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CSULB ACCT 310 - Cost-Volume-Profit Analysis

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Chapter 6 Notes Page 1 Please send comments and corrections to me at [email protected] Cost-Volume-Profit Analysis Understanding the relationship between a firm’s costs, profits and its volume levels is very important for strategic planning. When you are considering undertaking a new project, you will probably ask yourself, “How many units do I have to produce and sell in order to Break Even?” The feasibility of obtaining the level of production and sales indicated by that answer is very important in deciding whether or not to move forward on the project in question. Similarly, before undertaking a new project, you have to assure yourself that you can generate sufficient profits in order to meet the profit targets set by your firm. Thus, you might ask yourself, “How many units do I have to sell in order to produce a target income?” You could also ask, “If I increase my sales volume by 50%, what will be the impact on my profits?” This area is called Cost-Volume-Profit (CVP) Analysis. In this discussion we will assume that the following variables have the meanings given below: P = Selling Price Per Unit x = Units Produced and Sold V = Variable Cost Per Unit F = Total Fixed Costs Op = Operating Profits (Before Tax Profits) t = Tax rate Break-Even Point Your Sales Revenue is equal to the number of units sold times the price you get for each unit sold: Sales Revenue = Px Assume that you have a linear cost function, and your total costs equal the sum of your Variable Costs and Fixed Costs: Total Costs = Vx + F When you Break Even, your Sales Revenue minus your Total Costs are zero: Sales Revenue – Total Costs = 0 Breaking Even?Chapter 6 Notes Page 2 Please send comments and corrections to me at [email protected] This is the “Operating Income Approach” described in your book. If you move your Total Costs to the other side of the equation, you see that your Sales Revenue equals your Total Costs when you Break Even: Sales Revenue = Total Costs Now, solve for the number of units produced and sold (x) that satisfies this relationship: Revenue = Total Costs Px = Vx + F Px - Vx = F x(P - V) = F x = __F__ (FORMULA "A") (P -V) Formula "A" is the “Contribution Margin Approach” that is described in your book. You can see that both approaches are related and produce the same result. Break-Even Example Assume Bullock Net Co. is an Internet Service Provider. Bullock offers its customers various products and services related to the Internet. Bullock is considering selling router packages for its DSL customers. For this project, Bullock would have the following costs, revenues and tax rates: P = $200 V = $120 F = $2,000 Tax Rate (t) = 40% Using Formula “A”, we can compute the Break-Even Point in units: x = 2,000 (200 - 120) x = 2,000 80 x = 25 units Sometimes, you see the (P-V) replaced by the term "Contribution Margin Per Unit" (CMU): x = __F__ (FORMULA "A") CMUChapter 6 Notes Page 3 Please send comments and corrections to me at [email protected] This is way that your textbook presents Formula “A”. This makes sense if you think about it. Every time that you sell a unit, you earn the Contribution Margin per unit. The Contribution Margin per unit is the portion of the Sales Price that is left after paying the Variable Cost per unit. It is available to pay the Fixed Costs. If every time you sell a unit you earn $80 to help pay your Fixed Costs of $2,000, how many units do you need to sell in order to pay off the $2,000 completely? x = 2,000 = 25 80 Break-Even Point In Sales Dollars Taking Formula "A," you can multiply both sides of the equation by P: x = _F_ (P-V) Px = F x P (P-V) Recall what you do when you have a fraction in the denominator of a fraction: _a_ = (a)x(c) b/c b This works backwards as well: (a)x(c) = _a_ b b/c We can rewrite this equation: Px = __F__ (FORMULA "B") (P-V) PChapter 6 Notes Page 4 Please send comments and corrections to me at [email protected] Formula “B” gives you the Sales Revenue that you need in order to Break Even. The Denominator [(P-V)/P] is referred to as the “Contribution Margin Ratio”. It tells you, what percentage of every dollar of Sales Revenue goes to help pay off the Fixed Costs. You can see this if you break up the Contribution Margin Ratio: (P-V)/P P/P - V/P 1 - V/P V/P gives you the percentage of the Sales Price that goes to pay off the Variable Costs (the Variable Cost Ratio or Variable Margin). Thus, one minus the Variable Cost Ratio gives you the percentage of the Sales Price that is available to help pay the Fixed Costs. Sometimes Formula B is rewritten by replacing [(P-V)/P] with the Contribution Margin Ratio (CMR): Px = __F__ (FORMULA "B") CMR This is the way Formula B is presented in your book Break-Even Point In Sales Dollars Examples Let us continue using the Bullock example. Using Formula “B”, we can compute the Break-Even Point in Sales Revenue: Px = __2,000__ (200 - 120) 200 Px = 2,000 .40 Px = $5,000 So, what is the big deal? We already knew that Bullock needed to sell 25 units to Break Even by using Formula “A”. We also know that each unit sells for $200. We therefore know that selling the 25 units will produce Sales Revenue of $5,000. Why do we need a separate formula? We have the two formulas because sometimes you might not have enough information to use Formula “A”, but you will have enough information to use Formula “B”.Chapter 6 Notes Page 5 Please send comments and corrections to me at [email protected] For example, Cuba Radio Co produces portable sports radios. It has released the following Variable Costing Income Statement. This is the only financial information that we have regarding the Cuba’s operations: Sales Revenue: $100,000 (Px) Less Variable Costs: -30,000 (Vx) Contribution Margin: $ 70,000 (Px – Vx) Less Fixed Costs: -50,000 (F) Operating Profit: $ 20,000 (Px - Vx – F) What is the Break-Even point for Cuba? We do not know the number of units that Cuba sells in a year. We do not know the Price or the Variable Cost per unit. For


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CSULB ACCT 310 - Cost-Volume-Profit Analysis

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