{"id":122,"date":"2021-01-26T22:10:31","date_gmt":"2021-01-26T22:10:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/?post_type=chapter&p=122"},"modified":"2021-08-15T20:04:13","modified_gmt":"2021-08-15T20:04:13","slug":"introduction-to-single-base-system","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/chapter\/introduction-to-single-base-system\/","title":{"raw":"Introduction to Single-base System","rendered":"Introduction to Single-base System"},"content":{"raw":"

What you will learn to do: allocate manufacturing overhead using a single rate and a single base<\/h2>\r\nThe simplest way to allocate manufacturing overhead is to base the computation on some reasonable base.\r\n\r\nLet\u2019s assume you have obtained the following more detailed income statement for Yore Company:\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Yore Company\r\nIncome Statement (full absorption)\r\nFor the month ending October 31, 20XX<\/caption>\r\n
Description<\/th>\r\nAmount<\/th>\r\nAmount<\/th>\r\nTotal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Subcategory, <\/span>Sales<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n$ 1,072,400.00<\/td>\r\n<\/tr>\r\n
Subcategory, <\/span>\u00a0\u00a0\u00a0Variable manufacturing costs<\/strong><\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Direct Materials, basic<\/td>\r\n$ \u00a0 320,000<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Direct Labor, basic<\/td>\r\n264,000<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Total direct costs, basic<\/td>\r\nSingle Line<\/span><\/td>\r\n$\u00a0 584,000.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Direct Materials, deluxe<\/td>\r\n117,600<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Direct Labor, deluxe<\/td>\r\n112,000<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Total direct costs, deluxe<\/td>\r\nSingle Line<\/span><\/td>\r\n229,600.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0Fixed Manufacturing Costs<\/td>\r\n<\/td>\r\n188,000.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Cost of Goods Manufactured and Sold<\/td>\r\n<\/td>\r\nSingle Line<\/span><\/td>\r\n1,001,600.00<\/td>\r\n<\/tr>\r\n
Gross Profit<\/td>\r\n<\/td>\r\n<\/td>\r\nSingle Line<\/span>70,800.00<\/td>\r\n<\/tr>\r\n
Subcategory, <\/span>Selling, General, and Administrative Costs<\/strong><\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0Variable Selling, General, and Administrative<\/td>\r\n<\/td>\r\n18,800.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Subcategory, <\/span>\u00a0\u00a0\u00a0Fixed Selling, General, and Administrative<\/strong><\/td>\r\n<\/td>\r\n35,600.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Total Selling, General, and Administrative<\/td>\r\n<\/td>\r\n<\/td>\r\n54,400.00<\/td>\r\n<\/tr>\r\n
Net income from operations<\/td>\r\n<\/td>\r\n<\/td>\r\nSingle Line<\/span>$\u00a0 \u00a0 16,400.00Double line<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nBased on the sales data you received, you see that the company sold 3,760 purses in total, broken down like this:\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/th>\r\nUnits<\/th>\r\n$\/unit<\/th>\r\nTotal<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n
Sales<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\u00a0 Basic<\/td>\r\n3,200<\/td>\r\n$\u00a0 \u00a0 \u00a0 \u00a0 245.00<\/td>\r\n$ \u00a0 784,000.00<\/td>\r\n<\/tr>\r\n
\u00a0 Deluxe<\/td>\r\n560<\/td>\r\n$\u00a0 \u00a0 \u00a0 \u00a0 515.00<\/td>\r\n288,400.00<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0\u00a0\u00a0Total sales<\/td>\r\n3,760<\/td>\r\n<\/td>\r\n$\u00a0 1,072,400.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nThe sales manager calculated the cost of each purse by simply taking the total cost of goods manufactured and dividing it equally between all the purses:\r\n

$1,001,600 \/ 3,760 = 266.3829787234\u2026 which the sales manager rounded to $266.38 each.<\/p>\r\n\"OrangeHowever, it doesn\u2019t take into account the variable costs per type of purse that appear to be quite different.\r\n\r\nLet\u2019s take a look at three important numbers which comprise the total cost of goods manufactured:\r\n\r\nTotal variable direct costs for the basic purse = $584,000\r\n\r\nTotal variable direct costs for the deluxe purse = $229,600\r\n\r\nTotal fixed manufacturing overhead (not allocated to either type) = $188,000\r\n\r\nFrom the financial statements, you can figure out the variable cost per purse by dividing the total variable cost by the number of units for each type of purse:\r\n

    \r\n \t
  • Variable costs per basic purse = $182.50 ($584,000 \/ 3,200 units)<\/li>\r\n \t
  • Variable cost per deluxe purse = $410.00 ($229,600 \/ 560).<\/li>\r\n<\/ul>\r\nOne way to allocate the $188,000 in fixed manufacturing overhead would be to simply divide it by the number of units produced: $188,000 \/ 3,760 = $50 per unit. This would allocate an equal amount of factory overhead to each unit, making the total cost of each unit as follows:\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/th>\r\nBasic<\/th>\r\nDeluxe<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n
    Direct Variable Costs<\/td>\r\n182.50<\/td>\r\n$\u00a0 410.00<\/td>\r\n<\/tr>\r\n
    Allocated Fixed Costs<\/td>\r\n\u00a0 50.00<\/td>\r\n$\u00a0 50.00<\/td>\r\n<\/tr>\r\n
    Total manufacturing cost<\/td>\r\nSingle Line<\/span>$\u00a0 232.50Double line<\/span><\/td>\r\nSingle Line<\/span>$\u00a0 460.00Double line<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nWe can then determine a gross profit per unit that allocates direct variable costs to each product accurately and allocated the fixed overhead equally:\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/th>\r\nBasic<\/th>\r\nDeluxe<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n
    Sales Price<\/td>\r\n$\u00a0 245.00<\/td>\r\n$ 515.00<\/td>\r\n<\/tr>\r\n
    Less: Direct Variable Costs<\/td>\r\n182.50<\/td>\r\n$ \u00a0410.00<\/td>\r\n<\/tr>\r\n
    <\/td>\r\nSingle Line<\/span>62.50<\/td>\r\nSingle Line<\/span>$\u00a0 105.00<\/td>\r\n<\/tr>\r\n
    Less: Allocated Fixed Costs<\/td>\r\n\u00a0 50.00<\/td>\r\n$\u00a0 50.00<\/td>\r\n<\/tr>\r\n
    Gross profit per unit<\/td>\r\nSingle Line<\/span>$\u00a0 12.50Double line<\/span><\/td>\r\nSingle Line<\/span>$\u00a0 55.00Double line<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nTo check our work, let\u2019s multiply the gross profit per unit times the number of units sold:\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/th>\r\nBasic<\/th>\r\nDeluxe<\/th>\r\n<\/th>\r\n<\/tr>\r\n
    Gross profit per unit<\/td>\r\n$ \u00a0 \u00a0 \u00a0 \u00a0 12.50<\/td>\r\n$\u00a0 \u00a0 \u00a0 \u00a0 55.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    Times number of units sold<\/td>\r\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3,200<\/td>\r\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 560<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    Total gross profit<\/td>\r\nSingle Line<\/span>\u00a0 \u00a0 \u00a0 \u00a0 $ \u00a0 \u00a0 \u00a0 40,000Double line<\/span><\/td>\r\nSingle Line<\/span>\u00a0 \u00a0 \u00a0 $\u00a0 \u00a0 \u00a0 30,800Double line<\/span><\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    Total gross profit - basic<\/td>\r\n<\/td>\r\n<\/td>\r\n$ \u00a0 40,000.00<\/td>\r\n<\/tr>\r\n
    Total gross profit - deluxe<\/td>\r\n<\/td>\r\n<\/td>\r\n30,800.00<\/td>\r\n<\/tr>\r\n
    Total gross profit, all products<\/td>\r\n<\/td>\r\n<\/td>\r\nSingle Line<\/span>$ \u00a0 70,800.00Double line<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nThat agrees with the gross profit per the financial statements.\r\n\r\nSpreading fixed overhead over all the units equally is a fairly simple calculation. However, there may be a better way to allocate fixed manufacturing overhead. If the production manager is correct, and it takes more than twice as long to manufacture a single deluxe purse as it does to manufacture a single basic purse, perhaps the fixed manufacturing overhead allocation could be \u201cweighted.\" In other words, we could allocate more fixed overhead to the deluxe purse than to the basic purse. That would reflect the idea that if we shifted resources to produce more deluxe purses, our production capacity for basic purses would be reduced. In other words, if our total production capacity is 5,000 basic purses, it would only be 2,500 deluxe purses, or fewer, because they take longer to make (use more resources).\r\n\r\nTherefore, it might be more accurate to allocate more fixed overhead to deluxe purses, but we need a rational, logical way to accomplish that.\r\n\r\nManagerial accountants solve this issue by looking for a \u201cbase\u201d that accurately reflects the amount of fixed manufacturing overhead being physically allocated to a certain product line. The term \u201cbase\u201d is another word for the denominator of a fraction, the amount below the dividing line, that is considered the base of the division problem. For instance, in calculating a percentage, the base is 100 (thus the term \u201cper cent\u201d which means \u201cper 100\u201d or \u201cdivided by 100\u201d).\r\n

    Example: 45% = 45\/100<\/p>\r\nBut a base can be anything. Another example is the term \u201cper capita\u201d which means per person. In that case, the base would be the number of people. In 2018, China had a Gross Domestic Product (GDP) of almost $14 trillion (USD). Germany had a Gross Domestic Product of less than $4 trillion (USD). However, China had a population of 1.4 trillion versus Germany\u2019s 83 million. Using population as a base, the per capita GDP for each is:\r\n