Chapter 25, Problem 1MAD

Analyze Pacific Airways

Pacific Airways provides air travel services between Los Angeles and Seattle. Cost information per flight is as follows:

Each flight has a capacity of 150 seats, with an average of 125 seats sold per flight at an average ticket price of $180. Assume Pacific Airways is considering a new service that would provide tickets at half price. Passengers would need to fly standby to receive the discount, but would be provided a flight for a given day of travel. An analysis revealed that an average of 8 existing passengers would use the new discounted tickets for travel. In addition, 15 new passengers would be attracted to the offer.

1. a. Determine the contribution margin per passenger for the full-priced ticket.
2. b. Determine the break-even number of seats sold per flight.
3. c. Determine the contribution margin per passenger for discounted tickets.
4. d. Should Pacific Airways offer the discounted ticket plan? Answer the question by computing the incremental contribution margin per flight for the plan.

To determine

Compute the contribution margin per passenger for the full-priced ticket.

Explanation of Solution

Contribution Margin: The amount of sales revenue remained after the variable costs are incurred is called contribution margin. In other words, contribution margin is the surplus amount of revenue over variable costs.

The following is the formula to calculate the contribution margin:

Contribution Margin = Sales – Variable cost

Calculate the contribution margin per passenger.

$\begin{array}{c}\text{Contribution Margin = Ticket price }-\text{Variable Costs}\\ \text{= \$180 }-\$40\\ \text{= \$140}\end{array}$

The contribution margin per passenger at full fare is $140.

To determine

Compute the break-even number of seats sold per flight.

Explanation of Solution

Break-even: Break even refers to the point where the production can yield all the costs involved and any further production contributes to the profit.

Calculate the break even seats per flight.

$\begin{array}{c}\text{Break-even seats per flight = }\frac{\text{Fixed Costs per Flight}}{\text{Contribution Margin per Passenger}}\\ \text{= }\frac{\text{\$16,100}}{\$140}\\ \text{= 115 seats}\end{array}$

The break even seats per flight are 115 seats.

To determine

Compute the contribution margin per passenger for the discounted tickets.

Explanation of Solution

Contribution Margin: The amount of sales revenue remained after the variable costs are incurred is called contribution margin. In other words, contribution margin is the surplus amount of revenue over variable costs.

Calculate the contribution margin per passenger.

$\begin{array}{c}\text{Contribution Margin = Ticket price }-\text{Variable Costs}\\ \text{= \$90 }-\$40\\ \text{= \$50}\end{array}$

The contribution margin per passenger at discounted fare is $50.

To determine

Compute the incremental contribution margin per flight to decide on the proposal to allow discount.

Explanation of Solution

Contribution Margin: The amount of sales revenue remained after the variable costs are incurred is called contribution margin. In other words, contribution margin is the surplus amount of revenue over variable costs.

Calculate the incremental contribution margin per flight.

$\begin{array}{c}\begin{array}{l}\text{Incremental }\\ \text{Contribution Margin}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Gained Contribution }\\ \text{Margin }\left(1\right)\end{array}\right)-\left(\begin{array}{l}\text{Lost Contribution }\\ \text{Margin }\left(2\right)\end{array}\right)\\ \text{= \$1,150 }-\$1,120\\ \text{= \$30}\end{array}$

The incremental contribution margin per flight is $30.

Working Note (1):

Calculate the lost contribution margin from customers switching tickets.

$\begin{array}{c}\text{Lost Contribution Margin = Number of persons }\times \text{Ticket price}\\ \text{= 8 }\times \$140\\ \text{= \$1,120}\end{array}$

Working Note (2):

Calculate the gained contribution margin from discount customers.

$\begin{array}{c}\begin{array}{l}\text{Gained Contribution }\\ \text{Margin}\end{array}\}\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Number of switching passengers }\\ \text{+Number of new passengers}\end{array}\right)\\ \text{×}\left(\begin{array}{l}\text{Contribution margin}\\ \text{on discount fare tickets}\end{array}\right)\end{array}\right]\\ \text{= }\left[\left(8+15\right)\text{ × \$50}\right]\\ \text{= }23\text{ × \$50}\\ \text{= \$1,150}\end{array}$

Differential Analysis: Differential analysis refers to the analysis of differential revenue which a company could gain or differential cost which a company could incur based on the available alternative options of business.

Prepare the differential analysis table to analyze the effect of the new plan:

Differential Analysis of Company PA
Continue with No Change (Alt. 1) or Offer the Discount Plan (Alt. 2)
February 5
Particulars	No Change (Alternative 1)	Discount Plan (Alternative 2)	Differential Effect (Alternative 2)
Revenues per flight	(3) $22,500	(4) $23,130	$630
Costs per flight:
Plane depreciation	($9,500)	($9,500)	$0
Crew salaries	($900)	($900)	$0
Fuel	(5)  ($4,750)	(6)  ($5,020)	($270)
Ground salaries	(7)  ($2,600)	(8)  ($2,780)	($180)
Airport fees	($2,100)	($2,100)	$0
Passenger services	(9)  ($1,250)	(10)  ($1,400)	($150)
Income per flight	$1,400	$1,430	$30

Table (1)

The differential analysis of Company PA shows that the offer of Discount plan, has a greater differential income of $30.

Working Note (3):

Calculate the revenue per flight for existing plan.

$\begin{array}{c}\text{Revenue = Ticket price }\times \text{Number of seats}\\ \text{= }\$180\times 125\\ \text{= \$22,500}\end{array}$

Working Note (4):

Calculate the revenue per flight for new plan.

$\begin{array}{c}\text{Revenue = }\left(\begin{array}{l}\text{Full price }\times \\ \text{Number of seats}\end{array}\right)+\left(\begin{array}{l}\text{Discount price }\times \\ \text{Number of seats}\end{array}\right)\\ \text{= }\left(\$180\times 117\right)+\left(\$90\times 23\right)\\ =\text{ \$21,060+\$2,070}\\ \text{= \$23,130}\end{array}$

Working Note (5):

Calculate the fuel price for existing plan.

$\begin{array}{c}\text{Fuel Price = Fixed Costs +}\left(\text{Variable Costs}\times \text{Number of passengers}\right)\\ \text{= }\$2,500+\left(\text{\$18}\times 125\right)\\ \text{= }\$2,500+\$2,250\\ \text{= \$4,750}\end{array}$

Working Note (6):

Calculate the fuel price for new plan.

$\begin{array}{c}\text{Fuel Price = Fixed Costs +}\left(\text{Variable Costs}\times \text{Number of passengers}\right)\\ \text{= }\$2,500+\left(\text{\$18}\times 140\right)\\ \text{= }\$2,500+\$2,520\\ \text{= \$5,020}\end{array}$

Working Note (7):

Calculate the ground salaries for existing plan.

$\begin{array}{c}\text{Ground salaries = Fixed Costs +}\left(\text{Variable Costs}\times \text{Number of passengers}\right)\\ \text{= }\$1,100+\left(\text{\$12}\times 125\right)\\ \text{= }\$1,100+\$1,500\\ \text{= \$2,600}\end{array}$

Working Note (8):

Calculate the ground salaries for new plan.

$\begin{array}{c}\text{Ground salaries = Fixed Costs +}\left(\text{Variable Costs}\times \text{Number of passengers}\right)\\ \text{= }\$1,100+\left(\text{\$12}\times \text{ 140}\right)\\ \text{= }\$1,100+\$1,680\\ \text{= \$2,780}\end{array}$

Working Note (9):

Calculate the passenger services cost for existing plan.

$\begin{array}{c}\text{Passenger service cost = Variable Costs }\times \text{Number of passengers}\\ \text{= }\$10\times 125\\ \text{= }\$1,250\end{array}$

Working Note (10):

Calculate the passenger services cost for new plan.

$\begin{array}{c}\text{Passenger service cost = Variable Costs }\times \text{Number of passengers}\\ \text{= }\$10\times 140\\ \text{= }\$1,400\end{array}$