End of Chapter: Cost–Volume

Problem for Self-Study

Wembley Travel Agency specializes in flights between Los Angeles and London. It books passengers on United Airlines at $900 per round-trip ticket. Until last month, United paid Wembley a commission of 10% of the ticket price paid by each passenger. This commission was Wembley’s only source of revenues. Wembley’s fixed costs are $14,000 per month (for salaries, rent, and so on), and its variable costs, such as sales commissions and bonuses, are $20 per ticket purchased for a passenger.

United Airlines has just announced a revised payment schedule for all travel agents. It will now pay travel agents a 10% commission per ticket up to a maximum of $50. Any ticket costing more than $500 generates only a $50 commission, regardless of the ticket price. Wembley’s managers are concerned about how United’s new payment schedule will affect its breakeven point and profitability.

Under the old 10% commission structure, how many round-trip tickets must Wembley sell each month (a) to break even and (b) to earn an operating income of $7,000 per month?
How does United’s revised payment schedule affect your answers to (a) and (b) in requirement 1?

Solution

1. Wembley receives a 10% commission on each ticket: $10 % \times $ 900 = $ 90 .$ Thus,

$\begin{array}{rcl} Selling price & = & $ 90 per ticket \\ Variable cost per unit & = & $ 20 per ticket \\ Contribution margin per unit & = & $ 90 - $ 20 = $ 70 per ticket \\ Fixed costs & = & $ 14,000 per month \end{array}$

a. $\begin{matrix} Breakeven number \\ of tickets \end{matrix} = \frac{Fixed costs}{Contribution margin per unit} = \frac{$ 14,000}{$ 70 per ticket} = 200 tickets$

b. $inline style begin inline style text When?target operating income end text equals straight $ text 7,000 end text thin space text per month end text comma end style$

$\begin{array}{l} \begin{matrix} Quantity of tickets \\ required to be sold \end{matrix} & = & \frac{Fixed costs + Target operating income}{Contribution margin per unit} \\ = & \frac{$ 14,000 + $ 7,000}{$ 70 per ticket} = \frac{$ 21,000}{$ 70 per ticket} = 300 tickets \end{array}$

2. Under the new system, Wembley would receive only $50 on the $900 ticket. Thus,

$\begin{array}{rcl} Selling price & = & $ 50 per ticket \\ Variable cost per unit & = & $ 20 per ticket \\ Contribution margin per unit & = & $ 50 - $ 20 = $ 30 per ticket \\ Fixed costs & = & $ 14,000 per month \end{array}$

a. $\begin{matrix} Breakeven number \\ of tickets \end{matrix} = \frac{$ 14,000}{$ 30 per ticket} = 467 tickets (rounded up)$

b. $\begin{matrix} Quantity of tickets \\ required to be sold \end{matrix} = \frac{$ 21,000}{$ 30 per ticket} = 700 tickets$

The $50 cap on the commission paid per ticket causes the breakeven point to more than double (from 200 to 467 tickets) and the tickets required to be sold to earn $7,000 per month to also more than double (from 300 to 700 tickets). As would be expected, managers at Wembley reacted very negatively to the United Airlines announcement to change commission payments.