CHAPTER 3



AIM 2302

SOLUTIONS TO CVP PROBLEMS

1. CVP computations.

| | |Variable |Fixed |Total |Operating |Contribution |Contribution |

| |Revenues |Costs |Costs |Costs |Income |Margin |Margin % |

| | | | | | | | |

|a. |$2,000 |$ 500 |$300 |$ 800 |$1,200 |$1,500 |75.0% |

|b. |2,000 |1,500 |300 |1,800 |200 |500 |25.0% |

|c. |1,000 |700 |300 |1,000 |0 |300 |30.0% |

|d. |1,500 |900 |300 |1,200 |300 |600 |40.0% |

2. CVP computations.

Part A:

Sales ($25 per unit × 180,000 units) $4,500,000

Variable costs ($20 per unit × 180,000 units) 3,600,000

Contribution margin $ 900,000

Contribution margin (from above) $ 900,000

Fixed costs 800,000

Operating income $ 100,000

Part B:

Sales (from above) $4,500,000

Variable costs ($10 per unit × 180,000 units) 1,800,000

Contribution margin $2,700,000

Contribution margin $2,700,000

Fixed costs 2,500,000

Operating income $ 200,000

Part C:

Operating income is expected to increase by $100,000 if Ms. Schoenen’s proposal is accepted.

The management would consider other factors before making the final decision. It is likely that product quality would improve as a result of using state of the art equipment. Due to increased automation, probably many workers will have to be laid off. Patel’s management will have to consider the impact of such an action on employee morale. In addition, the proposal increases the company’s fixed costs dramatically. This will increase the company’s operating leverage and risk.

3. CVP analysis, changing revenues and costs.

Part A:

1. SP = 8% × $1,000 = $80 per ticket

VCU = $35 per ticket

CMU = $80 – $35 = $45 per ticket per ticket

FC = $22,000 a month

Q = [pic] = [pic]

= 489 tickets (rounded up)

2. Q = [pic] = [pic]

= [pic]

= 712 tickets (rounded up)

Part B:

1. SP = $80 per ticket

VCU = $29 per ticket

CMU = $80 – $29 = $51 per ticket

FC = $22,000 a month

Q = [pic] = [pic]

= 432 tickets (rounded up)

2. Q = [pic] = [pic]

= [pic]

= 628 tickets (rounded up)

3. CVP analysis, changing revenues and costs – Continued:

Part C:

1. SP = $48 per ticket

VCU = $29 per ticket

CMU = $48 – $29 = $19 per ticket

FC = $22,000 a month

Q = [pic] = [pic]

= 1,158 tickets (rounded up)

2. Q = [pic] = [pic]

= [pic]

= 1,685 tickets (rounded up)

Part D:

1. The $5 delivery fee can be treated as either an extra source of revenue (as done below) or as a cost offset. Either approach increases UCM by $5:

SP = $53 ($48 + $5) per ticket

VCU = $29 per ticket

CMU = $53 – $29 = $24 per ticket

FC = $22,000 a month

Q = [pic] = [pic]

= 917 tickets (rounded up)

2. Q = [pic] = [pic]

= [pic]

= 1,334 tickets (rounded up)

4. CVP exercises.

| | | | | | | | | |Budgeted |

| | | |Variable | |Contribution | |Fixed | |Operating |

| |Revenues | |Costs | |Margin | |Costs | |Income |

|Orig. |$10,000,000G | |$8,200,000G | |$1,800,000 | |$1,700,000G | |$100,000 |

|a. |10,000,000 | |8,020,000 | |1,980,000a | |1,700,000 | |280,000 |

|b. |10,000,000 | |8,380,000 | |1,620,000b | |1,700,000 | |(80,000) |

|c. |10,000,000 | |8,200,000 | |1,800,000 | |1,785,000c | |15,000 |

|d. |10,000,000 | |8,200,000 | |1,800,000 | |1,615,000d | |185,000 |

|e. |10,800,000e | |8,856,000f | |1,944,000 | |1,700,000 | |244,000 |

|f. |9,200,000g | |7,544,000h | |1,656,000 | |1,700,000 | |(44,000) |

|g. |11,000,000i | |9,020,000j | |1,980,000 | |1,870,000k | |110,000 |

|h. |10,000,000 | |7,790,000l | |2,210,000 | |1,785,000m | |425,000 |

Gstands for given.

a$1,800,000 × 1.10; b$1,800,000 × 0.90; c$1,700,000 × 1.05; d$1,700,000 × 0.95; e$10,000,000 × 1.08; f$8,200,000 × 1.08; g$10,000,000 × 0.92; h$8,200,000 × 0.92; i$10,000,000 × 0.10; j$8,200,000 × 1.10; k$1,700,000 × 1.10; l$8,200,000 × 0.95; m$1,700,000 × 1.05

5. CVP exercises.

1a. [Unit’s sold (Selling price – Variable costs)] – Fixed costs = Operating income

[5,000,000 ($0.50 – $0.30)] – $900,000 = $100,000

1b. Fixed costs ÷ Contribution margin per unit = Breakeven units

$900,000 ÷ [($0.50 – $0.30)] = 4,500,000 units

Breakeven units × Selling price = Breakeven revenues

| | |4,500,000 units × $0.50 per unit |= |$2,250,000 |

or,

Fixed costs ÷ Contribution margin ratio = Breakeven revenues

$900,000 ÷ 0.40 = $2,250,000

Contribution margin ratio = [pic]

= [pic] = 0.40

| | | | | |

|2. | |5,000,000 ($0.50 – $0.34) – $900,000 |= |$ (100,000) |

| | | | | |

|3. | |[5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)] |= |$ 110,000 |

| | | | | |

|4. | |[5,000,000 (1.4) ($0.40 – $0.27)] – [$900,000 (0.8)] |= |$ 190,000 |

| | | | | |

|5. | |$900,000( 1.1) ÷ ($0.50 – $0.30) |= |4,950,000 units |

| | | | | |

|6. | |($900,000 + $20,000) ÷ ($0.55 – $0.30) |= |3,680,000 units |

6. Athletic scholarships, CVP analysis.

1. Variable costs per scholarship offer:

Scholarship amount $20,000

Operating costs 2,000

Total variable costs $22,000

Let the number of scholarships be denoted by Q

$22,000 Q = $5,000,000 – $600,000

$22,000 Q = $4,400,000

Q = $4,400,000 ÷ $22,000 = 200 scholarships

2. Total budget for next year = $5,000,000 × (1.00 – 0.22) = $3,900,000

Then $22,000 Q = $3,900,000 – $600,000 = $3,300,000

Q = $3,300,000 ÷ $22,000 = 150 scholarships

3. Total budget for next year from above = $3,900,000

Fixed costs 600,000

Variable costs for scholarships $3,300,000

If the total number of scholarships is to remain at 200:

Variable cost per scholarship $3,300,000 ÷ 200 $16,500

Variable operating cost per scholarship 2,000

Amount per scholarship $14,500

7. CVP analysis, service firm.

1. Revenue per package $4,000

Variable cost per package 3,600

Contribution margin per package $ 400

Breakeven (units) = Fixed costs ÷ Contribution margin per package

= [pic] = 1,200 tour packages

2. Contribution margin ratio = [pic] = [pic] = 10%

Revenue to achieve target income = (Fixed costs + target OI) ÷ Contribution margin ratio

= [pic] = $5,800,000, or

7. CVP analysis, service firm – Continued:

Number of tour packages to earn $100,000 operating income:

[pic]= 1,450 tour packages

Revenues to earn $100,000 OI = 1,450 tour packages × $4,000 = $5,800,000.

3. Fixed costs = $480,000 + $24,000 = $504,000

Breakeven (units) = [pic]

Contribution margin per unit = [pic]

= [pic] = $420 per tour package

Desired variable cost per tour package = $4,000 – $420 = $3,580

Because the current variable cost per unit is $3,600, the unit variable cost will need to be reduced by $20 to achieve the breakeven point calculated in requirement 1.

Alternate Method: If fixed cost increases by $24,000, then total variable costs must be reduced by $24,000 to keep the breakeven point of 1,200 tour packages.

Therefore the variable cost per unit reduction = $24,000 ÷ 1,200 = $20 per tour package.

8. CVP, target income, service firm.

1. Revenue per child $600

Variable costs per child 200

Contribution margin per child $400

Breakeven quantity = [pic]

= [pic] = 14 children

8. CVP, target income, service firm – Continued:

2. Target quantity = [pic]

= [pic] = 40 children

3. Increase in fixed costs (rent increase: $4,000 - $2,000) $2,000

Divide by the number of children enrolled ÷ 40

Increase in fee per child $ 50

Therefore the fee per child will increase from $600 to $650.

9. CVP analysis.

1. Selling price $16.00

Variable costs per unit:

Purchase price $10.00

Shipping and handling 2.00 12.00

Contribution margin per unit (CMU) $ 4.00

Breakeven point in units = [pic] = [pic] = 150,000 units

2. Since Galaxy is operating above the breakeven point, any incremental contribution margin will increase operating income dollar for dollar.

Increase in units sales = 10% × 200,000 = 20,000

Incremental contribution margin = $4 × 20,000 = $80,000

Therefore, the increase in operating income will be equal to $80,000.

Galaxy’s operating income in 2003 would be $200,000 + $80,000 = $280,000.

3. Selling price $16.00

Variable costs:

Purchase price $10 × 130% $13.00

Shipping and handling 2.00 15.00

Contribution margin per unit $ 1.00

Target sales in units = [pic] = [pic] = 800,000 units

Target sales in dollars = $16 × 800,000 = $12,800,000

10. Breakeven analysis for a hospital.

Let P ( charges per patient-day that will lead the hospital to breakeven.

We want to determine “P” that would lead the hospital to breakeven at a level of 2,300 patient days.

Other data given in the problem are as follows:

Unit variable cost = $45.70

Fixed costs = $91,000.

At breakeven volume, the following relationship holds:

([pic]

The hospital needs to charge $85.27 per patient day to breakeven at a level of 2,300 patient days of volume of activity.

11. An increase in the fixed expenses of any enterprise will increase its break-even point. In a travel agency, more clients must be served before the fixed expenses are covered by the agency’s service fees.

12. A decrease in the variable expenses per pound of oysters results in an increase in the contribution margin per pound. This will reduce the company’s break-even sales volume.

13. When the sales price and unit variable cost increase by the same amount, the unit contribution margin remains unchanged. Therefore, the firm’s break-even point remains the same.

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