Cost-Volume-Profit Analysis and Decision-Making
In order to recover from the recent operating losses that the Biggie Widget Company has experienced, management has made some tentative new decisions and believes that the use of CVP analysis will be useful when evaluating these decisions.
Recall that current selling price for widgets is $200 per unit and that total assets reported on the balance sheet were valued at $6,786,651. Total Costs (TC) can be estimated based on product quantity (Q) using the following linear cost function:
TC = 104 Q + 1,300,000
I. Based on this information, determine each to the following
1. Unit contribution margin
2. Contribution margin ratio
3. Breakeven point
II. Determine the quantity of product that must be produced and sold in order to achieve an income equal to:
1. $140,000?
2. 10% of total assets?
III. Complete the following table:
Sales Quantity Revenue Variable Cost Fixed Costs Total Costs Operating income
5,000 units 1,000,000 520,000 1,300,000 1,820,000 2,820,000
10,000 units 2,000,000 1,040,000 1,300,000 2,340,000 4,340,000
15,000 units 3,000,000 1,560,000 1,300,000 2,860,000 5,860,000
20,000 units 4,000,000 2,080,000 1,300,000 3,380,000 7,380,000
30,000 units 6,000,000 3,120,000 1,300,000 4,420,000 10,420,000
IV. List the major assumptions of CVP analysis.
V. Prepare a contribution margin income statement based on April’s EXPECTED production quantity of 15,000 units of product. (This is the Base Case referred to later in this assignment.)
VI. Determine the Operating Leverage Index for this Base Case.
For several months, Biggie Widget Company has exhibited poor profit performance and has incurred net operating losses or low operating profits. Realizing that the company cannot continue to sustain this poor performance, management has proposed the following five changes and is considering whether to implement one or more of these changes in April.
Proposal A: Increase selling price from $200 per unit to $220 per unit (assume unit variable costs do not change).
Proposal B: Decrease the number of sales people from 135 to 90 while increasing their base salary from $3,000 per month to $3,500 per month, thereby decreasing total Sales People's Salaries from $405,000 to $315,000.
Proposal C: Increase advertising by $50,000 per month.
Proposal D: Certify a substitute for Material X called Material X2 which can be purchased for $3.50 per unit instead of $6.90, the current cost of Material X plus related freight. NOTE: The Company’s product requires four units of Material X (and X2).
Proposal E: Increase the rate for Sales People's Commissions from 12% to 16%.
Details related to the estimates of fixed and variable costs (excluding income taxes) based on the analysis of March data are:
Fixed Costs: . Unit Variable Costs: .
Sales People's Salaries $ 405,000 Sales People's Commissions $ 24.00
Advertising 297,200 Material X (4 units @ $6.90) 27.60
Other Fixed 598,800 Other Variable 52.40
Total Fixed Costs $1,300,000 Total Unit Variable Costs $104.00
Required:
1. For each proposal above, specify the new profit function that would result from implementing the proposal (the first is completed for you) and determine the new quantity needed to achieve the target profit, which is the same amount of profit as in the BASE CASE above.
New Profit Function Quantity Needed to Achieve Target Profit
A.
B.
C.
D.
E.
2. In general terms, describe how operating income changes as a result of increases and decreases in
A. Selling price.
B. Variable cost per unit.
C. Fixed costs.
A. Selling price, CVP affect the number of unit sold to breakeven point. Selling price per unit if to high BEP would be difficult to meet.
B. Variable cost per unit is -number of unit sold, total variable cost are unit variable cost time number of unit sold. Price X number of units; Variable cost per unit X no. of unit minus total fix cost C. Fixed costs are constant to relevant range. The total contribution margin is, number Unit sold and Contribution margin per unit. If price drop then contribution margin changes.
3. Assume that ALL five of the proposed decisions are implemented and that management wants to attain a target pre-tax profit of $140,000.
A. What is the new profit function? (HINT: Remember that sales commissions are determined as a percent of sales and that the unit selling price is changing.)
B. What is the dollar amount of the contribution margin per unit?
C. What is the breakeven quantity?
D. What is the quantity of finished product that must be produced and sold to attain the target profit equal to:
1. $140,000
2. 10% of total assets,
E. What is the total contribution margin when the target profit is equal to:
1. $140,000
2. 10% of total assets,
F. What is the value of operating leverage when the target profit is equal to:
1. $140,000
2. 10% of total assets,
Perez Corporation was organized on January 1, 2009. During its first year, the corporation issued 2,000 shares of $50 par value preferred stock and 100,000 shares of $10 par value common stock. At December 31, the company declared the following cash dividends: 2009, $6,000, 2010, $12,000, and 2011, $28,000.
I.
1. Unit contribution margin can be calculated by subtracting the unit variable cost from the selling price per unit. In this case, it would be $200 - $104 = $96.
2. Contribution margin ratio can be calculated by dividing the unit contribution margin by the selling price per unit. In this case, it would be $96 / $200 = 0.48 or 48%.
3. Breakeven point can be calculated by dividing the total fixed costs by the unit contribution margin. In this case, it would be $1,300,000 / $96 = 13,541.67 units. Since we can't have a fraction of a unit, the breakeven point would be 13,542 units.
II.
1. To achieve an income of $140,000, we can calculate the quantity of product using the profit function. The profit function is calculated as follows:
Profit = (Selling price per unit - Unit variable cost) x Quantity - Total fixed costs
So, rearranging the equation we get:
Quantity = (Profit + Total fixed costs) / (Selling price per unit - Unit variable cost)
Quantity = ($140,000 + $1,300,000) / ($200 - $104)
Quantity = $1,440,000 / $96
Quantity = 15,000 units
Therefore, in order to achieve an income of $140,000, 15,000 units of product must be produced and sold.
2. To achieve an income of 10% of total assets, we can calculate the dollar amount using the profit function. The profit function is calculated as follows:
Profit = (Selling price per unit - Unit variable cost) x Quantity - Total fixed costs
So, rearranging the equation we get:
Quantity = (Profit + Total fixed costs) / (Selling price per unit - Unit variable cost)
Quantity = (0.10 x Total assets + $1,300,000) / ($200 - $104)
Quantity = (0.10 x $6,786,651 + $1,300,000) / ($200 - $104)
Quantity = $678,665.10 + $1,300,000 / $96
Quantity = $1,978,665.10 / $96
Quantity = 20,611.77 units
Therefore, in order to achieve an income equal to 10% of total assets, approximately 20,612 units of product must be produced and sold.
III.
The table shows the sales quantity, revenue, variable cost, fixed costs, total costs, and operating income for different sales quantities:
Sales Quantity | Revenue | Variable Cost | Fixed Costs | Total Costs | Operating Income
------------------------------------------------------------------------------------------
5,000 units | $1,000,000 | $520,000 | $1,300,000 | $1,820,000 | $2,820,000
10,000 units | $2,000,000 | $1,040,000 | $1,300,000 | $2,340,000 | $4,340,000
15,000 units | $3,000,000 | $1,560,000 | $1,300,000 | $2,860,000 | $5,860,000
20,000 units | $4,000,000 | $2,080,000 | $1,300,000 | $3,380,000 | $7,380,000
30,000 units | $6,000,000 | $3,120,000 | $1,300,000 | $4,420,000 | $10,420,000
IV.
The major assumptions of CVP analysis include:
1. The selling price per unit is constant.
2. Variable costs per unit are constant.
3. Fixed costs remain constant within a relevant range of activity.
4. The sales mix remains constant.
5. All costs can be classified as either variable or fixed.
6. The volume of production and sales is the only factor impacting costs and revenues.
V.
To prepare a contribution margin income statement based on April's expected production quantity of 15,000 units of product, we need to calculate the total revenue and total variable costs.
Total revenue = Selling price per unit x Quantity = $200 x 15,000 = $3,000,000
Total variable costs = Unit variable cost x Quantity = $104 x 15,000 = $1,560,000
Contribution margin = Total revenue - Total variable costs = $3,000,000 - $1,560,000 = $1,440,000
Therefore, the contribution margin income statement based on April's expected production quantity of 15,000 units would show a contribution margin of $1,440,000.
VI.
The operating leverage index can be calculated by dividing the contribution margin by the operating income. In this case, it would be:
Operating leverage index = Contribution margin / Operating income
Operating leverage index = $1,440,000 / $5,860,000 = 0.2459 or 24.59%
Therefore, the operating leverage index for the base case is 24.59%.