Chapter 5

Chapter 5

Fixed Costs: costs that remain the same in total, but vary per unit when production volume changes (do vary on a per unit basis). Examples include rent, salary of a plant manager, insurance, taxes, and depreciation.

Variable costs: vary in direct proportion to changes in production volume but are fixed when expressed as per unit amounts. As production increases, variable costs increase in direct proportion to the change in volume.

Step costs: costs that vary with activity in steps and may look like and be treated as either variable costs or fixed costs; step costs are not technically fixed costs, but may be treated as such if they remain constant within a relevant range of production

Mixed costs: Costs that include both a fixed and variable component, making it difficult to predict the behavior of a mixed costs as production changes unless the cost is first separated into its fixed and variable components

Regression Analysis: uses statistical methods to fit a cost line (regression line) through a number of data points. Regression analysis statistically finds the line that minimizes the sum of the squared distance from each data point to the line.

R square: a measure of goodness of fit (how well the regression line fits the data); The proportion of dependent variable variation that is explained by the by changes in the independent variable. An R square of 1 indicates a perfect correlation between the dependent and independent variable.

High Low method

Change in cost / change in volume = variable cost per unit

Total Overhead costs = Fixed costs + (variable cost per unit)

Total Overhead costs - variable costs = fixed costs

In general, variable costs are relevant because vary with the level of production. Fixed costs are not relevant because they typically don't change as production changes.

Taxes

After tax cost = Pretax cost x (1 - tax rate)

After tax benefit = Pretax receipts x (1 - tax rate)

After tax income = Pretax income x (1 - tax rate)

Chapter 6

Cost-volume-profit (CVP) analysis: a tool that focuses on the relationship between a company's profits and 1) the prices of products and services, 2) the volume of products and services, 3) the per unit variable costs, 4) the total fixed costs, and 5) the mix or products or services produced

Assumptions of CVP analysis:

1) selling price is constant

2) costs are linear

3) sales mix used to calculate the weighted average contribution margin is constant

4) the amount of inventory is constant

Gross profit: the difference between sales and cost of goods sold.

Contribution margin per unit: The sales price per unit of product less all variable costs to produce and sell the unit of product; used to calculate the change in contribution margin resulting from a change in unit sales.

For every unit change in sales, contribution margin will increase or decrease by the contribution margin per unit multiplied by the increase or decrease in sales volume.

The company is at the break even point when the contribution margin just covers fixed expenses and the net income is zero.

Contribution margin ratio: the contribution margin divided by sales; used to calculate the change in contribution margin resulting from a dollar change in sales. It is calculated by dividing the contribution margin in dollars by sales dollars.

For every change in sales, contribution margin will increase or decrease by the contribution margin ratio multiplied by the increase or decrease in sales dollars.

Equations

Sales - variable costs - fixed costs = net income

Net income = (sales price per unit x volume) - (variable cost per unit x volume) - fixed costs; NI = SP(x) - VC(x) - FC

Because SP - VC = contribution margin (CM), the above equation can be simplified to:

NI = CM(x) - FC

Because NI = 0 at the break even point, total CM must equal FC.

CM(x) = FC

And the volume of sales in order to break even can be calculated by dividing FC by CM:

Break even (units) = fixed costs/contribution margin per unit

Break even ($) = fixed costs/contribution margin ratio

Break even calculations with multiple products: requires the calculation of an "average" contribution margin for all products produced and sold. The "weighted-average" contribution margin can be calculated by multiplying the unit contribution margin for each unit by the proportion of each unit in the sales mix and adding the resulting numbers.

Break even when using activity based costing:

Break-even (units) = fixed costs + batch level costs + product level costs / contribution margin per unit

Target Profit Analysis

Sales - variable costs - fixed costs = target profit (before tax)

Target profit = (sales price per unit x volume) - (variable cost per unit x volume) - fixed costs

Substituting symbols: TP (before tax) = SP(x) - VC(x) - FC

Because SP - VC = contribution margin, the equation can be simplified to:

TP(before tax) = CM(x) - FC or CM(x) = FC + TP (before tax)

Sales volume (to reach a target profit before tax) = [FC + TP(before tax)] / CM

In a multiple product environment:

Sales volume