Question

CVP Analysis

Chapter 5

Gryffindor House is a small theater located in Pittsburgh Pennsylvania. The theater contains 1,500 seats. You have recently been hired to manage the theater.   Profits at the theater have been all over the place and the board would like you to make some recommendations about pricing of tickets. The board would like to make a profit of $50,000 per run.  

There are two shows where some decisions should be made. The first show is Goblets of Fire and the second show is Flight of the Hippogriff.

Below is some information for Goblets of Fire

Ticket price $25

Variable costs $15

Fixed costs 2,000

It is expected that you will have 3 shows and that each show will be about 75% full. For the full run of the show (all 3 shows) For each question below use the information given to answer the question.   Show all work

1. What is the Net Operating Income for this show?
2. What is the Breakeven point for this show in units(seats)? Compare this to the expected number of units sold. Explain how this impacts the theater’s profits
3. Will Goblets of Fire meet the target profit set by the board?  
4. What is the Goblets of Fire’s margin of Safety?
5. You wonder if increasing the number of shows and adding a Thursday night show would increase profits.   Fixed costs would increase by $500.   You expect that you would sell about 60% of seats on a Thursday night. Should you add Thursday night? Explain and be sure to use your calculations to support your argument.

Below is some information for Flight of the Hippogriff

Ticket price $25

Variable costs $10

Fixed costs 4,000

It is expected that you will have 4 shows and that each show will be about 70% full. For the full run of the show (all 4 shows) For each question below use the information given to answer the question.   Show all work

6. What is the Net Operating Income for this show?
7. What is the Breakeven point for this show in units(seats)? Compare this to the expected number of units sold. Explain how this impacts the theater’s profits
8. Will Flight of the Hippogriff meet the target profit set by the board?  
9. What is the margin of Safety?
10. The performers in Flight of Hippogriff like to have a very full audience.   They discuss dropping ticket prices to $20. They think the shows will be 80% full with a price decrease. Do they have a good idea? Explain why or why. Support your position with calculations.
11. The board is thinking about spending an additional $1,500 on advertising. They estimate an increase of 2,000 seats sold. Do they have a good idea? Explain why or why. Support your position with calculations.

12. Calculate the degree of operating leverage for both shows.
13. Compare and contrast the price structure for the two shows? Detail the advantages and disadvantages. Be sure to use vocabulary from chapter 5.
14. Community theater serves a greater purpose than mere profits.   The board would like to raise prices of all tickets to $30. What are your thoughts on the price increase? What are the advantages or disadvantages? Given the information above would you recommend a price increase? Why or why not.

Answer 1

Workings for Goblets of Fire

Given

No. of seats = 1500

No. of shows = 3

Occupancy Level = 75%

Ticket Price = $ 25

Variable Cost = $ 15

Fixed Cost = $ 2,000

1. Computation of Net Operating Income

Net Operating Income = Gross Operating Income - Operating Expenses

Gross Operating Income = No.of shows * No. of seats * Occupancy * Ticket Price

= (3*1500*75%) *$ 25

= (4500*75%) * $ 25

= 3375 * $ 25

= $ 84,375

Operating Expenses = Variable expenses + Fixed Costs

Variable Expenses = No.of shows * No. of seats * Occupancy * Variable Costs

= (3*1500*75%) *$ 15

= (4500*75%) * $ 15

= 3375 * $ 15

= $ 50,625

Operating Costs = $ 50,625 + $ 2,000

= $ 52,625

Net Operating Profits = $ 84,375 - $ 52,625

Net Operating Profit = $ 31,750

2.Break-even point

Break even point = Fixed Costs /( Sales Price per unit - Variable Costs per unit)

= $ 2000/($25 - $ 15)

= 2000/ 10

Break even point = 200 seats

Break even point is lower than the expected number of units sold.The Gryffindor House will make profits if the occupancy per show is more than 200 seats.

3. Status of Target Sales achievement

The operating profits from Goblets of Fire is $ 31,750 which is lower than target profit of $ 50,000 hence it will not able to meet the target set by the Board.

4.Margin of Safety

Margin of Safety = [(Current Sales Level - Break even point)/Current Sales Level] *100

= [(3375-200)/3375] *100

=[3175/3375]*100

= 94.08%

5.Operating profit for Thursday's show

Given

Occupancy = 60%

Fixed Cost = $ 500

Gross Operating Income = 1500*60% * $ 25

= 900 *$ 25

=$ 22,500

Variable Costs = 1500*60% * $ 15

= 900 * $15

= $ 13,500

Net Operating Profit = $ 22,500 - $ 13500 - $ 500

= $ 8,500

Total Operating profit after running Thursday Show = $ 31,750 + $ 8,500

= $ 40,250

After increasing the number of shows by including an extra show on Thursday, the operating profits increased by $ 8,500

Workings for Flight of Hippogriff

Given

No. of seats = 1500

No. of shows = 4

Occupancy Level = 70%

Ticket Price = $ 25

Variable Cost = $ 15

Fixed Cost = $ 4,000

6.Computation of Net Operating Income

Net Operating Income = Gross Operating Income - Operating Expenses

Gross Operating Income = No.of shows * No. of seats * Occupancy * Ticket Price

= (4*1500*70%) *$ 25

= (6000*75%) * $ 25

= 4500 * $ 25

= $ 112,500

Operating Expenses = Variable expenses + Fixed Costs

Variable Expenses = No.of shows * No. of seats * Occupancy * Variable Costs

= (4*1500*70%) *$ 15

= (6000*75%) * $ 15

= 4500 * $ 15

= $ 67,500

Operating Costs = $ 67,500 + $ 4,000

= $ 71,500

Net Operating Profits = $ 112,500 - $ 71,500

Net Operating Profit = $ 41,000

7.Break-even point

Break even point = Fixed Costs /( Sales Price per unit - Variable Costs per unit)

= $ 4000/($25 - $ 15)

= 4000/ 10

Break even point = 400 seats

Break even point is lower than the expected number of units sold.The Gryffindor House will make profits if the occupancy per show is more than 400 seats.

8.Status of Achievement of Profit Targets

The operating profits from Flight of Hippogriff is $ 41,500 which is lower than target profit of $ 50,000 hence it will not able to meet the target set by the Board.

9.Margin of Safety

Margin of Safety = [(Current Sales Level - Break even point)/Current Sales Level] *100

= [(4500-400)/4500] *100

=[4100/4500]*100

= 91.11%

10.If Ticket prices are dropped to $ 20

Net Operating Income = Gross Operating Income - Operating Expenses

Gross Operating Income = No.of shows * No. of seats * Occupancy * Ticket Price

= (4*1500*80%) *$ 20

= (6000*80%) * $ 20

= 4800 * $ 20

= $ 96,000

Operating Expenses = Variable expenses + Fixed Costs

Variable Expenses = No.of shows * No. of seats * Occupancy * Variable Costs

= (4*1500*80%) *$ 15

= (6000*80%) * $ 15

= 4800 * $ 15

= $ 72,000

Operating Costs = $ 72,000 + $ 4,000

= $ 76,500

Net Operating Profits = $ 96,000 - $ 76,000

Net Operating Profit = $ 20,000

The idea is not good as if the idea is implemented,the operating profit will decrease by $ 15,000

11.With Advertisement

Net Operating Income = Gross Operating Income - Operating Expenses

Current Occupancy = 4500.After advertisement additional seats sold is 2000. Hence occupancy = 6500

Gross Operating Income

= (6500) *$ 25

= $ 162,500

Operating Expenses = Variable expenses + Fixed Costs

Variable Expenses = Occupancy * Variable Costs

= (6500) *$ 15

= $ 97,500

Operating Costs = $ 97,500 + $ 4,000 + $ 1,500

= $ 103,500

Net Operating Profits = $ 162,500 - $ 103,500

Net Operating Profit = $ 59,000

The idea is good as if the idea is implemented,the operating profit will increases by $ 18,000

12.Degree of Operating Leverage

Degree of Operating Leverage = %Change in Operating Income / %Change in Sales

Given

Sales in Scenario 1 = $ 96,000

Sales in Scenario 2 = $ 162,500

Sales in Original Scenario = $ 112,500

Operating Profit in Scenario 1 = $ 20,000

Operating Profit in Scenario 2 = $ 59,000

Operating Profit in Original Scenario = $ 41,000

In Scenario -1

% Change in Operating Profits = [($ 41000-$20000)/$ 20000]*100

=[ $21000/$ 20000]*100

1.05*100

=105%

% Change in Sales = [($112500-$96000)/$$96000]*100

=[ $16500/$96000]*100

0.1719*100

=17.19%

Degree of Operating Leverage = 105/17.19

= 6.11

Scenario -2

% Change in Operating Profits = [($ 59000-$41000)/$ 41000]*100

=[ $18000/$ 20000]*100

.4390*100

=43.90%

% Change in Sales = [($162500-$112500)/$$112500]*100

=[ $50000/$112500]*100

0.4444*100

=44.44%

Degree of Operating Leverage = 43.90/44.44

= 0.987

13. Comparison of the price structure of the two shows

The degree of operating leverage in scenario -1 where the price has been reduced to increase occupancy is very high.It means that a small increase in sales will result in a very big increase in operating profits. This means that the operational profits are price sensitive. We should not reduce the price of tickets to occupancy as it would result in a big drop in the operating profits.

The degree of operating leverage in scenarion -2 is less than 1.This means if we incur additional fixed costs to increase the occupancy the impact on the operational profits is not significant.

Looking at the degree of operational leverage in the two scenarios , where price is reduced in one case and additional fixed costs are incurred in the other, we can conclude that Gryffindor House should try to increase its occupancy level through advertisement or other promotional expenses and not through reduction in ticket prices.

14. Proposal to increase the price to $ 30

As seen in point 13 above, the degree of operating leverage with reference to change in price is very high. Hence with a small increase in price the operating profits will increase at a higher rate even if the occupancy level comes down,

Hence, the proposal to increase the ticket price to $ 30 should be accepted.