Transcript Hilton Maher Selto Chapter 12
McGraw-Hill/Irwin
12
Financial and Cost Volume-Profit Models
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
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Learning Objective 1
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Definition of Financial Models
Relationships between costs, revenues, & income.
Accurate, reliable simulations of relations among relevant costs, benefits, value and risk that are useful for supporting business decisions.
Pro forma financial statements.
Relationships between current investments and value.
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Objectives of Financial Modeling
To improve the quality of decisions To simulate accurately and reliably the relevant factors and relationships To allow flexible and responsive analyses
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Learning Objective 2
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Basic Cost-Volume-Profit (CVP) Model
Revenue
=
Variable Costs + Fixed Costs + Income Assumptions:
Revenue can be estimated as: sales price (P) × units sold (Q)
Total variable costs can be estimated as: variable cost per unit (V) × units sold (Q)
Total fixed costs (F) will remain constant over the relevant range.
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Basic CVP Model and the Break-Even Point
Revenue
=
Variable Costs + Fixed Costs + Income PQ = VQ + F + I At the break-even point income = 0 PQ = VQ + F Combining terms and solving for Q, the number of units that must be sold to break even: Q = F ÷ (P – V)
(P – V) is the unit contribution margin
Let’s see some numbers!
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Basic CVP Model and the Break-Even Point
The break-even point is the point in the volume of activity at which the organization’s revenues and expenses are equal.
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income $ 200,000 120,000 80,000 80,000 $ -
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Basic CVP Model and the Break-Even Point
Consider the following information developed by the accountant at Curl, Inc.: Sales (500 surf boards) Less: variable expenses Contribution margin Less: fixed expenses Net income Total $ 250,000 150,000 $ 100,000 80,000 $ 20,000 Per Unit $ 500 300 $ 200 Percent 100% 60% 40%
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Basic CVP Model and the Break-Even Point
For each additional surf board sold, Curl generates $200 in contribution margin.
Sales (500 surf boards) Less: variable expenses Contribution margin Less: fixed expenses Net income Total $ 250,000 150,000 $ 100,000 80,000 $ 20,000 Per Unit $ 500 300 $ 200 Percent 100% 60% 40%
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Basic CVP Model and the Break-Even Point
Fixed expenses Unit contribution margin = Break-even point (in units)
Sales (500 surf boards) Less: variable expenses Contribution margin Less: fixed expenses Net income Total $ 250,000 150,000 $ 100,000 80,000 $ 20,000 Per Unit $ 500 300 $ 200 Percent 100% 60% 40% $80,000 $200 = 400 surf boards
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Basic CVP Model and the Break-Even Point
Here is the proof!
Sales ( 400 surf boards) Less: variable expenses Contribution margin Less: fixed expenses Net income Total $ 200,000 120,000 $ 80,000 80,000 $ Per Unit $ 500 300 $ 200 Percent 100% 60% 40% 400 × $500 = $200,000 400 × $300 = $120,000
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Basic CVP Model and the Break-Even Point
Calculate the break-even point in
sales dollars
rather than units by using the contribution margin ratio.
Contribution margin Sales = CM Ratio Fixed expense CM Ratio = Break-even point (in sales dollars)
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Basic CVP Model and the Break-Even Point
Sales ( 400 surf boards) Less: variable expenses Contribution margin Less: fixed expenses Net income Total $ 200,000 120,000 $ 80,000 80,000 $ Per Unit $ 500 300 $ 200 Percent 100% 60% 40% $80,000 40% = $200,000 sales
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Basic CVP Model in Graphical Format
Summarizing CVP relationships in a graph makes more information available to managers in less space, and makes the relationships more intuitive.
Consider the following information for Curl, Inc.
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income (loss) 300 units $ 150,000 90,000 $ 60,000 80,000 $ (20,000) 400 units $ 200,000 120,000 $ 80,000 80,000 $ 500 units $ 250,000 150,000 $ 100,000 80,000 $ 20,000
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Basic CVP Model in Graphical Format
450,000 400,000 Break-even point Total sales 350,000 300,000 250,000 200,000 150,000 100,000 50,000 Total expenses 100 200 300 400 Fixed expenses Units Sold 500 600 700 800
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Profit-Volume Graph
Some managers like the profit-volume graph because it focuses on profits and volume.
$100,000 $80,000 $60,000 $40,000 $20,000 $ $(20,000) $ $(40,000) $(60,000) $(80,000) $(100,000) $50 $100 $150 $200 $250 $300 $350 $400 Break-even point 1 2 3 4 Units sold (00s) 5 6 7 8
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CVP and Target Income
We can determine the number of surfboards that Curl must sell to earn a profit of $100,000 using the contribution margin approach .
Fixed expenses + Target income Unit contribution margin = Units sold to earn the target income $80,000 + $100,000 $200 per surf board = 900 surf boards
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CVP and Target Income
We can also use the equation approach to get the same result.
Revenue = Variable costs + Fixed costs + Income ($500 × Q) = ($300 × Q) + $80,000 + $100,000 $200Q = $180,000 Q = 900 surf boards
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Operating Leverage
Reflects the risk of missing sales targets.
Measured as the ratio of contribution margin to operating income.
A high operating leverage is indicative of high committed costs (e.g. interest). A relatively small change in sales can lead to a loss.
A low operating leverage is indicative of low committed costs (e.g. interest). More of the costs are variable in nature.
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Operating Leverage
Operating leverage factor = Contribution margin Net income Sales Less: variable expenses Contribution margin Less: fixed expenses Net income Actual sales 500 Board $ 250,000 150,000 100,000 80,000 $ 20,000 $100,000 $20,000 = 5
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Operating Leverage
A measure of how a percentage change in sales will affect profits. If Curl increases its sales by 10%, what will be the percentage increase in net income?
Percent increase in sales Operating leverage factor Percent increase in profits 10% × 5 50%
Here’s the proof!
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Operating Leverage
Sales Less variable expenses Contribution margin Less fixed expenses Net income Actual sales (500) $ 250,000 150,000 100,000 80,000 $ 20,000 Increased sales (550) $ 275,000 165,000 110,000 80,000 $ 30,000 10% increase in sales from $250,000 to $275,000 . . .
. . . results in a 50% increase in income from $20,000 to $30,000.
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Learning Objective 3
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Computer Spreadsheet Models
1. Gather all the facts, assumptions and estimates for the model; i.e., parameters.
2. Describe the relations between the parameters. This usually results in an algebraic equation.
3. Separate the parameters from the formulas. Use cell addresses, instead of actual numbers.
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Learning Objective 4
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Modeling Taxes
We can adjust the basic CVP model to incorporate income taxes.
Use the following notation: A = Income after tax B = Income before tax T = Tax rate A = B – BT A = B (1 – T) or solving for B: B = A ÷ (1 – T)
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Modeling Multiple Products
When a company sells multiple products, modeling requires: 1. An estimate of the relative proportion of each product in the sales mix 2. A computation of the Weighted Average Unit Contribution Margin
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Modeling Multiple Products
For a company with more than one product, sal es mix is the relative combination in which a company’s products are sold.
Different products have different selling prices, cost structures, and contribution margins.
Let’s assume Curl sells surf boards and sail boards. Then we’ll calculate a break-even point that encompasses both products and their cost-price parameters.
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Modeling Multiple Products
Curl provides us with the following information: Description Surfboards Sailboards Total sold Selling price $ 500 1,000 Unit variable cost $ 300 450 Unit contribution Number of margin $ 200 550 boards 500 300 800 Sales mix computation Description Surfboards Sailboards Total sold Number of boards 500 300 800 % of Total 62.5% (500 ÷ 800) 37.5% (300 ÷ 800) 100.0%
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Modeling Multiple Products
Weighted-average unit contribution margin Description Contribution margin % of total Surfboards Sailboards $ 200 550 62.5% 37.5% Weighted-average contribution margin Weighted contribution $ 125.00
206.25
$ 331.25
$200 × 62.5%
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Modeling Multiple Products
Break-even point
Break-even point = Fixed expenses Weighted-average unit contribution margin Break-even point = $170,000 $331.25 Break-even point = 514 combined units Fixed costs increased from $80,000, due to expansion needed to sell multiple products.
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Modeling Multiple Products
The break-even point is 514 combined units. We can use the sales mix to find the number of units of each product that must be sold to break even.
Combined break-even sales 514 Product Surfboards Sailboards Total units % of total Individual sales 62.5% 37.5% 321 193 514 The break-even point of 514 units is valid only for the sales mix of 62.5% and 37.5%.
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Modeling Multiple Cost Drivers
An insight from activity-based costing: costs may be a function of multiple activities, not merely sales volume.
Some costs treated as fixed (when sales volume is the only activity) may now be considered variable.
Total Cost = (Unit variable cost × Sales units) + (Batch cost × Batch activity) + (Product cost × Product activity) + (Customer cost × Customer activity) + (Facility cost × Facility activity)
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Learning Objective 5
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Sensitivity Analysis
An examination of the changes in outcomes caused by changes in each of a model’s parameters.
For example, we can examine the impact on Curl’s profit (outcome) if the parameters of selling price, quantity sold, unit variable cost, and/or fixed costs change.
Because of the number of computations involved, computerized models are used for sensitivity analysis.
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Sensitivity Analysis
Estimate the likely range of each parameter.
Change one parameter to upper and lower end of range, keeping other parameters at the most likely values.
Estimate the most likely value of each parameter.
Record profit for each change and repeat process for all parameters.
Because of the number of computations involved, computerized models are used for sensitivity analysis.
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Sensitivity Analysis
Model elasticity
The ratio of percentage change in outcome (profit) to percentage change in an input parameter.
If greater than 1.0
: the change in parameter has a significant effect on profit .
If less than 1.0
on profit .
Because of the number of computations involved, computerized models are used for sensitivity analysis.
: the change in parameter has a negligible effect
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Scenario Analysis
Realistic combinations of changed parameters Best case scenario Realistic combination of highest prices and quantities, along with the lowest costs.
Worst case scenario Realistic combination of lowest prices and quantities, along with the highest costs.
Most likely case scenario Realistic combination of most likely prices and quantities, along with the most likely costs.
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Learning Objective 6
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Modeling Scarce Resources
Firms often face the problem of deciding how to best utilize a scarce resource.
Usually fixed costs are not affected by this particular decision, so management can focus on maximizing total throughput (usually equal to contribution margin).
Let’s look at the Rose Company example.
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Modeling Scarce Resources
Rose Company produces three products.
Selected data are shown below.
Selling price per unit Less variable expenses per unit Contribution margin per unit Current demand per week (units) Contribution margin ratio Processing time required on machine A1 per unit (min.) 1 Product 2 3 $ 60 $ 50 $ 40 35 20 $ 24 $ 15 $ 20 40% 1.00
30% 0.50
50% 0.80
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Modeling Scarce Resources
Operating time on machine A1 is the scarce resource, as it is being used at 100% of its capacity. There is excess capacity on all other machines. Machine A1 has a capacity of 2,400 minutes per week.
Which product should Rose emphasize next week?
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Modeling Scarce Resources
The key is the contribution margin per unit of the scarce resource.
Contribution margin per unit Minutes required to produce one unit Contribution margin per minute 1 $ 24 1.00
$ 24.00
Product 2 $ 15 0.50
$ 30.00
3 $ 20 0.80
$ 25.00
Product 2 should be emphasized because it has the highest contribution per minute on machine A1, the scarce resource. If there are no other considerations, the best plan would be to produce to meet current demand for Product 2 and then use remaining capacity to make Product 3.
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Modeling Scarce Resources
Let’s see how this plan would work.
Alloting Our Constrained Recource (Machine A1) Weekly demand for Product 2 Time required per unit Total time required to make Product 2 × 2,200 units 0.50
min.
1,100 min.
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Modeling Scarce Resources
Let’s see how this plan would work.
Alloting Our Constrained Recource (Machine A1) Weekly demand for Product 2 Time required per unit Total time required to make Product 2 × 2,200 units 0.50
min.
1,100 min.
Total time available Time used to make Product 2 Time available for Product 3 2,400 1,100 1,300 min.
min.
min.
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Modeling Scarce Resources
Let’s see how this plan would work.
Alloting Our Scarce Recource (Machine A1) Weekly demand for Product 2 Time required per unit Total time required to make Product 2 × 2,200 units 0.50
min.
1,100 min.
Total time available Time used to make Product 2 Time available for Product 3 Time required per unit Production of Product 3
Is this a problem?
÷ 2,400 1,100 1,300 0.80
1,625 min.
min.
min.
min.
units
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Modeling Scarce Resources
The market for Product 3 is only 1,500 units per week, so Rose should not produce 1,625 units.
So Rose should produce 1,500 units of Product 3, leaving time to produce how many Product 1?
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Modeling Scarce Resources
Alloting Our Scarce Recource (Machine A1) Weekly demand for Product 3 Time required per unit Total time required to make Product 3 × 1,500 units 0.80
min.
1,200 min.
Remaining time available Time used to make Product 3 Time available for Product 1 Time required per unit Production of Product 1 ÷ 1,300 1,200 100 1.00
100 min.
min.
min.
min.
units
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Modeling Scarce Resources
Suppose Rose Company could buy additional minutes of capacity on machine A1. How many additional minutes does Rose need to satisfy unmet sales demand?
Rose had only 100 minutes remaining for Product 1 which requires 1.00 minutes per unit. The weekly demand for Product 1 is 2,000 units. Rose needs an additional 1,900 minutes to produce enough Product 1 to satisfy demand.
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Modeling Scarce Resources
What is the maximum amount Rose would pay per minute for the additional 1,900 minutes to produce Product 1?
Contribution per minute for Product 1 is $24.00. Rose could pay up to $24.00 per minute for additional capacity.
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Modeling Scarce Resources
Now, assume that the demand for all three products is unlimited and that Rose company could again buy additional minutes of capacity on machine A1. What is the maximum amount Rose would pay per minute for additional capacity?
Contribution per minute for Product 2 is $30.00. Rose could pay up to $30.00 per minute for additional capacity as long as Product 2 could be sold.
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Learning Objective 7
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Theory of Constraints
Popularized in the book The Goal Seeks to improve product processes by focusing on constrained resources Measures process capacity, identifies constraints and responds effectively Pays close attention to “bottlenecks” that limit production or sales.
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Theory of Constraints – Six Step Process
1.
2.
3.
4.
5.
6.
Identify the appropriate measure of value created – this will typically be throughput.
Identify the organization’s bottleneck.
Use the bottleneck to produce only the most highly valued products.
Synchronize all other processes to the bottleneck.
Increase the bottleneck’s capacity or outsource the production of its output.
Avoid inertia; find the next bottleneck.
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Learning Objective 8
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Linear Programming
Applied to production situations with multiple products and constraints Constraints represent capacity limits of the processes and resources Used to help find the product mix that maximizes profits There may be many feasible input and output combinations that satisfy the constraints, but this technique helps find the optimum point at which profits are maximized Assumption: that all relationships in the model are linear
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