Certified Management Accountant
Direct Materials Variances
(Actual Purchase Cost) Actual Direct Materials Purchased Actual Direct Materials at Standard Price at Actual Price Materials Price (Rate) Variance
Sales‐Volume Variance
(Actual Qty - Budgeted Qty) × Budgeted Selling Price
Sales‐Price Variance
(Actual Selling Price - Budgeted Selling Price) × Actual Qty Sold
Variable Overhead Variances The variable overhead variances are calculated in a manner similar to the direct materials variances, as follows:
(Flexible Budget) Standard Volume of Allocation Base at Standard Application Rate Actual Volume of Allocation Base at Standard Application Rate Overhead Costs Actual Variable
Input Mix and Yield Variances
(Flexible Budget) Standard Input Mix Standard Total Input Quantity at Standard Price Standard Input Mix Actual Total Input Quantity at Standard Price Actual Input Mix Actual Total Input Quantity at Standard Price
Direct Labor Variances
(Flexible Budget) Standard Labor Hours For Actual Output at Standard Rate Actual Labor Hours at Standard Rate (Actual Cost) Actual Labor Hoursat Actual Rate
Fixed Overhead Variances
(Flexible Budget) Std Volume of Allocation Base at Std Application Rate (Static Budget) Budget Volume of Allocation Base at Std Application Rate (ACTUAL) Actual Fixed OH Cost
Direct Labor Yield Variance
(Standard # DL Hours Allowed for Actual Output -Actual # - DL Hours x Used) x Standard Average DL Rate Per Hour = Direct Labor Yield Variance
Direct Labor Mix Variance
(Standard DL Mix % - Actual DL Mix%) x Actual Total # DL Hours Used x Standard Individual DL Rate Per Hour - Standard DL Rate Per Hour = Direct Mix Labor Variance
Direct Labor Efficiency/Usage Variance
(Standard Labor Hours - Actual Labor Hours) × Standard Labor Rate
Direct Labor Price/Rate Variance
(Standard Labor Rate - Actual Labor Rate) × Actual Labor Hours
Material or Labor Mix Variance
(Standard Mix - Actual Mix) × Actual Total Quantity × Standard Price
Direct Materials Price/Rate VarianceMeasurement Point - At Time of Purchase
(Standard Price - Actual Price) × Actual Quantity of Materials Purchased
Direct Materials Price/Rate VarianceMeasurement Point At Time of Production
(Standard Price - Actual Price) × Actual Quantity of Materials Used
Direct Materials Efficiency/Usage Variance
(Standard Quantity of Material - Actual Quantity of Material Used) × Standard Price
Material or Labor Yield Variance
(Standard Total Quantity - Actual Total Quantity) × Standard Mix × Standard Price
Variable Overhead Efficiency Variance
(Standard Volume of Allocation Base - Actual Volume of Allocation Base) × Standard Application Rate
Fixed Overhead Efficiency/Volume Variance
(Standard Volume of Allocation Base - Actual Volume of Allocation Base) × Standard Application Rate fixed overhead efficiency variance, also called the fixed overhead volume variance, arises from differences between budgeted and actual volumes of the allocation base. It occurs because a fixed cost is being treated as a variable cost.
Effect of Sales Mix on Contribution Margin
(Static Budget) Budget Qty Units Sold at Standard Contrib. Margin (Flexible Budget) Actual Qty Units Sold at Standard Contrib. Margin
Sales/Revenue Variances
(Static Budget) Budget Qty Units Sold at Budget Price (Flexible Budget) Actual Qty Units Sold at Budget Price (Actual Revenue) Actual Qty Units Sold at Actual Price
Confidence Interval for Estimated Values of y
A confidence interval for an estimated y value can be constructed in a similar manner to the method described in the statistics section.
Exponential Smoothing
A method that iteratively calculates a weighted average by applying weights to the most recent observation and to prior period smoothed weighted averages. The weighting factor is based on experience and judgment. Exponential smoothing techniques can be made more sophisticated by making adjustments for trend and seasonality. The formula for simple (also called single) exponential smoothing is: y(t) = wy(t-1) + (1-w)f(t-1) where: f(t) is the exponential weighted moving average for time t y(t-1) is the observation for the previous period f(t-1) is the exponential weighted moving average for the previous period w is the weighting factor (also called the smoothing constant)
Coefficient of Determination (R2)
A ratio which indicates the proportion of variance in the dependent variable which is statistically explained (determined) by the independent variable using the regression equation. The total variation of the dependent variable y from its mean can be divided into the part explained by the regression equation and the part which is not explained, but is produced by chance. The values range from zero (no explanation) to 1 (all explained). It can also be expressed as a percentage, as in "x explains 70% of the variation in y." The CMA exam has required an understanding of the significance of this ratio, but has not required its computation.
Weighted Moving Average
Based on experience, we may assign weights to each of the prior periods.
TRANSFER PRICING
Cost‐based Price Market Price Negotiated Price
ROA Denominator issues
Denominator Issues It is in this figure that there are a wide variety of possibilities. The two issues are (a) which assets to use and (b) how to value the assets.
Learning Curve Analysis
Exponential Curve The reduction in time will follow an exponential curve. In other words, the production time per unit is reduced by a fixed percentage each time production is doubled. The actual formula is a logarithmic model, which is not likely to be tested on the CMA exam.
TC=(VCs x Qa) + FCs
Flexible Budget uses actual quantity
Expected Value of Perfect Information
If the decision maker had perfect knowledge as to which state of nature would occur, the decision offering the highest payoff could be selected. The difference between the expected value with the highest payoff (complete information) and the expected value calculated in the payoff table (condition of risk) is the amount one would be willing to pay to acquire perfect information. This can be useful when considering how much to spend to gather more data - cost vs. benefits. To calculate the expected value with complete knowledge, select the highest payoff for each state of nature, using the above example:
Three Variance Method
In the three variance method, the VOH Spending variance and the FOH Spending variance are combined. Both of these variances compare the amount actually spent with the flexible budget (based on input) amount.
Two Variance Method
In the two variance method the Budget/Spending variance from the three variance method is combined with the VOH Efficiency variance into a Controllable variance. The FOH Production Volume Variance is considered an Uncontrollable Variance.
Non‐Weighted Moving Average
In this procedure, values are forecast based on the mean value over a specific number of prior periods. Each of the prior periods is given equal weight.
Residual Income
Investment base Net income Cost of capital - at 10% Residual income ROIDivision A $100,000 $20,000 10,000 $10,000 20% Division B $600,000 $90,000 60,000 $30,000 15%
Economic Value Added (EVA)
Many large companies in the United States have begun to use this performance measure. It is a type of residual income calculation that takes into account (1) the after-tax operating income, (2) a required rate of return equal to the weighted-average cost of capital, and (3) investment measured as total assets less current liabilities.. Computation It is computed as after-tax operating income minus [the weighted-average cost of capital x (total assets less current liabilities)]. 3. Underlying Assumption The assumption underlying the use of this performance measure is that value is created only if the after-tax operating income exceeds the cost of investing the capital. The measure can be improved by earning more income from the same level of capital, by using less capital, or by investing in higher-return projects.
Market Value Added (MVA)
Market value added (MVA) is the difference between the market value of capital (debt plus equity) and the capital contributed by investors (i.e., book value of debt plus equity). A positive MVA means that the company has increased the value of capital contributed by investors, thus creating shareholder wealth.
TC=(VCs xQs) + FCs
Master Budget uses standard quantity
ROA
ROA =Profit Margin x Asset Turnover Income/Assets = Income/Sales x Sales/Total Assets
Fixed Overhead Spending Variance
The fixed overhead spending variance is simply the difference between actual and budgeted fixed overhead costs, as shown in Figure 2.5.
Median
The middle value of a group of data items ranked in size order by value.
Direct Materials Mix Variance
The mix variance measures the effect of the change in proportions of the individual direct material inputs used. The variance would be computed for each type of direct material input and added for the total mix variance. The direct materials mix variance is favorable if: There is increased percentage use of a material item over the standard and the standard cost is less than the average cost (i.e. relatively more was used of the cheaper input units) or There is decreased percentage use of a material item from the standard and the standard cost is greater than the average cost (i.e. relatively less was used of the more expensive input units).
t‐Statistic (t‐Value)
The population standard deviation is assumed to be normal, but it is unknown. The t-value of the slope coefficient (b) is used to evaluate the significance of the relationship between changes in the dependent variable (y) and the independent variable (x). The higher the t statistic, the less likely the relationship between the variables occurred by chance. After calculating the standard error of the coefficient b, we divide the standard error of the coefficient into the coefficient. This gives us a measure of the relative size of the standard error, or precision.
Standard Error of the Estimate (Se)
The range within which the true y is located. Under the regression equation assumptions, there is a 68.3% probability that the true y is within one Se of y′, and there is a 95.5% probability that the true y is within two Se of y′. Se is also called the standard error of the residuals, as it is the square root of the variances of the residuals (difference between the predicted and the actual values of the data points). ′ 2
Four Variance Method
The two variable and two fixed overhead variances together make up the four variance method of analyzing overhead variances.
Variable Overhead Spending Variance
The variable overhead spending variance is the difference between actual variable overhead costs and the expected amount of variable overhead cost, given the actual volume of the allocation base. It is not likely that an actual application rate will be given in a problem; calculations for overhead spending variances are typically done using total actual costs as shown in Figure 2.4.
Direct Materials Yield Variance
The yield variance measures the change in yield of a constant mix of direct material inputs. The variance would be computed for each type of direct material input and added to get the total yield variance. (Standard # Units DM Inputs Allowed For Actual Output - Actual # Units - DM Inputs Used) x Standard Average x Price Per Unit of DM Inputs = Direct Materials Yield Variance
ROA numerator issues
There are two major issues for measurement of income in the numerator: (a) income taxes, and (b) GAAP.
Mean
This is the arithmetic average of the sample data. It is the most widely used measure of central tendency. It can be more influenced by extreme values than the mode or median.
Mode
This is the value most frequently occurring. It does not have to be in the center of the data items. It could be at either end of the range of values, or both ends. If there are two modes, the group is called bimodal. This could be valuable information to determine if the population should actually be considered two populations, as in a stratified population.
Cash Flow Return on Investment (CFROI)
To avoid possible accrual accounting manipulation of performance measures and to increase focus on cash flows, managers may be evaluated using a cash flow return on investment (CFROI). CFROI, developed by Boston Consulting Group and Holt Value Associates, can be calculated by dividing operating inflation- adjusted cash flow by gross assets. Sometimes the denominator is calculated using the market value of equity; however, this measure is often unavailable for responsibility centers.
Simple Regression Equation The general form of the linear regression equation for one independent variable is y′ = a+bx
y′= the estimated value of the dependent variable (sometimes written as y^; when estimating a cost function, y′ is the estimated cost for a given level of the cost driver) x= the independent variable (when estimating a cost function, x is a cost driver) a= the point of intersection of the linear regression line with the Y axis (also called the intercept or the constant; when estimating a cost function, a is the fixed cost) b= the slope of the regression line (when estimating a cost function, b is the variable cost per unit of the cost driver)