Case Study 1
Springfield Express is a luxury passenger carrier in Texas. All seats are first class, and the following data are available:
Number of seats per passenger train car 90
Average load factor (percentage of seats filled) 70%
Average full passenger fare $ 160
Average variable cost per passenger $ 70
Fixed operating cost per month $3,150,000

a What is the break-even point in passengers and revenues per month?

Break-even point in passengers = fixed operating cost ÷ Contribution Margin Break-even point in passengers = $3,150,000 ÷ ($160 - $70) $3,150,000 ÷ $90 Break-even point in passengers = 35,000

Break-even point in revenue = Break-even point in passengers x Average full passenger fare Break-even point in revenue = 35,000 passengers x $160 Break-even point in revenue = $5,600,000

b What is the break-even point in number of passenger train cars per month?

Break-even point in passenger cars = Fixed expenses ÷ Contribution margin Contribution margin = Number of seats per passenger train car x Average variable cost per passenger x Number of seats per passenger train car Contribution margin = (90 x 70%) x 90 = Contribution margin = 63 x 90 = 5,670 Break-even point in passenger cars = Fixed expenses ÷ Contribution margin Break-even point in passenger cars = $3,150,000 ÷ 5,670 Break-even point in passenger cars = 555.55 or 556

c If Springfield Express raises its average passenger fare to $ 190, it is estimated that the average load factor will decrease to 60 percent. What will be the monthly break-even point in number of passenger cars? Break-even point in passenger cars = fixed operating cost ÷ Contribution Margin
Contribution margin = Average full passenger fare - Average variable cost per passenger x Average load factor x Number of seats per passenger train car Contribution margin = ($190 - $70) x 60% x 90 Contribution margin = $120 x 60% x 90 Contribution margin = 6,480 Break-even point in passenger cars = fixed operating cost ÷ Contribution Margin Break-even point in passenger cars = $3,150,000 ÷ 6,480 Break-even point in passenger cars = 486

d (Refer to original data.) Fuel cost is a significant variable cost to any railway. If crude oil increases by $ 20 per barrel, it is estimated that variable cost per passenger will rise to $ 90. What will be the new break-even point in passengers and in number of passenger train cars?

Break-even point in passenger cars = Fixed expenses ÷ Contribution margin
Contribution margin = Average full passenger fare - Average variable cost per passenger x Average load factor x Number of seats per passenger train car
Contribution margin = ($160 - $90) x 70% x 90
Contribution margin = $70 x 70% x 90
Contribution margin = $49 x 90
Contribution margin = 4,410

Break-even point in passenger cars = $3,150,000 ÷ 4,410
Break-even point in passenger cars = 714.29 or 714

Break-even point in passengers = Fixed expenses ÷ Contribution margin per unit
Break-even point in passengers = $3,150,000 ÷ ($160 - $90)
Break-even point in passengers = $3,150,000 ÷ $70
Break-even point in passengers = 45,000 e Springfield Express has experienced an increase in variable cost per passenger to $ 85 and an increase in total fixed cost to $ 3,600,000. The company has decided to raise the average fare to $ 205. If the tax rate is 30 percent, how many passengers per month are needed to generate an after-tax profit of $ 750,000?

Passengers needed to make a profit = (fixed expenses + profit) ÷ Contribution margin
Profit = After tax profit ÷ Tax rate
Profit = $750,000 ÷ 70%
Profit = $1,071,429

Contribution Margin per passenger = Average passenger fare – Average variable cost per passenger
Contribution Margin per