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 marginratio 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 / $100,000Units 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 / -$40,000CMt 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 unitsPrice / $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 / $150,000CMt 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 marginratio 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 unitsPrice / $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 / $150,000CMt at breakeven sales / $200,000
Revenue / $600,000