Theater owners have to make competitive bids for the right to show a movie. They must
sent the film distributor a proposal with
1. The length of run they provide.
2. The percentage of box office revenues that the theater will pay the distributor per
week. This usually on a sliding scale. The distributor may get up to 90% for the first week,
70% for the second, and so forth down to a minimum of 35%.Thus the longer the movie
plays, the smaller the percentage the theater owner pays.
In addition, the theater owner must guarantee a minimum total payment to the film
distributor, even if box office revenues are disastrously weak. For some "blockbuster"
movies, the guarantee may exceed $100,000. This guarantee is a fixed cost as long as the
accumulated sliding scale payments are less than the guarantee. Moreover, the sliding scale
payments become variable costs only to the extend that they exceed the guarantee.
A theater owner, Jane is trying to decide how much to guarantee the distributor for a three-
week run of Rocky IX. She has already decided to offer a 90%, 70%, and 50% sliding scale
over the three-week period. The weekly fixed "house expenses" for rent, climate control,
personnel, advertising, and other items are $5,000. The "house expenses" are fixed for the
entire three-week run of the movie. Allowing for lower prices for children, senior citizens,
and matinees, the average price per ticket is $6.
Jane expects to sell 8,000 tickets during the first week, 6,000 during the second, and 4,000
during the third. Her target operating income is $8,000 for the three week run.
(For purposes of this problem, ignore concession operations, which ordinarily add
significantly to a theater profits.)
REQUIRED:
1. Using Jane's predictions of ticket sales, compute the maximum guarantee that she
should bid.
2. Suppose Jane bids a guarantee of only $60,000. Compute the operating income for
the three-week period if (a) her original target weekly revenues are attained, (b) 65%
of her original target revenues are attained, and (c) 120% of her original target
revenues are attained.
3. Assume that Jane bids a $60,000 guarantee and attains her original target weekly
revenues. Compute (a) the total number of tickets sold where her total costs are no
longer affected by the guarantee, and (b) her breakeven point in terms of tickets
sold.
Hint: Compute (a) before (b). A graph could help.
To answer these questions, we need to follow the given information and calculations step by step. Let's start with the first question:
1. To compute the maximum guarantee that Jane should bid, we need to find the point where the sliding scale payments exceed the guarantee.
First, let's calculate the sliding scale payments for each week:
Week 1: 8,000 tickets * $6 per ticket * 90% = $43,200
Week 2: 6,000 tickets * $6 per ticket * 70% = $25,200
Week 3: 4,000 tickets * $6 per ticket * 50% = $12,000
The total sliding scale payments over the three-week period are $80,400.
Now, let's calculate the fixed costs for the three-week run:
Fixed costs = $5,000 * 3 weeks = $15,000
To find the maximum guarantee that Jane should bid, we need to determine the point where the total sliding scale payments exceed the fixed costs:
Maximum guarantee = Total sliding scale payments - Fixed costs = $80,400 - $15,000 = $65,400
Therefore, Jane should bid a maximum guarantee of $65,400.
2. Now, let's compute the operating income for the three-week period based on different scenarios:
(a) If Jane's original target weekly revenues are attained:
Week 1: 8,000 tickets * $6 per ticket = $48,000
Week 2: 6,000 tickets * $6 per ticket = $36,000
Week 3: 4,000 tickets * $6 per ticket = $24,000
Total revenue = $48,000 + $36,000 + $24,000 = $108,000
Operating income = Total revenue - Fixed costs - Guarantee
= $108,000 - $15,000 - $60,000 (Jane's bid) = $33,000
(b) If 65% of Jane's original target revenues are attained:
Revenues for each week would be 65% of the original target calculated in part (a).
Week 1: $48,000 * 65% = $31,200
Week 2: $36,000 * 65% = $23,400
Week 3: $24,000 * 65% = $15,600
Total revenue = $31,200 + $23,400 + $15,600 = $70,200
Operating income = Total revenue - Fixed costs - Guarantee
= $70,200 - $15,000 - $60,000 = -$4,800 (a loss)
(c) If 120% of Jane's original target revenues are attained:
Revenues for each week would be 120% of the original target calculated in part (a).
Week 1: $48,000 * 120% = $57,600
Week 2: $36,000 * 120% = $43,200
Week 3: $24,000 * 120% = $28,800
Total revenue = $57,600 + $43,200 + $28,800 = $129,600
Operating income = Total revenue - Fixed costs - Guarantee
= $129,600 - $15,000 - $60,000 = $54,600
Therefore, the operating income for the three-week period would be $33,000 if Jane's original target weekly revenues are attained, a loss of -$4,800 if only 65% of the target revenues are attained, and $54,600 if 120% of the target revenues are attained.
3. Now, let's assume Jane bids a guarantee of $60,000 and attains her original target weekly revenues:
To compute the total number of tickets sold where Jane's total costs are no longer affected by the guarantee, we need to find the point where the sliding scale payments exceed the guarantee. Since Jane has bid $60,000, the sliding scale payments are limited by that guarantee.
First, let's calculate the sliding scale payments based on the target weekly revenues:
Week 1: 8,000 tickets * $6 per ticket * 90% = $43,200
Week 2: 6,000 tickets * $6 per ticket * 70% = $25,200
Week 3: 4,000 tickets * $6 per ticket * 50% = $12,000
Total sliding scale payments = $43,200 + $25,200 + $12,000 = $80,400
Since the sliding scale payments ($80,400) exceed the guarantee ($60,000), Jane's total costs are no longer affected by the guarantee. Therefore, the total number of tickets sold in this case is 8,000 + 6,000 + 4,000 = 18,000 tickets.
To calculate the breakeven point in terms of tickets sold, we need to consider the fixed costs and guarantee:
Total fixed costs = $15,000
Breakeven point = (Fixed costs + Guarantee) / Revenue per ticket
= ($15,000 + $60,000) / $6 per ticket = 12,500 tickets
Therefore, the breakeven point in terms of tickets sold would be 12,500 tickets.
In summary:
1. Jane should bid a maximum guarantee of $65,400.
2. The operating income for the three-week period would be $33,000 if Jane's original target weekly revenues are attained, a loss of -$4,800 if only 65% of the target revenues are attained, and $54,600 if 120% of the target revenues are attained.
3. Assuming Jane bids a guarantee of $60,000 and attains her original target weekly revenues, the total number of tickets sold where her total costs are no longer affected by the guarantee is 18,000 tickets. The breakeven point in terms of tickets sold is 12,500 tickets.