Part I
1. A company has a cost of goods sold of $100 per unit on a product sold. The product is sold at a price of $120 per unit. Calculate the percentage markup and percentage margin, respectively.
2. Priyanka makes an investment in Natalie's business for $1000 in 2014 and sold one year later for $1200. Priyanka also invests $2000 in Rahul's business in 2014 and assume for now that definitely received $2,800 in 2017. Calculate the return-on-investment for each stock, and discuss which is the better investment.
3. Why do companies make a distinction between fixed and variable costs?
4. What constitutes a fixed cost or variable cost in the following list?
- Building a factory
- The wages of secretarial staff
- The wages of factory workers
- The cost of advertising to a specific person using an online ad
- Milk and butter used to sell ice cream
Part II
1. Suppose that a firm has a short-run total cost curve given by TC = 7000 - 15Q^2+ Q^3
(a) What are the fixed costs of the firm? The variable costs?
(b) What are the average variable costs?
(c) What is the meaning of marginal costs? What does it help a firm to determine? Derive the marginal cost curve from the total cost curve above.
2. Application of Elasticity (use the official formula, NOT the midpoint)
Use this question for parts a and b: Suppose you work for the university bookstore. The current price of an IIT tee shirt is $15, and the bookstore normally sells 200 per week. The elasticity of demand, based upon prior research, is estimated to be 0.75. In an attempt to raise revenue, the bookstore is considering raising the price to $16.5 (a rise of 10%).
(a) Can you estimate what will happen to quantity demanded? Hint: use the original elasticity formula E = (%changeQ) / (%changeP)
(b) Can you estimate what will happen to revenue? Will it rise or fall? By how much?
Use the demand function for airbags given by the following schedule for part c.
Price Quantity Demanded (At each level)
200 14
150 38
100 56
50 66
(c) What is the total revenue collected by the firm at each price?
(d) If the price drops from $200 to $150, what is the total quantity demanded for the product?
3. Marketing Math Application
Chuck Ravarty is the CEO of Hawkporter, a local transportation company that operates a shuttlebus service between Midway Airport and a number of smaller Illinois towns within a 100 mile radius of the airport. The service operates in both directions and each bus has a maximum capacity of 60 passengers.
In 2004, the company had total transportation (ticket) revenues of $10 million on its Midway business. It operated 5000 trips (a round trip counts as two trips) using its fleet of four buses and carried a total of 250,000 passengers during the year.
Hawkporter's total costs of operations (including maintenance) for 2004 were $6.0 million, yielding a net profit of $4.0 million. Fixed costs include $150,000 for operating the Midway counter and $250,000 for the Chicago office and staff. Depreciation, maintenance and insurance costs per bus are $85,000. The variable cost per incremental passenger is $5. The remaining elements in Hawkporter's operating and maintenance costs (e.g., gas, tolls, driver pay, etc.) vary by number of trips.
(A) What is Hawkporter's contribution margin per (incremental) passenger on its Midway service?
(B) What was Hawkporter's breakeven passenger volume for its 2004 operations (assuming a fixed schedule of 5000 trips using the four buses)?
(C) What was Hawkporter's variable operating cost per (incremental) trip in 2004?
(D) Demand has grown during 2004-05 and projections for 2006 suggest continuing growth. Some of Chuck's drivers have reported significant passenger complaints about crowded or full buses and excessively long waits. In order to improve service quality, Chuck is considering adding another van to his fleet and operating 1,000 more trips in the same service area in 2006 (i.e., a total of 6,000 trips). However, at this new operating level, the fixed depreciation, maintenance and insurance costs will be $100,000 per bus. Variable per trip costs in 2006 will also increase by about $25 due to high fuel costs and increased driver wages. Assuming unchanged ticket prices, what will be Buffporter's breakeven passenger volume for its 2006 operations if Chuck implements this decision (i.e., gets the new bus and operates a schedule of 6,000 trips using five buses)?
(E) Again, assuming unchanged ticket prices, what would the total passenger load need to be for Chuck to make the same profit in 2006 as in 2004 ($4.0 million)?
(F) Chuck is afraid that if he makes no changes to improve customer service, his demand may drop by as much as 10% below the 2004 level. With the improved service, he expects to hold market share even as 2006 demand is expected to be about 10% above the 2004 level. Should Chuck add the bus on purely economic considerations?
(G) Another option for Chuck is to add the bus to improve service, but also to raise the per trip fare by $3.00 across the board. Chuck anticipates that this might result in a somewhat lower demand for his service. Identify the demand levels at which the price increase would leave him worse off in 2006 than (a) improving the service but without a price change in 2006; (b) making no changes in
2006 to improve the service from its 2004 level. Assume variable per trip costs in 2006 will increase as indicated in Part D. (15%)
(H) What advice will you give Chuck based on your analysis? Justify your answer on both financial and marketing considerations.
4. Marketing Math Application #2
3. Marketing Math Application
Atrium, a manufacturer of upscale designer tee-shirts, is considering launching an Internet operation to sell its product direct to consumers in addition to distributing through traditional bricksand-mortar retail stores, which it is currently doing. Management believes an Internet presence should augment its retail operation. Atrium tee-shirts, made of 100% refined woven cotton, feature batik prints. The cost of producing Atrium designer tee-shirts is $5.50 per shirt. Capacity is not expected to be a constraint, and the fixed costs of production are sunk.
Internet: To sell tee-shirts through the Web, the company must hire a Web page architect to design the page and maintain it over the course of a year. The salary for a Web page architect is $60,000, including expenses and benefits. The cost of shipping on Internet orders, which will be included in the retail price of the tee-shirts, is estimated to be $4.20 per shirt.
Retail store distribution: A retail chain has a standing offer to carry Atrium tee-shirts for a year in exchange for a 35% margin (which is the percentage of MSRP that will go to the retail store). For the last several years, this is the arrangement Atrium used for selling its shirts. Additional in-store promotion and a local print advertising campaign for a year will cost Atrium an estimated $89,000.
You may need to make some assumptions. Please state them clearly and show your calculations.
1. If Atrium can sell 7,500 tee-shirts from its Web page, what's the break-even price for online operation? At this price, what is the break-even volume?
2. If a manager came to you with the calculations you did above that suggest profitability of online operations, what possible issues/cautions would you raise? (Hint: is the online division an SBU unrelated to the rest of the company?)
3. If Atrium tee-shirts sell at the MSRP of $32 at the retail stores, how many tee-shirts must Atrium sell to break even on retail operations?
4. If Atrium sells 5,000 tee-shirts online at $40 a piece, what is Atrium's profit for online operation? What is the ROI (return on investment)? (You may need some assumptions on what constitutes an investment for the latter question. State and justify them.)
5. Suppose, Atrium can sell 5,000 tee-shirts at $40 a piece, but if it lowers the price to $35 a piece, it can sell an additional 1,000 tee-shirts. What is the demand elasticity? Is demand elastic?