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

Formula :
Revenue = Units Sold * Unit price
Contribution Margin = Revenue – All Variable Cost
Contribution Margin Ratio = Contribution Margin/Selling Price
Break Even Points in Units = (Total Fixed Costs + Target Profit )/Contribution Margin
Break Even Points in Sales = (Total Fixed Costs + Target Profit )/Contribution Margin Ratio
Margin of Safety = Revenue - Break Even Points in Sales
Degree of Operating Leverage = Contribution Margin/Net Income
Net Income = Revenue – Total Variable Cost – Total Fixed Cost
Unit Product Cost using Absorption Cost = (Total Variable Cost + Total Fixed Cost)/# of units

a. What is the break-even point in passengers and revenues per month?
Contribution margin per passenger = $160 - $70  $90
Contribution margin ratio= $90/$160  56.25%
Break-even point in passengers = Fixed costs/Contribution Margin =3,150,000/$90
Passengers 35,000 passengers
Break-even point in dollars = Fixed Costs/Contribution Margin Ratio = 3,150,000/56.25%
$5,600,000

b. Compute # of seats per train car (remember load factor?) 90 x 70% = 63 seats
If you know # of BE passengers for one train car and the grand total of passengers, you can compute # of train cars (rounded) =35,000 passengers/63 per train car = 555.55 (or) 556 rounded

c. Contribution margin = $190 - $70  $120
Break-even point in passengers = fixed costs/ contribution margin = 3,150,000/$120  26,250
Passengers =26,250
Train cars (rounded) = 26,250/(90 x 60%) = 26,250/54  486.11 (or) 486 rounded.

d. Contribution margin =$160 - $90 = $70
Break-even point in passengers = fixed costs/contribution margin = $3,150,000/$70 Passengers =45,000 Train cars (rounded) = 45,000/(90 x 70%) = 45,000/63 = 714.3 (or) 714 rounded.

e. Before tax profit less the tax rate times the before tax profit = after-tax income =
After-tax required income = $750,000
Before-tax required income = $750,000/(1 - .30)  $1,071,428.57
Then, proceed to compute # of passengers -= 38,929 rounded (workings below)
New contribution margin = $205 - $85 = $120
Target passengers required = (New fixed costs + Target before-tax profit)/New contribution margin
 ($3,600,000 + $1,071,428.57)/$120  38,928.57 (or) 38,929 passengers rounded.

f. # of discounted seats = (90 x 80%) – (90 x 70%) = 72 – 63 = 9 seats
Contribution margin for discounted fares X# of discounted seats = $ each train X$? train cars per day X ? days per month= $? minus $ additional fixed costs = $?pretax income.

Contribution margin for discounted fares = $120 - $70 = $50
Total contribution margin from discounted fares = $50 per seat x 9 seats = $450 per train car
$450 per train car x 50 train cars per day x 30 days per month =