Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 12 Financial and Cost- Volume-Profit Models

12-2 Learning Objective 1

12-3 Definition of Financial Models Accurate, reliable simulations of relations among relevant costs, benefits, value and risk that are useful for supporting business decisions. Relationships between costs, revenues, & income. Relationships between current investments and value. Pro forma financial statements.

12-4 Objectives of Financial Modeling To improve the quality of decisions To simulate accurately and reliably the relevant factors and relationships To simulate accurately and reliably the relevant factors and relationships To allow flexible and responsive analyses

12-5 Learning Objective 2

12-6 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. 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.

12-7 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) 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! Basic CVP Model and the Break-Even Point

12-8 The break-even point is the point in the volume of activity at which the organization’s revenues and expenses are equal. Basic CVP Model and the Break-Even Point

12-9 Consider the following information developed by the accountant at Curl, Inc.: Basic CVP Model and the Break-Even Point

12-10 For each additional surf board sold, Curl generates $200 in contribution margin. Basic CVP Model and the Break-Even Point

12-11 Fixed expenses Unit contribution margin = Break-even point (in units) $80,000 $200 = 400 surf boards Basic CVP Model and the Break-Even Point

12-12 Here is the proof! 400 × $500 = $200, × $300 = $120,000 Basic CVP Model and the Break-Even Point

12-13 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) = Basic CVP Model and the Break-Even Point

12-14 $80,000 40% $200,000 sales = Basic CVP Model and the Break-Even Point

12-15 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. Basic CVP Model in Graphical Format

12-16 Units Sold Sales in Dollars Profit area Loss area Break-evenpointBreak-evenpoint Fixed expenses Total expenses Total sales Basic CVP Model in Graphical Format

Profit Units sold (00s) Some managers like the profit-volume graph because it focuses on profits and volume. Some managers like the profit-volume graph because it focuses on profits and volume. Profit area Loss area Break-even point Break-even point Profit-Volume Graph

12-18 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 CVP and Target Income

12-19 Revenue = Variable costs + Fixed costs + Income ($500 × Q) ($300 × Q) = +$80,000 + $100,000 $200Q= $180,000 Q = 900 surf boards We can also use the equation approach to get the same result. CVP and Target Income

12-20 Operating Leverage Reflects the risk of missing sales targets. Measured as the ratio of contribution margin to operating income. 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.

12-21 Contribution margin Net income Operating leverage factor = $100,000 $20,000 = 5 Operating Leverage

12-22 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? Operating Leverage Here’s the proof!

12-23 Operating Leverage 10% increase in sales from $250,000 to $275, % increase in sales from $250,000 to $275, results in a 50% increase in income from $20,000 to $30, results in a 50% increase in income from $20,000 to $30,000.

12-24 Learning Objective 3

12-25 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.

12-26 Learning Objective 4

12-27 Modeling 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) 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) We can adjust the basic CVP model to incorporate income taxes.

12-28 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 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

12-29 For a company with more than one product, sales 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. For a company with more than one product, sales 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. Modeling Multiple Products

12-30 Curl provides us with the following information: Modeling Multiple Products Sales mix computation

12-31 Weighted-average unit contribution margin $200 × 62.5% Modeling Multiple Products

12-32 Break-even point Break-even point = Fixed expenses Weighted-average unit contribution margin Break-even point = $170,000 $ Break-even point = 514 combined units Modeling Multiple Products Fixed costs increased from $80,000, due to expansion needed to sell multiple products.

12-33 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. Modeling Multiple Products The break-even point of 514 units is valid only for the sales mix of 62.5% and 37.5%.

12-34 Modeling Multiple Cost Drivers An insight from activity-based costing: costs may be a function of multiple activities, not merely sales volume. Total Cost = (Unit variable cost × Sales units) + (Batch cost × Batch activity) + (Product cost × Product activity) + (Customer cost × Customer activity) + (Facility cost × Facility activity) Some costs treated as fixed (when sales volume is the only activity) may now be considered variable.

12-35 Learning Objective 5

12-36 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.

12-37 Sensitivity Analysis  Estimate the most likely value of each parameter.  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. Because of the number of computations involved, computerized models are used for sensitivity analysis.  Record profit for each change and repeat process for all parameters.

12-38 Sensitivity Analysis Because of the number of computations involved, computerized models are used for 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: the change in parameter has a negligible effect on profit.

12-39 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.

12-40 Learning Objective 6

12-41 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. 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.

12-42 Rose Company produces three products. Selected data are shown below. Modeling Scarce Resources

12-43 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? 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? Modeling Scarce Resources

12-44 The key is the contribution margin per unit of the scarce resource. Product 2 should be emphasized because it has the highest contribution per minute on machine A1, the scarce resource. Modeling Scarce Resources 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.

12-45 Let’s see how this plan would work. Modeling Scarce Resources

12-46 Let’s see how this plan would work. Modeling Scarce Resources

12-47 Let’s see how this plan would work. Modeling Scarce Resources Is this a problem?

12-48 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?

12-49 Modeling Scarce Resources

12-50 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? 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.

12-51 What is the maximum amount Rose would pay per minute for the additional 1,900 minutes to produce Product 1? Modeling Scarce Resources Contribution per minute for Product 1 is $ Rose could pay up to $24.00 per minute for additional capacity.

12-52 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? 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 $ Rose could pay up to $30.00 per minute for additional capacity as long as Product 2 could be sold.

12-53 Learning Objective 7

12-54 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.

12-55 Theory of Constraints – Six Step Process 1. Identify the appropriate measure of value created – this will typically be throughput. 2. Identify the organization’s bottleneck. 3. Use the bottleneck to produce only the most highly valued products. 4. Synchronize all other processes to the bottleneck. 5. Increase the bottleneck’s capacity or outsource the production of its output. 6. Avoid inertia; find the next bottleneck.

12-56 Learning Objective 8

12-57 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

12-58 End of Chapter 12