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cvp_analysis.pptCVP 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 = 0
Two 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 PDA Sim
- Default Values:
- p = $250 (you can change this after SLP1)
- c = $140 (does not change in the simulation)
- Unit Contr. Margin = $110
- From Default Run Year 2006:
- R&D costs = 6,666,667
- (33% of 20,000,000 budget, you decide allocation %)
- Other Fixed Costs = 70,000,000 (does not change)
- Total Fixed Costs = 76,666,667 (R&D + Other Fixed)
- 2006 unit sales volume: 1,766,216
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Using X5 from PDA Sim
- Let’s validate the results in the Sim and calculate Profit
- P = (p – c)V – F
- P = (250 – 140) 1,766,216 – 76,666,667
- = (110) 1,766,216 – 76,666,667
- = 194,283,760 - 76,666,667
- = 117,617,093
- Profit from Default Sim for X5 in 2006 = 117,617,097
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Using X5 from PDA Sim
- Let’s estimate what will happen in 2007 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 10%)
- Sales Volume V = 1,439,609 (from 2007 default run)
- Profit = (225 – 140) 1,439,609 – 72,000,000
- = (85) 1,439,609 – 72,000,000
- = 122,366,765 – 72,000,000
- = 50,366,765
- Profit = 81,690,327 from 2007, 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 2007 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 2007, default run (81,690,327)
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Using X5 from PDA Sim
- Profit, P = 81,690,327
- Volume = ?
- P = (p – c)V – F
- (P + F)/(p – c) = V
- (81,690,327 + 72,000,000)/(85) = V
- 153,690,327 / 85 = 1,808,121.49
- V = 1,808,122 units to achieve the same profit
- If you lower the price to $225 and reduce the R&D to 10%, does the reduce price cause an increase in Volume so that the profit is the same?
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Determining Strategy: X5 Example
- Default run 2007
- p = 250
- c = 140
- Unit Contr. Margin = 100
- R&D (33%) = 6,666,667
- Other Fixed = 70,000,000
- Profit = 81,690,327
- Volume = 1,439,609
- Possible strategy 2007
- p = 225
- c = 140
- ucm = 85
- R&D (10%) = 2,000,000
- Other Fixed = 70,000,000
- Profit = 81,690,327
- Volume = 1,808,122
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 PDA 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 (PDA 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 PDA SIM
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Default X5 2006
Price: $250
R&D%: 33%
X5 Financials for 2006
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Default X5 Market Report for the year 2006
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USING CVP Calculator:
Variable cost/unit: $140
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.
| R&D Total Budget | $ 20,000,000 |
| R&D% Allocation | 33% |
| R&D Costs | $ 6,600,000 |
| Fixed Costs | $ 70,000,000 |
| Total Fixed Costs | $ 76,600,000 |
| Target Profit | $117,617,097 |
| Variable Cost/Unit | $ 140.00 |
| Price | $ 250.00 |
| Volume | 1,765,610 |
| Sales Revenue | $ 441,402,493.18 |
| ROS | 26.65% |
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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 2006 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: $250.
- And let’s shoot for the same profit: $117,617,097
- If you put these into the CVP Calculator, this says you need less volume: 1,732,883 units.
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Price: $250
R&D: 15%
Volume: 1,732,883
| R&D Total Budget | $ 20,000,000 |
| R&D% Allocation | 15% |
| R&D Costs | $ 3,000,000 |
| Fixed Costs | $ 70,000,000 |
| Total Fixed Costs | $ 73,000,000 |
| Target Profit | $117,617,097 |
| Variable Cost/Unit | $ 140.00 |
| Price | $ 250.00 |
| Volume | 1,732,883 |
| Sales Revenue | $ 433,220,675.00 |
| ROS | 27.15% |
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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%
Price = $247.96
| Volume | 1,765,610 |
| Price | $ 247.96 |
| Sales Revenue | $ 437,802,497.00 |
| ROS | 26.87% |
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What happens in SIM?
- Let’s run the sim with our revised strategy for X5 for 2006.
- Price: $248
- R&D%: 15%
X5 Financials for 2006
| This Year | Last Year | % Change | |
| Revenue | |||
| Sales Volume | 1,835,367 | 1,448,031 | 27% |
| Revenue Volume | 455,170,904 | 362,007,649 | 26% |
| Cost | |||
| Variable Costs | 256,951,317 | 202,724,283 | 27% |
| Fixed Costs | 70,000,000 | 70,000,000 | 0% |
| R & D Costs | 3,703,704 | 6,666,667 | -44% |
| Total Costs | 330,655,021 | 279,390,950 | 18% |
| Profit | |||
| Total Profit | 124,515,884 | 82,616,699 | 51% |
| Total Profitability | 27% | 23% | 20% |
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Results do not match!!
- Volume sold: 1,835,367
- Profit earned: 124,515,88
- We don’t get the same results that were predicted by the CVP!!
In the CVP we used a Volume of: 1,765,610
But in the SIM, when we lowered the price just a bit down to $248, we got a volume of: 1,835,367.
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 | $ 20,000,000 |
| R&D% Allocation | 15% |
| R&D Costs | $ 3,000,000 |
| Fixed Costs | $ 70,000,000 |
| Total Fixed Costs | $ 73,000,000 |
| Target Profit | $124,515,884 |
| Variable Cost/Unit | $ 140.00 |
| Price | $ 248.00 |
| Volume | 1,828,851 |
| Sales Revenue | $ 453,554,992.89 |
| ROS | 27.45% |
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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.
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