 * Not accounting for any additional facility cost. Katja wondered what other scenarios she could test. W80A05 Do N ot C op y or P os t This document is authorized for educator review use only by Virgilio Pernito, HE OTHER until Sep 2023. Copying or posting is an infringement of copyright.
[email protected] or 617.783.7860 8 Katja’s Danish Bread: Exercises in Price, Demand, Cost, and Capacity Exercise E: Pricing Decision over January, February and March What if the same price and demand schedule that held for March also held for January and February? Katja considered whether doing her calculations over a quarter (vs. for March alone, as in Exercise B) would lead her to price her bread differently for the January, February and March timeframe. Remember that the demand schedule for March is: Price - Demand Schedule for March Price Volume $6.95 8,000 $6.75 10,000 $6.55 12,000 $6.45 12,500 $6.00 15,000 $5.85 15,300 $5.70