Question

break-even sales and sales mix for a service company

zero turbulence airline provides air transportation services between los angeles, california, and kona, hawaii. a single los angeles to kona round-trip flight has the following operating statistics:

fuel: $7,000
flight crew salaries: 3,200
airplane depreciation: 3,480
variable cost per passenger-business class: 140
variable cost per passenger-economy class: 120
round-trip ticket price-business class: 800
round-trip ticket price-economy class: 300

it is assumed that the fuel, crew salaries, and airplane depreciation are fixed, regardless of the number of seats sold for the round-trip flight.

a. compute the break-even number of seats sold on a single round-trip flight for the overall company product, m. assume that the overall product mix is 10% business class and 90% economy class tickets.
total number of seats at break-even: seats

b. how many business class and economy class seats would be sold at the break-even point?
business class seats at break-even: seats
economy class seats at break-even: seats

Explanation:

Calculate total fixed costs

$$ \text{Total Fixed Costs} = \text{Fuel} + \text{Flight crew salaries} + \text{Airplane depreciation} $$

$$ \text{Total Fixed Costs} = \$7,000 + \$3,200 + \$3,480 = \$13,680 $$

Calculate unit contribution margins and weighted average contribution margin

$$ \text{UCM}_{\text{Business}} = \text{Price}_{\text{Business}} - \text{Variable Cost}_{\text{Business}} = \$800 - \$140 = \$660 $$

$$ \text{UCM}_{\text{Economy}} = \text{Price}_{\text{Economy}} - \text{Variable Cost}_{\text{Economy}} = \$300 - \$120 = \$180 $$

$$ \text{Weighted Average UCM} = (0.10 \times \$660) + (0.90 \times \$180) = \$66 + \$162 = \$228 $$

Calculate break-even seats and allocation by class

$$ \text{Total Break-Even Seats} = \frac{\text{Total Fixed Costs}}{\text{Weighted Average UCM}} = \frac{\$13,680}{\$228} = 60 \text{ seats} $$

$$ \text{Business Class Seats} = 60 \times 0.10 = 6 \text{ seats} $$

$$ \text{Economy Class Seats} = 60 \times 0.90 = 54 \text{ seats} $$

Answer:

Question a

Total number of seats at break-even: <blank>60</blank> seats

Question b

Business class seats at break-even: <blank>6</blank> seats
Economy class seats at break-even: <blank>54</blank> seats