# Accounting exercises 4: Break-even-Analysis

by Clemens Werkmeister

### 1. Standard break-even analysis for city trips

A travel agency is organizing weekend trips to different cities. The package includes the transfer by coach and the overnight stay in a B&B. It is offered for 99 € per person. The coach costs 500 € per weekend, fuel 300 €, the driver 350 € per weekend; administration is charged at 100 € per weekend trip. The B&B costs 55 € per person, the salespersons get a commission of 10 € per passenger.
a. Calculate the fixed and the variable costs of a trip.
b. Calculate the sales revenue and the contribution margin per passenger.
c. Explain the cost-volume-profit-relationship with a break-even-chart.
d. How many passengers will the agency have to find in order to break even?
e. The target profit per trip is 100 €. What happens to the break-even-point?
f. If the travel agency expects 45 passengers. What are the margins of safety, with respect to the two break-even-points?

### 2. Evaluating product concepts with a break-even analyses

The production of a TV game show causes direct costs of 30.000 €. Additio-nally, the host John Doe gets 5.000 € per show and an attendance-related bonus of 1.000 € per percentage point of attendance (ppa, or “Quote”). The show is financed by advertising. There is a fixed sales revenue of 10.000 € per show and atten¬dance-related revenues of 3.000 € per percentage point of attendance.
a. Calculate the profit per show and the way it depends on the attendance.
b. Calculate the break-even-point of the show.
c. The production management is considering to contract Will Willis, the famous game show host. Will asks for a fixed salary of 25.000 € per show. In which case is it worth to contract Will?
d. What happens if the production company is charging an overhead rate of 20 % on all direct costs?

### 3. Package break-even analysis

Lamark Printers Ltd. produces and sells inkjet printer and special ink. Printer manufacturing and selling causes fixed costs of 100.000 € and variable costs of 50 €/printer. Printers are sold for 60 €. Ink cartridges have variable cost of 2 €/ cartridge and are sold for 9 €/cartridges. The fixed costs of ink cartridge merchandising are 10.000 €.
a. Calculate the contribution margins of printers and ink cartridges.
b. What are the individual break-even-points of printers and ink cartridges?
c. Lamark Printers expect to sell 10 ink cartridges for every printer they sell. Calculate the sales revenue, the variable costs and the unit contribution per package. How many packages need to be sold to break-even?

### 4. Multi-product break-even analysis

Hot Coffee Inc’s main product is the Hot Machine, a coffee machine for the strongest and hottest coffee. The machines are produced at the company’s plant with fixed costs of 20.000 € and variable manufacturing costs of 40 €. The machines are sold locally by the sales department and worldwide by the international department. The fixed costs of the sales department are 7.000 €, with variable selling costs of 10 €/machine. The international department causes fixed costs of 10.000 € and variable selling costs of 40 €/machine.
a. Calculate the costs and profit if Hot Coffee is expecting to sell 300 machines at the local market and 200 machines worldwide.
b. Determine the sales of machines on the local and the worldwide market that are necessary to cover the direct fixed costs.
c. Determine the break-even-points for local and worldwide sales, if the joint fixed costs are allocated
- evenly among the two markets
- in proportion to their direct fixed costs
- in proportion to the unit sales price.
d. Explain the cost-volume-profit-relationship with a break-even-chart.
e. Define the break-even-line with respect to direct and joint fixed costs.