4 SLP - MKT599

CVP Analysis

Cost, Volume, Profit

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.

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)

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

Using CVP

• Breakeven analysis

• Profit, price, Volume analysis

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

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.

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.

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.

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

Check & Validate…

• Check: Income = Total Costs • p VBE = c VBE + F ?? • 300(250) = 100(250) + 50000 • 75000 = 25000 + 50000 • 75000 = 75000

Breakeven Graph

INCOME = pV

FIXED COSTS + VARIABLE COSTS

FIXED COSTS

Breakeven: Income = Total Costs

VBE

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.

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.

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.

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

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

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

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)

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?

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

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

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)

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.

USING THE CVP CALCULATOR

An Example for X5 in the PDA SIM

Default X5 2006 This Year Last Year % Change

Revenue Sales Volume 1,766,216 1,448,031 22% Revenue Volume

441,554,008 362,007,649 22%

Cost Variable Costs 247,270,244 202,724,283 22% Fixed Costs 70,000,000 70,000,000 0% R & D Costs 6,666,667 6,666,667 0% Total Costs 323,936,911 279,390,950 16%

Profit Total Profit 117,617,097 82,616,699 42% Total Profitability

27% 23% 17%

Price: $250 R&D%: 33% X5 Financials for 2006

This Year Last Year % Change

Customer Base Installed Base 3,167,351 1,875,622 69% Remaining Customers

2,857,649 4,149,378 -31%

Market Saturation 53% 31% 69%

Sales Volume First-Time Customers

1,502,270 1,291,729 16%

Repeat Sales 263,946 156,302 69% Total Sales 1,766,216 1,448,031 22%

Default X5 Market Report for the year 2006

USING CVP Calculator:

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

Variable cost/unit: $140 Price $ 250.00

Volume 1,765,610

Sales Revenue $ 441,402,493.18

ROS 26.65%

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.

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.

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%

What price if Volume does not change?

• Price = ? • Same volume as

default run • Same profit as

default run • R&D%: 15%

Volume 1,765,610

Price $ 247.96

Sales Revenue $ 437,802,497.00

ROS 26.87%

Price = $247.96

What happens in SIM? • Let’s run the

sim with our revised strategy for X5 for 2006.

• Price: $248 • R&D%:

15%

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%

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

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%

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.

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.