Weber State University



Challenging Cost Volume Profit Problems--Answers

Notation:

P = price

X = units

PX therefore = revenue

V = variable cost per unit

VX therefore = total variable costs

F = fixed costs

( = profit

Contribution margin = revenue (PX) minus variable expenses (VX)

CMt = total contribution margin which is PX - VX

CMr = contribution margin ratio which is (PX – VX)/PX or (P – V)/P

CMu = contribution margin per unit which is P - V

VEr = variable expense ratio which is (PX – CM)/PX or V/P or VX/PX

PX – VX – F = ( is one target sales formula (good for solving target sales at breakeven or a certain profit problems).

(F + ()/CMu = target sales (in units) at breakeven or a certain level of profit.

(F + ()/CMr = target sales (in dollars) at breakeven or a certain level of profit.

Current sales – breakeven sales = margin of safety

At breakeven, CMt = F

1. Chu Accessories makes an Oriental lamp. It's variable expense ratio is 40%. Current revenue was $100,000 for the year with sales of 10,000 lamps. The firm’s current profit is $15,000. What are their fixed costs?

Answer:

It is always good to begin by writing down what we know, and then to evaluate the above formulas and definitions to see what formulas may apply.

|Revenue |$100,000 |

|Units sold |10,000 |

|Profit |$15,000 |

|Variable expense ratio |.40 |

We know that 1 – variable expense ratio = contribution margin ratio

Contribution margin ratio (CMr) = 1 - .40 = .60

We also know that CMr = (PX – VX)/PX

So . . .

.60 = ($100,000 – VX)/$100,000

$60,000 = $100,000 – VX

VX = $40,000

Since PX – VX – F = (

$100,000 - $40,000 – F = $15,000

$100,000 - $40,000 - $15,000 = F

F = $45,000

2. Given the above information, what is the variable cost per unit?

V = VX/X = $40,000/10,000 = $4.00

3. MaryAnne Uniforms makes one style of uniform. Currently the company is operating at a loss of $40,000 per year. At current sales their total contribution margin is $70,000. Their contribution margin ratio is .50.

What is breakeven sales dollars?

What we know:

|( at current sales |-$40,000 |

|CMt at current sales |$70,000 |

|CMr |.50 |

Answer:

We know that at breakeven CMt = F

However we are $40,000 short of paying our fixed costs

So breakeven contribution margin must be $70,000 + $40,000

So since CMt = F then F must be $110,000

We know that (F/CMr) = breakeven sales

So ($110,000/.50) = $220,000 breakeven sales

To check our answer:

$220,000 - .50(220,000) - $110,000 = (

$220,000 – $110,000 - $110,000 = 0

4. Lundgren Manufacturing makes Bobbledumks. The following information is given:

|Breakeven sales in units |65,000 units |

|Price |$20 |

|Fixed Costs |$120,000 |

What is the CMr at 75,000 units of sales?

Answer :

We know CMr stays the same at any level of sales.

PX – VX – F = 0

(65,000)($20) – (65,000)V - $120,000 = 0

$1,300,000 – 65,000V - $120,000 = 0

$1,180,000 = 65,000V

V = $18.15

Since CMr = (P – V)/P

CMr = ($20.00 - $18.15)/$20.00 = .09

5. Given the information above, what is the margin of safety at 75,000 units of sales?

Margin of Safety = Current Sales – Breakeven Sales

Margin of Safety = (75,000)($20) – (65,000)($20) = $200,000

6. Given the information below, calculate the CMr.

|Margin of safety |$150,000 |

|CMt at breakeven sales |$200,000 |

|Revenue |$600,000 |

At breakeven F = CMt

At breakeven F = $200,000

At any level of sales within the relevant range F = $200,000

PX – VX – F = (

To find breakeven sales deduct margin of safety from current sales

Then substitute this into our formula

($600,000 - $150,000) – VX - $200,000 = 0

So VX = $250,000

CMr = (PX – VX)/PX = ($600,000 - $250,000)/$600,000 = .58

Challenging Cost Volume Profit Problems

Notation:

P = price

X = units

PX therefore = revenue

V = variable cost per unit

VX therefore = total variable costs

F = fixed costs

( = profit

Contribution margin = revenue (PX) minus variable expenses (VX)

CMt = total contribution margin which is PX - VX

CMr = contribution margin ratio which is (PX – VX)/PX or (P – V)/P

CMu = contribution margin per unit which is P - V

VEr = variable expense ratio which is (PX – CM)/PX or V/P or VX/PX

PX – VX – F = ( is one target sales formula (good for solving target sales at breakeven or a certain profit problems).

(F + ()/CMu = target sales (in units) at breakeven or a certain level of profit.

(F + ()/CMr = target sales (in dollars) at breakeven or a certain level of profit.

Current sales – breakeven sales = margin of safety

At breakeven, CMt = F

1. Chu Accessories makes an Oriental lamp. It's variable expense ratio is 40%. Current revenue was $100,000 for the year with sales of 10,000 lamps. The firm’s current profit is $15,000. What are their fixed costs?

2. Given the above information, what is the variable cost per unit?

V = VX/X = $40,000/10,000 = $4.00

3. MaryAnne Uniforms makes one style of uniform. Currently the company is operating at a loss of $40,000 per year. At current sales their total contribution margin is $70,000. Their contribution margin ratio is .50.

What is breakeven sales dollars?

4. Lundgren Manufacturing makes Bobbledumks. The following information is given:

|Breakeven sales in units |65,000 units |

|Price |$20 |

|Fixed Costs |$120,000 |

What is the CMr at 75,000 units of sales?

5. Given the information above, what is the margin of safety at 75,000 units of sales?

Margin of Safety = Current Sales – Breakeven Sales

Margin of Safety = (75,000)($20) – (65,000)($20) = $200,000

6. Given the information below, calculate the CMr.

|Margin of safety |$150,000 |

|CMt at breakeven sales |$200,000 |

|Revenue |$600,000 |

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