I don't know which formulas to use for these questions.
Many churches sponsor bingo games, a tradition stemming from the time when only specific nonprofit
institutions were allowed to sponsor games of chance. Reverend Justin Olds, the pastor of a new parish in Orange County, is investigating the desirability of conducting weekly bingo nights.
The parish has no hall, but a local hotel would be willing to commit its hall for a lump-sum rental of
$600 per night. The rent would include cleaning, setting up and taking down the tables and chairs,
and so on.
1. A local printer would provide bingo cards in return for free advertising. Local merchants would
donate door prizes. The services of clerks, callers, security force, and others would be donated by
volunteers. Admission would be $4.00 per person, entitling the player to 1 card; extra cards would
be $1.50 each. Many persons buy extra cards so there would be an average of 4 cards played per person. What is the maximum in total cash prizes that the church may award and still break even
if 200 persons attend each weekly session?
2. Suppose the total cash prizes are $1,100. What will be the church’s operating income if 100 persons
attend? If 200 persons attend? If 300 persons attend? Briefly explain the effects of the cost behavior on income.
3. After operating for 10 months, Reverend Olds is thinking of negotiating a different rental
arrangement but keeping the prize money unchanged at $1,100. Suppose the rent is $200 per night plus $2 per person. Compute the operating income for attendance of 100, 200, and 300 persons,
respectively. Explain why the results differ from those in requirement 2.
1) 4+1.5+1.5+1.5=8.5 per person spent. (4 cards per person, first costs 4, next three cost 1.5 each).
8.5(per person) * 200(people) = $1700
$1700 - $600 (rent) = $1100.
$1,100 could be spent in prizes and still break even.
2) If 100 people attended ($850 total revenue), then the church would operate at a significant loss.
$850-$600 (rent) = $250 - $1,100 = ($850)
An $850 loss would be taken each night. Already did 200, and if 300 attend then:
300 * 8.5 = 2550
2550-600=1950-1100=850 (profit of 850)
And on and on...
As more people attend, you make more since the cost doesn't change based on how many people are there (it's all fixed cost according to the problem).
3) Now the problem changes. Fixed costs are now 200, and variable costs are 2. Basically, that means that instead of taking in 8.50 per person, $2 of each 8.50 goes to cost. That means that now each customer brings 6.50 to cover that fixed cost. Now, 6.50 * 100= 650, 6.50 * 200= 1300, 6.50 * 300=1950. You've got to cover 200 in rent, and 1100 in prizes. You cannot do that with only 100 people attending, as you can see you'll take a loss of 650 in that scenario. You must have 200 show up to break even, and 300 will generate a profit. The results are different because less profit (although the same amount of revenue) is generated per person in this new scenario, as a variable cost has been introduced.
To answer these questions, we need to use various formulas related to revenue, cost, and income. Let's break it down step-by-step:
1. To find the maximum total cash prizes that the church may award and still break even if 200 persons attend each weekly session, we need to calculate the total costs and then subtract them from the revenue.
a. Revenue formula:
Total Revenue = (Admission Price x Number of Attendees) + (Extra Card Price x Average Extra Cards Sold per Person x Number of Attendees)
In this case:
Admission Price = $4.00
Number of Attendees = 200
Extra Card Price = $1.50
Average Extra Cards Sold per Person = 4
Total Revenue = (4 x 200) + (1.50 x 4 x 200)
b. Cost formula:
Total Cost = Rental Cost
In this case, the Rental Cost is a lump-sum rental of $600 per night.
Total Cost = $600
c. Maximum Total Cash Prizes (Break-even point) formula:
Maximum Total Cash Prizes = Total Revenue - Total Cost
Substituting the values:
Maximum Total Cash Prizes = (4 x 200) + (1.50 x 4 x 200) - $600
Now, you can calculate the maximum total cash prizes the church may award and still break even.
2. To calculate the church's operating income at different levels of attendance with total cash prizes of $1,100, we need to consider the revenue and costs.
a. Revenue formula:
Total Revenue = (Admission Price x Number of Attendees) + (Extra Card Price x Average Extra Cards Sold per Person x Number of Attendees)
In this case:
Admission Price = $4.00
Extra Card Price = $1.50
Average Extra Cards Sold per Person = 4
b. Cost formula:
Total Cost = Rental Cost
In the given scenario, the Rental Cost is a lump-sum rental of $600 per night.
c. Operating Income formula:
Operating Income = Total Revenue - Total Cost
Substituting the given values:
For 100 attendees:
Total Revenue = (4 x 100) + (1.50 x 4 x 100)
Total Cost = $600
Operating Income = (4 x 100) + (1.50 x 4 x 100) - $600
You can repeat the above calculations for 200 attendees and 300 attendees to find the church's operating income at different attendance levels.
3. To calculate the church's operating income with a different rental arrangement and total cash prizes of $1,100, we need to modify the cost formula.
a. Revenue formula:
Total Revenue = (Admission Price x Number of Attendees) + (Extra Card Price x Average Extra Cards Sold per Person x Number of Attendees)
In this case:
Admission Price = $4.00
Extra Card Price = $1.50
Average Extra Cards Sold per Person = 4
b. Cost formula:
Total Cost = Rental Cost + (Additional Cost per Person x Number of Attendees)
In this case:
Rental Cost = $200 per night
Additional Cost per Person = $2.00
c. Operating Income formula:
Operating Income = Total Revenue - Total Cost
Substitute the given values:
For 100 attendees:
Total Revenue = (4 x 100) + (1.50 x 4 x 100)
Total Cost = (200 x 1) + (2 x 100)
Operating Income = (4 x 100) + (1.50 x 4 x 100) - ((200 x 1) + (2 x 100))
Repeat the above calculations for 200 attendees and 300 attendees to find the church's operating income at different attendance levels. The difference from requirement 2 comes from the change in rental cost structure.
Please note that the calculations provided are based on the information given in the question.
To answer these questions, we will need to make some calculations and use some formulas. I will guide you through the steps and explain the formulas along the way.
1. Let's start with the first question: What is the maximum in total cash prizes that the church may award and still break even if 200 persons attend each weekly session?
To break even, the total revenue from ticket sales must cover the expenses, including the rental fee, the cost of printing the bingo cards, and any additional expenses. The revenue will come from the admission fee and the sale of extra cards.
First, calculate the revenue from the admission fee:
- The admission fee is $4.00 per person.
- Since 200 people attend each session, the revenue from the admission fee would be 200 x $4.00 = $800.00.
Next, calculate the revenue from the sale of extra cards:
- The average number of extra cards played per person is given as 4.
- The cost of each extra card is $1.50.
- So, the revenue from the sale of extra cards would be 200 x 4 x $1.50 = $1,200.00.
Now, calculate the total revenue:
- The total revenue is the sum of the revenue from the admission fee and the revenue from the sale of extra cards.
- Total revenue = $800.00 + $1,200.00 = $2,000.00.
To break even, the total expenses must be equal to the total revenue. The expenses include the rental fee, the cost of printing the bingo cards, and any additional expenses.
- The rental fee for the hall is $600.00 per night.
- Printing the bingo cards is provided for free in return for advertising, so there is no cost for that.
Therefore, the maximum in total cash prizes that the church may award and still break even is $2,000.00 - $600.00 = $1,400.00.
2. Now let's move on to the second question: What will be the church's operating income if 100 persons attend? If 200 persons attend? If 300 persons attend?
To calculate the operating income, we need to consider the revenue from ticket sales and subtract the expenses.
The revenue will come from the admission fee and the sale of extra cards, and the expenses include the rental fee.
For each attendance scenario, we will calculate the revenue and the expenses separately:
- If 100 persons attend:
- Revenue from the admission fee: 100 x $4.00 = $400.00
- Revenue from the sale of extra cards: 100 x 4 x $1.50 = $600.00
- Total revenue: $400.00 + $600.00 = $1,000.00
- Expenses (rental fee): $600.00
Operating income: $1,000.00 - $600.00 = $400.00
- If 200 persons attend (already calculated in question 1):
- Revenue from the admission fee: 200 x $4.00 = $800.00
- Revenue from the sale of extra cards: 200 x 4 x $1.50 = $1,200.00
- Total revenue: $800.00 + $1,200.00 = $2,000.00
- Expenses (rental fee): $600.00
Operating income: $2,000.00 - $600.00 = $1,400.00
- If 300 persons attend:
- Revenue from the admission fee: 300 x $4.00 = $1,200.00
- Revenue from the sale of extra cards: 300 x 4 x $1.50 = $1,800.00
- Total revenue: $1,200.00 + $1,800.00 = $3,000.00
- Expenses (rental fee): $600.00
Operating income: $3,000.00 - $600.00 = $2,400.00
The effect of cost behavior on income can be observed by comparing the changes in attendance and the resulting revenue and expenses. As the number of attendees increases, the revenue from ticket sales increases, resulting in higher operating income. However, the rental fee remains the same in this scenario, so the increase in expenses is not proportional to the increase in revenue.
3. Moving on to the third question: Compute the operating income for attendance of 100, 200, and 300 persons, respectively, assuming a different rental arrangement but keeping the prize money unchanged at $1,100.
In this scenario, the rental arrangement is changed, and the expenses will now include the new rental fee. The rental fee is given as $200 per night plus $2 per person.
- If 100 persons attend:
- Rental fee: $200.00 + (100 x $2.00) = $200.00 + $200.00 = $400.00
- Expenses (rental fee): $400.00
- Operating income: $1,000.00 - $400.00 = $600.00
- If 200 persons attend:
- Rental fee: $200.00 + (200 x $2.00) = $200.00 + $400.00 = $600.00
- Expenses (rental fee): $600.00
- Operating income: $1,400.00 - $600.00 = $800.00
- If 300 persons attend:
- Rental fee: $200.00 + (300 x $2.00) = $200.00 + $600.00 = $800.00
- Expenses (rental fee): $800.00
- Operating income: $2,400.00 - $800.00 = $1,600.00
The results differ from those in requirement 2 because the rental fee is calculated differently in this scenario, which affects the total expenses and, consequently, the operating income.