1. CVP Analysis
Cost, Volume, Profit

2. 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.

3. 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)

4. 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
= – 50000
= $250,000

5. Using CVP
Breakeven analysis
Profit, price, Volume analysis

6. 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

7. 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.

8. 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.

9. Breakeven: 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.

10. 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

11. Check & Validate… Check: Income = Total Costs p VBE = c VBE + F ??
300(250) = 100(250)
75000 =
75000 = 75000

12. Breakeven Graph INCOME = pV Breakeven: Income = Total Costs
FIXED COSTS + VARIABLE COSTS
FIXED COSTS
Breakeven:
Income = Total Costs
VBE

13. 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.

14. Example Breakeven price
pBE = (c V + F)/V or c + F/V
c = 100 (per unit)
F = 50000
V = 1500 units
pBE = [100(1500) ]/1500
= [ ]/1500
= [200000]/1500
= $133.33/unit
If you price the item at $ then if you sell, 1500 units, you will Breakeven.

15. 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.

16. 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

17. 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, ,260,000
= 143,922,720
Profit from Default Sim for X5 in 2012 = 143,922,720

18. 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

19. 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)

20. Using X5 from Tablet Sim Profit, P = 92,059,892 Volume = ?
P = (p – c)V – F
(P + F)/(p – c) = V
(92,059, ,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?

21. 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

22. 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

23. 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)

24. 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.

25. USING THE CVP CALCULATOR
An Example for X5 in the Tablet SIM

26. Default X5 2012 222,634,008 Price: $265 R&D%: 33% This Year Last Year
X5 Financials for 2012
This Year
Last Year
% Change
Revenue
Sales Volume
1,859,856
1,535,407
21%
Revenue Volume
492,861,819
406,882,843
Cost
Variable Costs
269,679,108
222,634,008
Fixed Costs
72,000,000 0%
R & D Costs
7,260,000
Total Costs
348,939,108
301,894,008
16%
Profit
Total Profit
143,922,711
104,988,835
42%
Total Profitability
29%
23%
17%

27. Default X5 Market Report for the year 2012
This Year
Last Year
% Change
Customer Base
Installed Base
3,246,936
1,875,622
69%
Remaining Customers
2,779,064
4,149,378
-31%
Market Saturation
54%
31%
Sales Volume
First-Time Customers
1,575,220
1,369,625
15%
Repeat Sales
284,636
165,782
72%
Total Sales
1,859,856
1,535,407
21%

28. USING CVP Calculator:
Variable cost/unit: $145
Price $
Volume
1,859,856
Sales Revenue
$ 492,861,820
ROS
29.20%
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 $
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 % for the R&D Allocation and the CVP Calculator is using 33%. So we will ignore the difference.

29. 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.

30. Price: $265 R&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 $
Price $
Volume
1,826,856
Sales Revenue
$ 484,116,820.00
ROS
29.73%

31. What price if Volume does not change?
Same volume as default run
Same profit as default run
R&D%: 15%
Volume
1,859,856
Price $
Sales Revenue
$ 488,901,831.00
ROS
29.44%
Price = $262.87

32. What happens in SIM? Price: $263 R&D%: 15%
X5 Financials for 2006
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
Revenue
Sales 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
Fixed Costs
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%

33. 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

34. 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 $
Price
$ 263
Volume
1,928,810
Sales Revenue $
507, 277,
ROS
30.63%

35. 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.

36. 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.