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CVP Analysis
Cost, Volume, Profit
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What is CVP?
• Uses a specific cost-profit-volume formula to study the relationship of the costs, price, sales volume and profit.
• Profit = (price – vcost/unit)*Volume – Total Fixed Costs.
• Price and vcost are per unit.
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Developing the formula
• Profit = (price – vcost/unit)*Volume – Total Fixed Costs.
• price and vcost are per unit.• P = (p – c)V – F (Basic Formula)• P = profit• p = price (per unit)• c = Variable cost/unit• F = total Fixed Costs• V = Sales Volume (units sold)
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Example Using Basic Formula
• P = (p – c)V – F• price (p) = $300/unit• vcost (c) = $100/unit• Total Fixed Costs = $50,000• If you sell 1,500 units, what is the profit?• P = (300 – 100)1500 – 50000• = (200)1500 – 50000• = 300000 – 50000• = $250,000
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Using CVP
• Breakeven analysis
• Profit, price, Volume analysis
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Using CVP for Breakeven
Breakeven is the situation where no profit or loss is generated.
• Income = Costs• In the Basic Formula, Profit = 0Two ways to use:• Breakeven Volume: VBE
• Breakeven price: pBE
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Calculating Breakeven Volume• Breakeven Volume is the quantity that will
generate Profit = 0 for given costs and price.• Using the formula, we need to determine what V
is when P = 0.• P = (p – c)V – F• 0 = (p – c) VBE – F• F = (p – c) VBE
• F/(p – c) = VBE
• VBE is being use to denote specifically the Breakeven Volume.
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Contribution Margin
• VBE = F/(p – c)
• The breakeven volume is calculated by Total Fixed costs divided by price minus variable costs.
• (p – c) is often called the Contribution Margin (per unit) or Unit Contribution Margin.
• Another way of looking at breakeven is it is the sales volume where Income = Costs.
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Breakeven: Income = Costs
• Income = Costs• P = (p – c)V – F• 0 = (p – c) VBE – F
• 0 = p VBE – c VBE – F
• p VBE = c VBE + F
• p VBE is the income and c VBE + F are the total costs, Variable Costs + Fixed Costs.
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Example of Breakeven Calculations
• VBE = F/(p – c)
• price (p) = $300/unit• vcost (c) = $100/unit• Total Fixed Costs = $50,000• What the Breakeven volume?• VBE = 50000/(300 – 100)
• VBE = 50000/200
• VBE = 250 units
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Check & Validate…
• Check: Income = Total Costs• p VBE = c VBE + F ??
• 300(250) = 100(250) + 50000• 75000 = 25000 + 50000• 75000 = 75000
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Breakeven Graph
INCOME = pV
FIXED COSTS + VARIABLE COSTS
FIXED COSTS
Breakeven: Income = Total Costs
VBE
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Breakeven Price
• Let’s say you know the volume and you want to know the price that will generate a breakeven situation: i.e. P = 0
• 0 = pBE V – c V – F
• pBE V = c V + F
• pBE = (c V + F)/V
• Breakeven price is calculated by dividing the Total Costs by the Volume.
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Example Breakeven price• pBE = (c V + F)/V or c + F/V• c = 100 (per unit)• F = 50000• V = 1500 units• pBE = [100(1500) + 50000]/1500• = [150000 + 50000]/1500• = [200000]/1500• = $133.33/unit• If you price the item at $133.33 then if you sell,
1500 units, you will Breakeven.
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Example Breakeven price
• pBE = (c V + F)/V or c + F/V
• c = 100 (per unit)• F = 50000• V = 1500 units• pBE = $133.33
• If you price it higher than $133.33, and you sell 1500 units, you will make a profit.
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Using X5 from Tablet Sim• Default Values:• p = $265 (you can change this after SLP1)• c = $120 (does not change in the simulation)• Unit Contr. Margin = $145• From Default Run Year 2012:• R&D costs = 7,260,000 – (33% of 22,000,000 budget, you decide allocation %)
• Other Fixed Costs = 72,000,000 (does not change)• Total Fixed Costs = 79,260,000 (R&D + Other Fixed)• 2012 unit sales volume: 1,859,856
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Using X5 from Tablet Sim• Let’s validate the results in the Sim and
calculate Profit• P = (p – c)V – F• P = (265 – 145) 1,859,856 – 79,260,000• = (120) 1,859,856 – 79,260,000• = 223,182,720 - 79,260,000• = 143,922,720• Profit from Default Sim for X5 in 2012 =
143,922,720
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Using X5 from Tablet Sim
• Let’s estimate what will happen in 2013 if we lower R&D and we lower the price.
• R&D% = 10% (of 20,000,000)• R&D = 2,000,000• Price p = $225 (down from $250 by 15%)• Sales Volume V = 1,427,666 (from 2013 default run)• Profit = (225 – 145) 1,427,666 – 74,000,000• = (80) 1,427,666 – 74,000,000• = 114,213,280 – 74,000,000• = 40,213,280 • Profit = 92,059,892 from 2013, default run
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Using X5 from PDA Sim
• So if you lower your price to $225 and decrease R&D and the volume does not change from the default volume, you will earn less profit in 2013 that you did in the default run.
• BUT, if you lower the price will that help to increase the volume?
• Maybe, but what does the volume need to be to obtain the same profit that was earned in 2013, default run (92,059,892)
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Using X5 from Tablet Sim• Profit, P = 92,059,892• Volume = ?• P = (p – c)V – F• (P + F)/(p – c) = V• (92,059,892 + 74,000,000)/(85) = V• 166,059,892/ 80 = 2,075,748.65• V = 2,075,749 units to achieve the same profit• If you lower the price to $225 and reduce the
R&D to 10%, does the reduced price cause an increase in Volume so that the profit is the same?
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Determining Strategy: X5 Example
• Default run 2013• p = 265• c = 145• Unit Contr. Margin = 120• R&D (33%) = 7,260,000• Other Fixed = 72,000,000• Profit = 92,059,892 • Volume = 1,427,666
• Possible strategy 2013• p = 225• c = 145• ucm = 80• R&D (10%) = 2,000,000• Other Fixed = 70,000,000• Profit = 81,690,327 • Volume = 2,075,749
If you lower price from $250 to $225 in 2007, will volume go up to or higher than 81,690,327
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Breakeven Formulas• P = (p – c)V – F• For Breakeven, set P = 0
Breakeven Volume• VBE = F/(p – c)
Breakeven Price• pBE = (c V + F)/V or
• pBE = c + F/V
• REMEMBER: in the Tablet Sim, you need to consider that R&D is part of Fixed Costs, so here F = Fo + R
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Other CVP Formulas
Use F = Fo + R (sim fixed costs)
• Price, for a given Profit, Volume and Costs• p* = (P + Fo + R + cV) / V
• Volume, for a given price, Profit and Costs• V* = (P + Fo + R) / (p – c)
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Application of CVP in the PDA Sim
• When should you use Breakeven?• How do you deal with multiple years?• How do you deal with multiple products?
• Give these questions some thought.• Experiment with CVP.
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USING THE CVP CALCULATOR
An Example for X5 in the Tablet SIM
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Default X5 2012Price: $265R&D%: 33%X5 Financials for 2012
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Default X5 Market Report for the year 2012
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USING CVP Calculator:
R&D Total Budget $ 22,000,000
R&D% Allocation 33%
R&D Costs $ 7,260,000
Fixed Costs $ 72,000,000
Total Fixed Costs $ 79,260,000
Target Profit $143,992,711
Variable Cost/Unit $ 145.00
Variable cost/unit: $145 Price $ 265.00
Volume 1,859,856
Sales Revenue $ 492,861,820
ROS 29.20%
Note that the results from the CVP Calculator are nearly the same as you get in the SIM. The only difference is because the SIM must be using 33.3333% for the R&D Allocation and the CVP Calculator is using 33%. So we will ignore the difference.
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Now let’s develop a Revised Strategy
Now, let’s try to develop a different price and R&D allocation for 2012 for our Revised Strategy using the
• CVP Calculator. Should we lower R&D or increase it? Should we lower the price or increase it? How much profit do we want? How much will we sell?
• Let’s lower the R&D%, say down to 15% - why? I will leave that up to you decide why we might want to do this.
• Let’s leave the price the same for this first estimate: $265.
• And let’s shoot for the same profit: $143,922,711• If you put these into the CVP Calculator, this says you
need less volume: 1,826,856 units.
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Price: $265R&D: 15% Volume: 1,826,856
R&D Total Budget $ 22,000,000 R&D% Allocation 15%
R&D Costs $ 3,300,000
Fixed Costs $ 75,300,000
Total Fixed Costs $ 75,000,000
Target Profit $143,922,711
Variable Cost/Unit $ 145.00
Price $ 265.00
Volume 1,826,856
Sales Revenue $ 484,116,820.00
ROS 29.73%
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What price if Volume does not change?
• Price = ?• Same volume as
default run• Same profit as
default run• R&D%: 15%
Volume 1,859,856
Price $ 262.87
Sales Revenue $ 488,901,831.00
ROS 29.44%
Price = $262.87
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What happens in SIM?• Let’s run the
sim with our revised strategy for X5 for 2012.
• Price: $263• R&D%:
15%
This Year Last Year % Change
RevenueSales Volume 1,928,810 1,535,407 26%
Revenue Volume
507,277,039 406,882,843 25%
Cost
Variable Costs 279,677,455 222,634,008 26%
Fixed Costs 72,000,000 72,000,000 0%
R & D Costs 3,300,000 7,260,000 -55%
Total Costs 354,977,455 301,894, 008 19%
Profit
Total Profit 152, 299,584 104,988,835 45%
Total Profitability
30% 23% 15%
X5 Financials for 2006
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Results do not match!!• Volume sold: 1,928,810• Profit earned: 152,299,584• We don’t get the same results that were
predicted by the CVP!!In the CVP we used a Volume of: 1,859,856 But in the SIM, when we lowered the price just a
bit down to $263, we got a volume of: 1,928,810.
We will get this same result in the CVP calculator if we put in the actual profit earned in the SIM
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CVP Calculator with Revised Strategy Results
R&D Total Budget $ 22,000,000 R&D% Allocation 15%
R&D Costs $ 3,000,000 Fixed Costs $ 70,000,000 Total Fixed Costs $ 73,000,000
Target Profit $152,299,584
Variable Cost/Unit $ 145.00
Price $ 263
Volume 1,928,810
Sales Revenue $ 507, 277, 038.92
ROS 30.63%
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Why does the SIM not match your predictions with the CVP Calculator?• The SIM gives you the results based on your
inputs of price and R&D%• It will determine how much you sell based on
the price – usually a lower price will generate a higher sales volume and vice versa, depending on the price elasticity.
• The CVP calculator does not know the price:demand curve – it is simply telling you how much you need to sell for a given Price and a Target Profit.
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Some final thoughts• So what is missing is the relationship between price and
demand.• Demand is based on based price and the performance (how
much is being spent on R&D).• You need to use CVP to help you determine or predict a price in
your revised strategy.• Then based on the results you get, you can begin to understand
the price:demand relationship.• That is why you get to run the SIM several times as you learn
more about price:demand.• And of course demand is related to how much you spend on
R&D.• And each product is more or less sensitive to price and product
development efforts.