Cost-Volume-Profit Analysis: Break-Even Point and Profit Targets - Prof. Michael Constas, Study notes of Cost Accounting

Download Cost-Volume-Profit Analysis: Break-Even Point and Profit Targets - Prof. Michael Constas and more Study notes Cost Accounting in PDF only on Docsity! Chapter 6 Notes Page 1 Please send comments and corrections to me at mconstas@csulb.edu 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 mconstas@csulb.edu 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") CMU Chapter 6 Notes Page 5 Please send comments and corrections to me at mconstas@csulb.edu 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 all we know, Cuba sells one radio for $100,000 each (or 100,000 radios for $1 each). So, we cannot use Formula “A”. Although you do not know the price or the Variable Cost per unit, you are still able to calculate the Contribution Margin Ratio. Contribution Margin = Px - Vx = (P-V)x = (P-V) Sales Revenue Px Px P Thus, we can use Formula “B”. The Contribution Margin Ratio is .70 (70,000/100,000), and the Break-Even Point in Sales Revenue is: Px = F/CMR = 50,000/.70 = $71,428.57 Keep in mind that the reason that Cuba’s Sales Revenue is lower than it was before is because Cuba sold fewer units. Cuba’s price and Variable Cost per unit remained unchanged. Let's check if Cuba Breaks Even at this Sales Revenue figure: Sales Revenue: $ 71,428.57 P[.7142857(old unit volume)] Less Variable Costs (30%): -21,428.57 -V[.7142857(old unit volume)] Contribution Margin: $50,000 .7142857 (old Contribution Margin) Less Fixed Costs: -$50,000 Operating Profit: $ 0 Chapter 6 Notes Page 6 Please send comments and corrections to me at mconstas@csulb.edu Profit Targets You can use this same analysis to figure out how many units you need to sell in order to generate a target before-tax profit (Operating Profits). Operating Profits are determined as follows: Operating Profits = Revenue - Costs Op = Px - Vx - F If you move the costs to the other side of the equation, you end up with: Px = Vx + F + Op If you solve for x, you will see how many units you need to produce and sell in order to generate your target Operating Profits: Px = Vx + F + Op Px - Vx = F + Op x(P - V) = F + Op x = (F + Op) Modified Formula “A” (P - V) Or x = (F + Op) CMU As was true with Formula “B”, we can multiply both sides of Modified Formula “A” by price to produce the formula that gives the Sales Revenue that is necessary to produce the target Operating Profits: x = (F + Op) (P - V) Px = (F + Op)P (P - V) Px = _(F + Op)_ Modified Formula “B” (P - V) P Or Px = (F + Op) CMR Chapter 6 Notes Page 7 Please send comments and corrections to me at mconstas@csulb.edu Profit Target Example Assume that Bullock Net Co. has established a target Operating Profits figure of $40,000. Using Modified Formula “A”, you can determine the number of units that Bullock will need to sell in order to generate this target: x = (2,000 + 40,000) (200 - 120) x = 42,000 80 x = 525 units If you think about it, it makes sense to add the Fixed Costs and the Target Operating Profits together and then divide by the Contribution Margin. If you make $80 every time you sell a unit, then you have to sell 25 units to Break Even (2,000/80). After you Break Even, you make $80 of profits every time that you sell a unit, and you have to sell 500 units in order to generate Operating Profits of $40,000 (40,000/80). Using Modified Formula “B”, you can determine the Sales Revenue that Bullock will need in order to generate Operating Profits of $40,000: x = (2,000 + 40,000) (200 - 120) 200 x = 42,000 .4 x = $105,000 After-Tax Profit Targets The Operating Profits to which we have been referring do not include tax expense. Once you subtract your tax expense from your Operating Profits, you have your Net Income. If you want to know how many units that you need to produce and sell in order to generate a target Net Income (or after-tax profit), just convert the after-tax number into a before-tax number. You can then substitute the before-tax profit figure in the above formulas. Chapter 6 Notes Page 10 Please send comments and corrections to me at mconstas@csulb.edu Baskets = F/CMbasket Baskets = 2,000/ 5 Baskets = 400 Baskets You now describe the units of fruit contained in the Baskets: Bananas: There are 3 Bananas in every Basket, so we need to sell 3 x 400 Baskets = 1200 Bananas in order to Break-Even. Oranges: There is one Orange in every Basket, so we need to sell 400 Oranges in order to Break-Even. With the Weighted Average Contribution Margin Method, we calculate the Weighted Average Contribution Margin for one unit of fruit, using the given sales mix. CMwa = .75 CMbanana + .25 CMorange CMwa = .75 (1) + .25 (2) CMwa = .75 + .5 = $1.25 The Break-Even Point in units is: x = F/CMwa x = 2,000/ 1.25 x = 1600 units Since we know that the total units of fruit sold should be 1600, and we know the sales mix is 75%:25%: Bananas: .75 (1600) = 1200 Bananas Oranges: .25 (1600) = 400 Oranges Margin of Safety The "Margin Of Safety" is the amount of sales (in dollars or units) by which the actual sales of the company exceeds the Break-Even Point. We know that Bullock’s Break- Even Point is 25 units or $5,000. If Bullock really sells 40 units (Sales Revenue of $8,000), then its Margin Of Safety is 15 units (40-25) or $3,000 ($8,000 - $5,000). Operating Leverage If you take the total Contribution Margin and divide it by the Operating Profits, this gives you the Operating Leverage (or degree of Operating Leverage). For example, if Bullock Net Co had actual sales of 40 units, its Operating Profits would be calculated as follows: Chapter 6 Notes Page 11 Please send comments and corrections to me at mconstas@csulb.edu Revenue: $ 8,000 (200x40) Variable Costs: -$4,800 (120x40) Contribution Margin: $ 3,200 Fixed Costs: -$2,000 Operating Profits: $1,200 The Operating Leverage is calculated as follows: Contribution Margin = $3,200 = 2.67 Operating Profits $1,200 Chapter 6 Notes Page 12 Please send comments and corrections to me at mconstas@csulb.edu The Operating Leverage of 2.67 indicates that if Bullock can increase its sales by 50%, then its Operating Profits will increase by 2.67 x 50% or 133%. Thus, the Operating Profits of $1,200 will increase by $1,600 (1.33 x $1,200) to $2,800. This calculation assumes that the Price, Variable Cost per Unit, and the Fixed Costs do not change. You are assuming that the increase in sales is caused by a 50% increase in the number of units sold (x): OLD NEW Revenue: $ 8,000 (200x40) $12,000 (200 x 60) Variable Costs: -$4,800 (120x40) -$7,200 (120 x 60) Contribution Margin: $ 3,200 $4,800 (80 x 60) Fixed Costs: -$2,000 -$2,000 Operating Profit: $1,200 $2,800