Accounting question

Question

There are three sources of revenue for the concert:
Tickets will be sold for $16.00 each.
A large multinational corporation headquartered in Chicago will donate $2.50 per ticket sold.
Each concert attendee is expected to spend an average of $18.00 for parking, food, and merchandise.

On the expense side, there are also three components:
The band has agreed to perform for $6.00 per ticket sold.
The organizers will pay several companies to operate the parking, food, and merchandise concessions. They will pay $22,000 plus 15% of all parking, food, and merchandise revenue.
The organizers will pay the pavilion $95,000 plus $10.00 per person attending to cover its operating expenses (production, maintenance, advertising, etc.).

Part A
1. What is the estimated contribution margin per ticket sold for the benefit concert?

2. What are the estimated total fixed costs for the benefit concert?

Part B
3. What is the estimated profit from the benefit concert if 12,000 tickets are sold?

4. How many tickets must be sold in order for concert profit to be $90,000?

5. Assuming a tax rate of 39% on profits from the concert, what must dollar ticket sales be in order for after-tax concert profits to be $90,000?

Part C
6. Assume that the organizers can negotiate the fixed payment for the pavilion's operating expenses. If the organizers expect to sell 12,000 tickets, how much can they afford to pay and still earn a profit of $90,000 (ignore taxes)?

Answer 1

1. Revenue per ticket including the donations and attendee spending is $36.50 (16+2.5+18). Contribution margin is defined to be revenue less the variable costs. In this case, the variable costs are the band's $6 fee per ticket sold, the 15%  for parking and such, and the $10 per person operating expenses. Therefore, the contribution margin is 36.5 less 6, less 2.7 (15% of $18), and less 10 which equals $17.8 per ticket. 

 

2. The total fixed costs is the sum of all costs that are not dependent on the number of tickets sold. In this case, the fixed costs are the fixed component of the concessions and such which is $22000 and the fixed component of the operating expenses which is $95000. The 15% and the $10 per person component of the two parts listed above are variable costs since they are dependent on the number of tickets sold. Therefore, those are not included. The fixed cost is then calculated to be $117000.

 

3. The estimated total profit is $96600. You multiply the contribution margin by 12000 which is $213600 and subtract that from the fixed costs. 

 

4. In order to determine the desired profit, you use break even analysis except you want your desired profit to be $90,000. The formula for that is (fixed cost+desired profit) divided by contribution margin per ticket. By substituting the numbers into the equation, you get (117000+90000)/17.8 which gives you 11629.2 tickets. You cannot sell 11629.2 tickets so round up to get 11630 tickets. You must sell 11630 tickets to achieve a $90000 profit before taxes. You can verify by multiplying this figure to the contribution margin and subtracting the fixed costs. It will be above $90000 by a little bit though since I rounded up. 

 

5. This is similar to the previous question except you want to figure out the dollar figure instead of unit figure and there is tax involved. Since you want to earn $90,000 after tax, you simply figure out how much you need to make before tax. In this case, that means you keep 61% of your profits so you must earn $147541 to retain $90000 in profit after tax ($90000/0.61). The formula for break even in dollar sales is different from the above; the formula is (total fixed cost plus desired profit) divided by contribution margin ratio. The contribution margin ratio is simply the contribution margin over revenue, so the ratio for this question is 0.49, or 49%, after rounding to the nearest 10th. With these two figures, you can now calculate the dollar ticket sales by substituting these numbers in the equation to get $539,879.60 (117000+147541)/0.49. You can verify this by dividing this number by the revenue per ticket, multiplying it by the contribution margin ratio, subtracting fixed costs, and multiplying it by 0.61. You should get an answer near $90,000 after that.

 

6. If I'm understanding this part correctly, this part asks us to remove the variable portion of the operating expenses. If that is the case, the contribution margin is no longer $17.8 since the variable component is gone. The contribution margin is now $10 greater since the organizers only want to pay a fixed cost so it would be $27.8. Once again, we want to use break even analysis. The equation is then 12000=((fixed cost+90000)/27.8) since we already know the ticket sales number. By solving for fixed cost, we get that the fixed cost needs to be $243600 by multiplying 12000 by 27.8 and subtracting the product by 90,000. Since we already know one portion of the fixed cost from the parking/concession expenses to be $22000, that means that the organizers can only afford to pay $221600 in fixed costs for the operating expenses (243600-22000). 

 

Hope this helps.