208 Understanding the Numbers So, as you can see, the pieces fit together quite logically. The points underlying these pieces can be summarized quite briefly: 1. First, we saw the need to distinguish between basic, ideal, and currently attainable standards. 2. Second, we saw the wisdom of distinguishing flexible from static budgets. 3. Third, we noted that our standards are the foundation stones on which these budgets are based. 4. We noted that all cost variances follow one simple formula: Actual Cost less Budgeted Cost equals Standard Cost Variance. 5. 6. Flexible budgets adjust variable cost and their variances for volume. 7. Volume has no effect on fixed costs or the variances derived from fixed costs. VARIABLE COST BUDGETS “That’s fine, but what am I going to do with these variances?” Tom asked a lit- tle impatiently. “Everything that I’ve seen so far may help top management, but it’s not much help to me.” “Good point, Tom. That’s why we need to examine productivity, which is the relationship between inputs and outputs. We’ll enhance your produc- tivity and your control over costs if we can focus on the elements that go into your costs.” With that Jane began to explain how in a typical cost accounting system the variable cost of a product or service is a function of: 1. The hours of labor (both direct and indirect) that go into a product. 2. The units of material that are used. 3. The other components of overhead. 4. The unit cost of each of these items. “Let’s call the amount of input that goes into one unit of output the pro- ductivity rate. For instance, one might need 500 pages or sheets of paper and 16 minutes of labor to produce a ream of letterhead. The material productivity rate is 500 pages per ream; the labor productivity rate is 18 minutes or 0.30 hour per ream. When the expected cost of the inputs is attached to the ex- pected productivity rates, a standard cost is said to result. The productivity Activity Variances Flexible Budget Static Budget Price Variances Actual Results Flexible Budget Activity Indices Flexible Budget Static Budget Price Indices Actual Results Flexible Budget =− =− = = Measuring Productivity 209 rates themselves are also known as standards. They are typically established by engineers.” As before, Jane began sketching out a numerical illustration of the points that she was making. Her sketches appear in Exhibit 7.3. “These are the stan- dards,” she said, “that determine the variable portion of the budget for pro- duction. Note the assumption here that variable overhead is a function of machine hours, or how long the machine runs. Other assumptions are possible but we will stick with this one in our example. “Fixed overhead is a little different because it does not really have a pro- ductivity rate. Let’s just put down the fixed overhead on a budgeted and an ac- tual basis, and we can come back and discuss the details later.” From these standards she began to derive the standard variable cost of the product; also its actual variable cost: Standard Cost Material Cost Labor Cost Variable Overhead Cost pages per page) hours $5.00 per hour) ( . hours $ . per hour) per ream Actual Cost Material Cost Labor Cost Variable Overhead Cost pages per page) hours $6.00 per hour) ( . hours $ . per hour) =++ =× + × +× =++ = =++ =× + × +× =+ ($. (. $. $. $. $. ($. (. $. $ 500 0 008 0 30 010 1500 400 150 150 700 500 0 007 0 25 0 125 10 00 350 1150 125 625 .$. $. + = per ream EXHIBIT 7.3 Standards and actuals for letterhead paper. Budgeted Actual Material: Productivity rate (pages per ream) 500 500 Cost per unit of input (per page) $0.008 $0.007 Cost per unit of output (per ream) $4.00 $3.50 Labor: Productivity rate (labor hours per ream) 0.30 0.25 Wage per unit of input (per labor hour) $5.00 $6.00 Wage per unit of output (per ream) $1.50 $1.50 Variable Overhead: Productivity rate (machine hours per ream) 0.10 0.125 Cost per unit of input (per machine hour) $15.00 $10.00 Cost per unit of output (per ream) $1.50 $1.25 210 Understanding the Numbers Jane then used these numbers to show how the budgeted and actual variable costs in Exhibit 7.1 were derived. For the static budget: For the flexible budget: For the actual costs: Material Indices Jane also used the standards in Exhibit 7.3 to show Tom how indices for each of the components of the variable costs could be determined and interpreted. Consider first the material costs: In words, the material portion of the variable cost fell 12.5% from the flexi- ble budget to the actual because of the 12.5% decrease in the cost of paper from $0.008 per page to $0.007 per page. There were no efficiencies or Material Index Actual Costs Flexible Budget per page pages per ream reams) per page pages per ream reams) = = = ×× ×× = × × =×× = $, $, ($ . , ($ . , . . , , . 4 200 4 800 0 007 500 1 200 0 008 500 1 200 0 007 0 008 500 500 1 200 1 200 0 875 1 00 1 00 0 875 Material Costs per ream reams Labor Costs per ream reams Variable OH per ream reams Total Variable Costs as reported in Exhibit 7.1 =×= =×= =×= = $. , $, $. , $, $. , $, $, 3 50 1 200 4 200 1 50 1 200 1 800 1 25 1 200 1 500 7 500 Material Costs per ream reams Labor Costs per ream reams Variable OH per ream reams Total Variable Costs as reported in Exhibit 7.1 =×= =×= =×= = $. , $, $. , $, $. , $, $, 4 00 1 200 4 800 1 50 1 200 1 800 1 50 1 200 1 800 8 400 Material Costs per ream reams Labor Costs per ream reams Variable OH per ream reams Total Variable Costs as reported in Exhibit 7.1 =×= =×= =×= = $. , $, $. , $, $. , $, $, 4 00 1 000 4 000 1 50 1 000 1 500 1 50 1 000 1 500 7 000 Measuring Productivity 211 inefficiencies in the use of the paper: The number of pages actually used per ream was equal to budget. Labor Indices Jane then performed an identical analysis for labor costs: In words, the labor portion of the variable cost remained the same from flexi- ble to actual because the rise of 20% in the hourly wage was exactly offset by the 16.67% decrease in the time to produce a ream of letterhead. “I’ve just realized that what we have here,” said Tom, “is a great way to measure increases in productivity. Dana keeps on talking about how our pro- ductivity is falling. One way to counteract that is to check how efficiently people are working. Before one measures physical productivity, though, one has to eliminate the wage effect, which is just what you have shown me how to do here.” Variable Overhead Indices “I think I can now do the variable overhead analysis myself,” said Tom. “I just take the three components of the actual cost and divide that by the three com- ponents of the flexible budget. Check me if you will.” Variable OH Index Actual Costs Flexible Budget $0. .15 ) $1 . . 0 ) = = = ×× ×× =×× =×× = $, $, (, (, $. $. . . , , . 1 500 1 800 1 00 0 2 1 200 5 00 0 1 1 200 10 00 15 00 0 125 010 1 200 1 200 0 667 1 25 1 00 0 833 Labor Index Actual Costs Flexible Budget $ . per hour . 5 hours per ream reams) $ . per hour . 0 hours per ream reams) = = = ×× ×× =×× =× × = $, $, (, (, $. $. . . , , . . 1 800 1 800 6 00 0 2 1 200 5 00 0 3 1 200 600 500 025 030 1 200 1 200 120 0833 100 100 212 Understanding the Numbers “I can even tell you what that means in words: The overhead portion of the variable cost declined 16.67% from the flexible budget because the hourly overhead rate fell by 33.33% while the overhead used per ream rose 25%. How do you like that explanation?” Variance Analysis “Another way, in fact the more traditional way, to think about this,” said Jane, “is to focus on the numbers rather than the percentages. The cost of the paper fell 0.001 cents per page while the company used 600,000 pages (500 pages per ream × 1,200 reams.) This price drop saved $600; since this price variance is favorable, it’s denoted by an F. The company used the amount of paper that was budgeted, so the usage variance is zero. “In the case of labor, the wage paid was $1.00 per hour more than planned, which over the 300 hours that were worked meant an unfavorable wage variance of $300 denoted by a U. Employees actually worked 300 hours (0.25 hours per ream × 1,200 reams), whereas the plan was for them to work 360 hours (0.30 × 1,200 reams). That saved 60 hours, which, at the standard wage rate of $5.00, saved $300. The wage variance and the use variance offset one another here. “Finally, the variable overhead rate was $5.00 per machine hour less than ex- pected. This gives a favorable rate variance of $750 or $5.00 × 150 actual ma- chine hours. The base on which variable overhead was applied, namely machine hours, increased by 30 hours since the budget called for just 120 ma- chine hours. At the standard rate of $15.00 per hour this gives an unfavorable usage variance of $450 or $15.00 × 30 machine hours. This leaves a favorable difference of $300. “All this is summarized in Exhibit 7.4.” Overhead Variance 150 0 hours $15.00 per hour 10.00 per hour 1 0 hours =− () × [] +− () × [] = 12 15 00 5 300 $. $ Labor Variance 300 60 hours $5.00 per hour 6.00 per hour 300 hours =− () × [] +− () × [] = 3 500 0 $. $ Materials Variance 600, 000 600, 000 pages $0.008 per page 0.007 per page 600,000 pages =− () × [] +− () × [] = $. $ 0 008 600 F Measuring Productivity 213 Rev iew “One last question, Jane: Where do these variable overhead rates come from?” “That’s another subject altogether,” said Jane. “Do you want a cup of cof- fee? I’m bushed. But before we break, let’s summarize what we’ve learned. 1. The cost of a product consists of material, labor, and overhead. 2. Each of these components is made up of a productivity rate multiplied by a unit cost for that component. 3. Standard Costs = Standard Productivity Rates × Standard Unit Costs 4. Actual Costs = Actual Productivity Rates × Actual Unit Costs 5. Price Indices = Actual Unit Costs/Standard Costs 6. Activity Indices = Actual Productivity Rate/Standard Productivity Rate.” COLLECTING STANDARDS After their coffee break, Jane and Tom shifted their conversation to how to de- velop these standard costs. Jane reminded Tom that standard costs are made up of two parts: 1. A standard cost per unit times. 2. A standard usage, or quantity of units of input per unit of output. She pointed out that he was responsible for defining the amount of mate- rial and labor that should go into the product. The purchasing department was responsible for determining the amount that should be paid for materials, the personnel department determined wages. There are, as she explained, several ways to determine the appropriate usage. Engineering Studies “First, one can do an engineering study. In other words, one can look at the specifications of the product. Many products that are designed by engineers have quite detailed and explicit instructions on what materials should go into them. These standards often include an allowance for waste, though this isn’t necessary. Where they do not include such an allowance they border on the ideal. EXHIBIT 7.4 Variance analysis. Rate Variance Usage Variance Total Variance Materials $600 F $0 $600 F Labor 300 U 300 F 0 Variable overhead 450 U 750 F 300 F 214 Understanding the Numbers “To take an obvious example, most automobiles have one battery, and an engineering statement would so state. A perfection standard would call for 1 battery per automobile. When it comes to actual production, however, it would not be unusual for one or more batteries to be damaged during installation.If 10,100 batteries are used in the manufacture of 10,000 cars, then it might ap- pear as if each automobile actually had 1.01 batteries. One might, therefore, want to set as one’s standard a currently attainable goal of 1.01 batteries on av- erage, thus providing a 1% allowance for wastage.” Time and Motion Studies “Time and motion studies are the usual way in which engineering standards are set for the labor component,” Jane explained. “An engineer watches over labor- ers as they work and determines how much time it should take for each part of the production process. When doing this, it is vital that the engineer gain labor’s cooperation. If not, disastrous results can occur. I love the following quotation:” You got to use your noodle while you’re working and think your work out ahead as you go along! You got to add in movements you know you ain’t going to make when you’re running the job! Remember, if you don’t screw them, they’re going to screw you! Every moment counts! When the time-study man came around, I set the speed at 180. I knew damn well he would ask me to push it up, so I started low enough. He finally pushed me up to 445, and I ran the job later at 610. If I’d started out at 445, they’d have timed it at 610. Then I got him on the reaming, too. I ran the reamer for him at 130 speed and .025 feed. He asked me if I couldn’t run the reamer any faster than that, and I told him I had to run the reamer slow to keep the hole size. I showed him two pieces with oversize holes that the day man ran. I picked them out for the occasion! But later on I ran the reamer at 610 speed and .018 feed, same as the drill. So I didn’t have to change gears. 3 Tom smiled appreciatively at the story. As an old floor hand, he understood the sentiments completely. Motivation “This raises a broader question, you know,” said Tom. “Should we invite people to participate in setting the standards? Will it make them more motivated? I’ve pondered this from a variety of angles. What’s interesting about it is that par- ticipation doesn’t always work. “What I have discovered from my reading around the topic is that many people prefer to be told what to do. This seems to be particularly true for peo- ple who find their jobs boring and for those with a more authoritarian person- ality. So one has to be really careful when inviting people to participate.” “You know more about this than I do,” responded Jane. “How do you han- dle feedback, then. That’s a sort of after-the-fact participation isn’t it.” Measuring Productivity 215 “Well, I don’t know about after the fact, but everyone that I’ve read—and my own experience for that matter—indicates that timely feedback is essential and a good motivator. People really need to know, and know as soon as possi- ble, how they have done. That’s especially true when they’ve done a good job, because it really builds their self-esteem. And in some cases, it makes them want to participate more before the fact in the next round. “Of course, I don’t want to lead you to think that a little participation and a lot of feedback is all one needs. These are what the psychologists call intrin- sic motivators. People need these, but they also need extrinsic motivators like better pay for doing a better job. “And, the other problem that I’ve encountered is that the more you focus people’s attention on one goal, the more they tend to ignore other goals. It’s only human nature: Ask salespeople to increase their turnover, and they’ll sell goods at a loss. “That’s one of the reasons why I have misgivings about calling in a bunch of engineers to set standards. It’s much easier to time how long a job should take and reward people for quantity than to measure and to reward quality. I really rely upon the innate good sense of my staff to provide quality products. Too much emphasis on measurement can make my task of maintaining quality much more difficult.” Past Data “Probably, then, an easier way,” Jane said, “to get the data you need for your business is to go back over your past records to see how much time various jobs have taken and how much material was used in the past. Some of that will have to be adjusted for changes in machines, changes in personnel, different kinds of material, and so on. But you know all that better than I do.” “Enough!” Tom exclaimed. “Enough for now! I’ll come over tomorrow night and we can talk some more. We still need to discuss fixed overheads as you promised.” FIXED COST BUDGETS “Fixed costs,” Jane started out the next night after the two had gathered again, “are both easier and more difficult to control than variable costs. They are eas- ier because there are no components into which to break them. Their variance is simply: Their index is simply: Actual Fixed Costs Budgeted Fixed Costs Actual Fixed Costs Budgeted Fixed Costs− 216 Understanding the Numbers In our case, the budgeted fixed costs were $4,000 and the actual fixed costs were $4,680. The variance was simply $680, which means a 17% increase. “Fixed costs are more difficult to control than variable costs because one cannot create an illusion of control through the elaborate computation of price, mix, and usage variances or indices.” “How, then, does one control fixed costs?” asked Tom. “First,” Jane replied, “one must recognize that if costs are truly fixed, there is no reason to control them. Consider depreciation costs as an example. Once one has purchased an item, the total depreciation costs are set—unless one disposes of the machinery when a disposal cost will substitute for the de- preciation cost. No control is possible here. The control in this case has to be exerted when the machinery is purchased. Thereafter, it is a sunk cost that cannot be controlled. In other words, controlling fixed costs is in the first place a matter of timing. “Traditional variance analysis uses one cost driver only, the volume of production. More modern variance analysis, such as that in activity based cost- ing, uses multiple cost drivers. 4 For example, setup costs may not vary with vol- ume of production but might vary with the number of batches. What appears at first glance to be a fixed cost may just be variable with respect to some other driver. The analysis of variance proceeds exactly as before except that one changes the driver from units produced to number of batches. One converts the fixed cost into a quasi-variable cost by finding and using the appropriate cost driver. “Controlling fixed costs is also a matter of scale. Consider the machine again. Assume one has just one machine with a capacity of 1,000 boxes of greeting cards per day. Its cost is certainly fixed within this range. However, if the analysis is being done in terms of tens of thousands of boxes, and if the corporation has a hundred of these machines, then it is possible to think of ma- chine costs as being a variable. One can ask, in other words, what the cost would be to produce an additional ‘unit’ of 1,000 boxes. “This last question points to the fact that most fixed costs are usually only fixed within the context of a particular analysis. Consider, for instance, the ink you use in production. Assume its price is reset by a cartel every three months. Assume also that its planned usage is reset at the same time. A budgetary con- trol system that computed variances every month and set the budgeted price and quantity to those of the latest quarter might show a variance of zero each month. This might lead everyone to believe that they were dealing with a fixed cost. However, were the same analysis to be done on an annual basis, with prices and quantities set at the start of the year, a substantial variance could arise. The example points up the old truism that all costs are variable in the long run. “The example above also points up the need to set your net large enough to catch the fish you want. Many fixed costs cannot be controlled by a monthly, or even annual, budget system because they change too slowly. One needs a coarser net, that is, an annual, triennial, or even longer budgetary system to Measuring Productivity 217 capture their change. The reverse is also true. A net that is too fine can capture a great deal of random noise. Consider, for instance, a product whose price fluctuates randomly around a fixed mean. If all you want is to see the true ex- ceptions, then you should set the net to capture only those fluctuations that are greater than a certain number of standard deviations away from the mean. “In short, fixed costs are best controlled in the long run and at a more ag- gregate level. In other words, it is important in the budgetary control of fixed costs to establish appropriate time and space horizons for one’s analysis.” “Those are all good points,” said Tom, “and it’s good to be reminded of them. What you haven’t yet told me, though, is whether there is a fixed over- head rate like the variable overhead rate that you had in Exhibit 7.3 and how the fixed overhead rate fits into the whole picture.” “Well, fixed overhead does and doesn’t have a rate,” responded Jane. “The rate itself comes from knowing the total fixed overhead and dividing it by the volume; for example, the budgeted fixed overhead of $4,000 divided by the budgeted 1,000 units gives us a fixed overhead rate of $4.00. In a sense, fixed overhead rates are secondary—unlike variable overhead rates, which are pri- mary, meaning that fixed overhead rates are computed by dividing the total overhead by volume. Total variable overhead, on the other hand, is computed by multiplying the variable overhead rate by the volume. In other words, fixed overhead computes just the other way round from variable overhead. “Variable overhead rates are used in computing variances and indices. Fixed overhead rates are completely ignored in this context. Their main pur- pose is to give you an estimate of the total product cost. We computed earlier that the estimated variable cost of a ream of letterhead was $7.00. We can now add the $4.00 fixed cost in and say the estimated total cost of a ream is $11.00. So fixed overhead rates fit in when calculating unit product costs. It’s just that they don’t fit into the rest of the budgetary control systems. But let’s talk about standard cost systems when all this might become clearer. Let’s pick it up to- morrow when we are both fresher.” STANDARD COST ACCOUNTING SYSTEMS “Companies rarely enter their budgets into their ledgers. Usually budgetary control takes place outside of the books of the company. In other words, the budget is typically drawn up using spreadsheets outside of the general ledger system. At the end of the period under investigation, the actual results are drawn out of the ledger and transferred to the spreadsheet where the compar- isons are done. Two exceptions to this general rule occur.” Government Accounting “The first exception does not affect private companies but does affect state and local governments. It is common practice in their accounting systems to . should go into the product. The purchasing department was responsible for determining the amount that should be paid for materials, the personnel department determined wages. There are, as she. seems to be particularly true for peo- ple who find their jobs boring and for those with a more authoritarian person- ality. So one has to be really careful when inviting people to participate.” “You. And in some cases, it makes them want to participate more before the fact in the next round. “Of course, I don’t want to lead you to think that a little participation and a lot of feedback is all