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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