5-1 成本習性: 分析與應用 第五章 Managers who understand how costs behave are better able to predict costs and make decisions under various circumstances. This chapter explores the meaning of variable, fixed, and mixed costs (the relative proportions of which define an organization’s cost structure). It also introduces a new income statement called the contribution approach.

學習目標 1 瞭解固定與變動成本的 習性以及如何利用它們 來預測成本 5-2 學習目標 1 瞭解固定與變動成本的 習性以及如何利用它們 來預測成本 Learning objective number 1 is to understand how fixed and variable costs behave and how to use them to predict costs.

回想一下我們在第2章針對成本習性所做的整理 5-3 成本習性型態 回想一下我們在第2章針對成本習性所做的整理 We discussed this table in an earlier chapter. Let’s concentrate on variable costs in total. Recall that total variable cost is proportional to the activity level within the relevant range. As activity increases, total variable cost increases, and as activity decreases, total variable cost decreases.

作業基礎 產量 行駛里程數 人工時數 機器時數 變動成本發生原因的衡量方式 5-4 作業基礎 產量 行駛里程數 人工時數 機器時數 變動成本發生原因的衡量方式 An activity base (also called a cost driver) is a measure of what causes the incurrence of variable costs. As the level of the activity base increases, the total variable cost increases proportionally. Units produced (or sold) is not the only activity base within companies. A cost can be considered variable if it varies with activity bases such as miles driven, machine hours, or labor hours.

所謂變動成本，即總成本會隨著作業水準變動同向等比例變動之成本項目。 你的長途電話費是依據通話時間(分鐘)來計費的。 5-5 舉例說明純粹式變動成本 所謂變動成本，即總成本會隨著作業水準變動同向等比例變動之成本項目。 你的長途電話費是依據通話時間(分鐘)來計費的。 長途電話費 As an example of an activity base, consider your total long distance telephone bill. The activity base is the number of minutes that you talk. A true variable cost is one whose total dollar amount varies in direct proportion to changes in the level of activity. On your land-line, your total long distance telephone bill is determined by the number of minutes you talk. An activity base, or cost driver, is a measure of what causes the incurrence of variable costs. As the level of activity base increases, the variable cost increases proportionally. 通話時間(分鐘)

回想一下我們在第2章針對成本習性所做的整理 5-6 成本習性型態 回想一下我們在第2章針對成本習性所做的整理 On a per unit basis, variable costs remain the same over a wide range of activity.

若以單位為基礎來表達變動成本的話，變動成本維持不變。每分鐘的通話費用是固定的，例如，每分鐘$0.10。 5-7 舉例說明單位變動成本 若以單位為基礎來表達變動成本的話，變動成本維持不變。每分鐘的通話費用是固定的，例如，每分鐘$0.10。 每分鐘的電話費 A variable cost remains constant if expressed on a per unit basis. Referring to the telephone example, the cost per minute talked is constant (e.g., 10 cents per minute). 通話時間(分鐘)

變動成本的比重 每個組織的變動成本比重各不相同。例如 . . . 擁有大量設備投資的公用 事業，其變動 製造業常常擁有 成本項目較少。 5-8 變動成本的比重 每個組織的變動成本比重各不相同。例如 . . . 擁有大量設備投資的公用 事業，其變動 成本項目較少。 製造業常常擁有 許多變動成本項目。 A public utility has huge investments in property, plant and equipment, so it will tend to have fewer variable costs than a less capital intensive industry. In contrast, a merchandising company usually has a high proportion of variable costs like cost of goods sold. Service companies, like law firms and CPA firms, also tend to have a high proportion of variable costs. 買賣業通常擁有高比例 的變動成本，如銷貨成本。 服務業通常擁有高比例的 變動成本。

變動成本例子 買賣業–銷貨成本 製造業 –直接材料、直接人工與變動製造費用 買賣業與製造業 – 佣金、運輸成本與事務性成本，如帳務處理成本 5-9 變動成本例子 買賣業–銷貨成本 製造業 –直接材料、直接人工與變動製造費用 買賣業與製造業 – 佣金、運輸成本與事務性成本，如帳務處理成本 服務業 – 物料、差旅與事務性成本 Here are some examples of variable costs that are likely present in many types of businesses.

直接材料是純粹式變動成本(或稱比例式變動成本)，因為期間內所耗用的材料量會隨著生產作業水準呈等比例同向變動。 5-10 純粹式變動成本 直接材料是純粹式變動成本(或稱比例式變動成本)，因為期間內所耗用的材料量會隨著生產作業水準呈等比例同向變動。 成本 Recall that we previously stated that true variable costs vary directly and proportionately with changes in activity. Direct material is an example of a cost that behaves in a true variable pattern. Now let’s look at what are known as step-variable costs. 產量

只能以大量方式取得的資源 (如維修人工) 且其成本只有在相當大範圍的作業量變動時才會增加或減少。 5-11 階梯式變動成本 只能以大量方式取得的資源 (如維修人工) 且其成本只有在相當大範圍的作業量變動時才會增加或減少。 此種成本稱為階梯式變動成本。 產量 成本 A step variable cost remains constant within a narrow range of activity, so it tends to look like a fixed cost. Maintenance workers are often considered to be a variable cost, but this labor cost does not behave as a true variable cost. For example, fairly wide changes in the level of production will cause a change in the number of maintenance workers employed, thereby increasing the total maintenance cost.

生產作業水準的小範圍變動不可能影響維修人工的雇用人數。 5-12 階梯式變動成本 生產作業水準的小範圍變動不可能影響維修人工的雇用人數。 產量 成本 For a step-variable cost, total cost increases to a new higher level when we reach the next higher range of activity. For example, a maintenance worker is obtainable only as a whole person who is capable of working approximately two thousand hours per year.

只有在作業水準變動相當大的情況下，維修人工的雇用人數才會有所改變。 5-13 階梯式變動成本 只有在作業水準變動相當大的情況下，維修人工的雇用人數才會有所改變。 產量 成本 Only fairly wide changes in the level of activity will cause a change in a step-variable cost. Maintenance workers are obtainable only in large chunks of a whole person who is capable of working approximately two thousand hours a year.

在攸關範圍內，有一條直線可近似曲線變動成本。 5-14 線性假設與攸關範圍 攸關範圍 在攸關範圍內，有一條直線可近似曲線變動成本。 經濟學家的 曲線成本函數 總成本 會計學家的近似曲線 成本直線 (單位變動 成本固定) Part I Economists correctly point out that many costs that accountants classify as variable costs actually behave in a curvilinear fashion. Part II In many important decisions, accountants tend to treat costs as linear in nature. Part III As long as the company is operating within the relevant range of activity, the accountant’s approximation of the economist’s curvilinear cost function seems to work quite well. The relevant range is the range of activity within which the assumptions made about cost behavior are valid. 作業量

成本習性型態 讓我們來觀察固定成本習性吧！ 5-15 成本習性型態 讓我們來觀察固定成本習性吧！ Now, let’s look at fixed costs. Total fixed costs remain constant within the relevant range of activity.

舉例說明固定成本 固定成本乃作業水準變動時，其總額能維持固定的成本。 5-16 舉例說明固定成本 固定成本乃作業水準變動時，其總額能維持固定的成本。 你每個月的基本電話費可能是固定的，若多打幾通市內電話也不會改變你的基本電話費。. 每月基本電話費 If you have a land-line in your home, you pay a flat connection fee that is the same every month. This fee is fixed because it does not change in total regardless of the number of calls made. 市內電話通數

回想一下我們在第2章針對成本習性所做的整理 5-17 成本習性型態 回想一下我們在第2章針對成本習性所做的整理 Finally, fixed cost per unit decreases as activity level goes up.

舉例說明單位固定成本 每通市內電話的固定成本隨著撥打次數增加而降低。 平均單位固定成本會隨著作業水準增加而減少。 每通市內電話的 5-18 舉例說明單位固定成本 平均單位固定成本會隨著作業水準增加而減少。 每通市內電話的固定成本隨著撥打次數增加而降低。 每通市內電話的 每月基本電話費 As you make more and more local calls, the connection fee cost per call decreases. If your connection fee is $15 and you make one local call per month, the average connection fee is $15 per call. However, if you make 100 local calls per month, the average connection fee drops to 15¢ per call. 市內電話通數

或許可以依據目前的管理決策而在短期內加以修改 5-19 固定成本種類 既定的 長期的、無法在 短期內顯著降低 可裁決的 或許可以依據目前的管理決策而在短期內加以修改 Part I One type of fixed cost is known as committed fixed costs. These are long-term fixed costs that cannot be significantly reduced in the short term. Some examples include depreciation on manufacturing facilities and real estate taxes on factory property. Part II Another type of fixed cost is known as discretionary fixed costs. These fixed costs may be altered in the short-term by current management decisions. Some examples of discretionary fixed costs include advertising and research and development costs. 例子 設備折舊與 財產稅 例子 廣告與研發

偏向固定成本之趨勢 許多產業有偏向較多固定成本支出、較少變動成本支出的趨勢。 因為知識性員工大多為 因為機器取代許多先前由 5-20 偏向固定成本之趨勢 許多產業有偏向較多固定成本支出、較少變動成本支出的趨勢。 因為機器取代許多先前由 人力完成的工作，所以 企業現在需要 “知識性員工” ，較不需要勞力型人工。 因為知識性員工大多為 固定支薪人員，受過高度 訓練且不易取代，所以， 這些重要員工的薪酬成本 相當固定，而非變動 成本。 Part I In many industries, we see a trend toward greater fixed costs, relative to variable costs. In the past fifteen years, we have seen computers and robotics take over many mundane tasks previously performed by humans. Part II In today’s world economy, knowledge workers are in demand for their experience and knowledge rather than their muscle. Most knowledge workers tend to be salaried, highly trained and very difficult to replace. The cost of these valued employees tends to be fixed rather than variable.

人工成本是變動的或固定的? 薪資成本的習性每個國家不同，取決於該國的勞工法令、勞工契約與習俗。 5-21 人工成本是變動的或固定的? 薪資成本的習性每個國家不同，取決於該國的勞工法令、勞工契約與習俗。 在法國、德國、中國與日本，管理階層不太能調整人力， 因此這些國家的人工成本在本質上較為固定。 In much of Europe, China, and Japan, management has little flexibility in adjusting the size of the labor force. Labor costs tend to be viewed as more fixed than variable. In recent years, we have seen some changes in management’s flexibility. In the U.S. and United Kingdom, management has much greater latitude to adjust the size of the labor force. Labor costs in some industries are still viewed as more variable than fixed. 在美國 和英國 ，管理階層有較大彈性來調整人力， 因此這些國家的人工成本在本質上較為變動。

在一個很寬廣的作業量範圍內，總成本不會變動，如果作業量增加至下一個較大的作業範圍內，則總成本會隨之跳至一個較高的水準。 5-22 固定成本與攸關範圍 在一個很寬廣的作業量範圍內，總成本不會變動，如果作業量增加至下一個較大的作業範圍內，則總成本會隨之跳至一個較高的水準。 90 攸關 範圍 60 租金(000) 30 Fixed costs only stay constant in total within the relevant range of activity. As we adjust the relevant range of activity upward or downward, we see changes in total fixed costs. These upward or downward adjustments are generally very wide. 0 1,000 2,000 3,000 租用面積 (平方英尺)

固定成本與攸關範圍 固定成本的攸關作業範圍即 成本圖形呈現水平線的作業範圍。 5-23 固定成本與攸關範圍 固定成本的攸關作業範圍即 成本圖形呈現水平線的作業範圍。 例子: 辦公室每年的租金為$30,000，可用面積為1,000平方英尺，若要擴大租用面積，必須以1,000平方英尺為單位來增加租用面積，隨著業務量的增加，勢必增加租用面積，進而增加總租金成本。 An example of changes in total fixed costs might be rent for office space. A company can rent 1,000 square feet of office space for $30,000 per year. If the company fills its current space and needs additional office space, the next 1,000 square feet will cost an additional $30,000 per year. So when a company needs 1,000 square feet of office space, the fixed office rent is $30,000. If another 1,000 square feet are needed, the fixed office rent will be $60,000.

固定成本的階梯寬度較大(階梯寬度代表作業範圍) 5-24 固定成本與攸關範圍 階梯式變動成本的調整速度較快，且 . . . 固定成本的階梯寬度較大(階梯寬度代表作業範圍) 此種固定成本與 階梯式變動成本 有何差異？ The question becomes, how do changes in fixed costs outside the relevant range differ from step-variable costs? While this step-function pattern appears similar to the idea of step-variable costs, there are two important differences between step-variable costs and fixed costs. First, step-variable costs can often be adjusted quickly as conditions change, whereas fixed costs cannot be changed easily. The second difference is that the width of the steps for fixed costs is wider than the width of the steps for step-variable costs. For example, a step-variable cost such as maintenance workers may have steps with a width of 40 hours a week. However, fixed costs may have steps that have a width of thousands or tens of thousands of hours of activity.

隨堂測驗  以下有關成本習性之說法哪一個是正確的? 每單位固定成本隨著作業水準變動而變動 每單位變動成本在攸關範圍內是固定不變的 5-25 隨堂測驗  以下有關成本習性之說法哪一個是正確的? 每單位固定成本隨著作業水準變動而變動 每單位變動成本在攸關範圍內是固定不變的 總固定成本在攸關範圍內是固定不變的 總變動成本在攸關範圍內是固定不變的 See how you do on this question. There can be more than one correct answer. Be careful and take your time.

隨堂測驗  總變動成本在攸關範圍內是固定不變的 以下有關成本習性之說法哪一個是正確的? 每單位固定成本隨著作業水準變動而變動 5-26 隨堂測驗  以下有關成本習性之說法哪一個是正確的? 每單位固定成本隨著作業水準變動而變動 每單位變動成本在攸關範圍內是固定不變的 總固定成本在攸關範圍內是固定不變的 總變動成本在攸關範圍內是固定不變的 Number 4 is not correct because total variable costs increase as activity increases within the relevant range and decrease as activity decreases within the relevant range.

混合成本 混合成本擁有固定與變動兩種成分。 見以下電費之例。 Y 總混合成本 總電費 X 作業量 (千瓦小時) 每千瓦小時的變動成本 5-27 混合成本 混合成本擁有固定與變動兩種成分。 見以下電費之例。 X Y 總混合成本 總電費 A mixed cost has both a fixed and variable element. If you pay your utility bill, you know that a portion of your total bill is fixed. This is the standard monthly utility charge. The variable portion of your utility costs depends upon the number of kilowatt hours you consume. In other words, your total utility bill has both a fixed and variable element. The graph demonstrates the nature of a normal utility bill. 每千瓦小時的變動成本 每月固定 電費 作業量 (千瓦小時)

混合成本 Y 總混合成本 總電費 X 每月固定 電費 作業量 (千瓦小時) 每千瓦小時的變動成本 5-28 混合成本 X Y 總混合成本 總電費 The mixed cost line can be expressed with the equation Y = A + B*X. This equation should look familiar, from your algebra and statistics classes. In the equation, Y is the total mixed cost; A is the total fixed cost (or the vertical intercept of the line); B is the variable cost per unit of activity (or the slope of the line), and X is the actual level of activity. In our utility example, Y is the total mixed cost; A is the total fixed monthly utility charge; B is the cost per kilowatt hour consumed, and X is the number of kilowatt hours consumed. 每千瓦小時的變動成本 每月固定 電費 作業量 (千瓦小時)

如果你每月的固定電費是$40，每千瓦小時的變動成本是 $0.03，在每月作業水準為 2,000 千瓦小時的情況下，請問你每月的電費為多少? 5-29 舉例說明混合成本 如果你每月的固定電費是$40，每千瓦小時的變動成本是 $0.03，在每月作業水準為 2,000 千瓦小時的情況下，請問你每月的電費為多少? Y = a + bX Y = $40 + ($0.03 × 2,000) Y = $100 Part I Read through this short question to see if you can calculate the total utility bill for the month. Part II The total bill is $100. How did you do?

工程法：成本估計乃基於生產方法的評估，以及材料、人工與製造費用方面的需求評估。 5-30 混合成本分析 帳戶分析與工程法 帳戶分析法：分析師依據其對於 帳戶內成本之習性的認知， 將每一帳戶區分為變動或固定。 We can analyze mixed costs by looking at each account and classifying the cost as variable, fixed or mixed based on the cost behavior over time. A more sophisticated way to analyze the nature of a cost is to ask our engineers to evaluate each cost in terms of production methods, material requirements, labor usage and overhead. 工程法：成本估計乃基於生產方法的評估，以及材料、人工與製造費用方面的需求評估。

5-31 學習目標 2 利用散佈圖診斷成本習性 Learning objective number 2 is to use a scattergraph plot to diagnose cost behavior.

* 散佈圖法 在圖上描繪資料點 (總成本 vs. 作業量) Y 20 10 X 0 1 2 3 4 維修成本 (000) 病人日數(000) 5-32 散佈圖法 在圖上描繪資料點 (總成本 vs. 作業量) 0 1 2 3 4 * 維修成本 (000) 10 20 病人日數(000) X Y A scattergraph plot is a quick and easy way to isolate the fixed and variable components of a mixed cost. The first step is to identify the cost, which is referred to as the dependent variable, and plot it on the Y axis. The activity, referred to as the independent variable, is plotted on the X axis. If the plotted dots do not appear to be linear, do not analyze the data any further. If there does appear to be a linear relationship between the level of activity and cost, we will continue our analysis.

畫一條經過資料點的直線，使得直線 上下方的資料點數相當。 5-33 散佈圖法 畫一條經過資料點的直線，使得直線 上下方的資料點數相當。 0 1 2 3 4 * 維修成本 (000) 10 20 病人日數(000) X Y Next, we draw a straight line where, roughly speaking, an equal number of points reside above and below the line. Make sure that the straight line goes through at least one data point on the scattergraph.

* 散佈圖法 利用某一資料點估計總作業量與總成本 Y 20 10 X 0 1 2 3 4 維修總成本 = $11,000 維修成本 5-34 散佈圖法 利用某一資料點估計總作業量與總成本 0 1 2 3 4 * 維修成本 (000) 10 20 病人日數(000) X Y 維修總成本 = $11,000 截距 = 固定成本: $10,000 Part I Where the straight line crosses the Y axis determines the estimate of total fixed costs. In this case, the fixed costs are $10,000. Part II Next, select one data point to estimate the variable cost per patient day. In our example, we used the first data point that was on the straight line. From this point, we estimate the total number of patient days and the total maintenance cost. Part III Our estimate of the total number of patient days at this data point is 800, and the estimate of the total maintenance cost is $11,000. We will use this information to estimate the variable cost per patient day. 病人日數 = 800

約略快速地估計單位變動成本並決定成本公式。 5-35 散佈圖法 約略快速地估計單位變動成本並決定成本公式。 單位變動成本 = $1,000 800 = $1.25/病人日 Part I The calculations include: Subtract the fixed cost from the total estimated cost for 800 patient days. We arrive at an estimate of the total variable cost for 800 patients of $1,000. Part II Divide the total variable cost by the 800 patients, which yields a variable cost per patient day of $1.25. We can use this information to complete our basic cost equation. Part III Our maintenance cost equation tells us that the Y, the total maintenance cost, is $10,000, the total fixed cost, plus $1.25 times X, the number of patient days. Y = $10,000 + $1.25X 病人日數 總維修成本

5-36 學習目標 3 利用高低點法分析 混合成本 Learning objective number 3 is to analyze a mixed cost using the high-low method.

高低點法 以下為維修時數與維修總成本的六個月資料 5-37 高低點法 以下為維修時數與維修總成本的六個月資料 The high-low method can be used to analyze mixed costs, if a scattergraph plot reveals an approximately linear relationship between the X and Y variables. We will use the data shown in the Excel spreadsheet to determine the fixed and variable portions of maintenance costs. We have collected data about the number of hours of maintenance and total cost incurred. Let’s see how the high-low method works.

維修成本的每小時變動成本等於成本變動量除以時數變動量 5-38 高低點法 維修成本的每小時變動成本等於成本變動量除以時數變動量 Part II The first step in the process is to identify the high level of activity and its related total cost and the low level of activity with its related total cost. You can see that the high level of activity is 800 hours with a cost of $9,800 dollars. The low level of activity is 500 hours with a related total cost of $7,400. Now, we subtract the low level of activity from the high level and do the same for the costs we have identified. In our case, the change in level of activity and cost is 300 hours and $2,400, respectively. The variable cost per unit of activity is determined by dividing the change in total cost by the change in activity. For our maintenance example, we divide $2,400 by 300 and determine that the variable cost per hour of maintenance is $8.00. = $8.00/時 $2,400 300

高低點法 總固定成本 = 總成本 – 總變動成本 總固定成本 = $9,800 – ($8/小時 × 800 小時) 5-39 高低點法 總固定成本 = 總成本 – 總變動成本 Part I Here is the equation we will use to calculate total fixed cost. Part II We can substitute known data to estimated total fixed cost. We know that at 800 hours of maintenance, total cost is $9,800. We just calculated the variable cost per unit of activity at $8. So we will multiply the 800 hours of activity times the $8 variable rate per unit. Part III By solving the equation, we see that total fixed cost is equal to $3,400. We can now construct an equation to estimate total maintenance cost at any level of activity within the relevant range. 總固定成本 = $9,800 – ($8/小時 × 800 小時) 總固定成本 = $9,800 – $6,400 總固定成本 = $3,400

5-40 高低點法 Y = $3,400 + $8.00X 維修費用的成本公式 Our basic equation of Y is equal to $3,400 (our total fixed cost) plus $8 times the actual level of activity. You can verify the equation by calculating total maintenance costs at 500 hours, the low level of activity. It will be worth your time to make the calculation.

5-41 隨堂測驗  銷售80,000單位時，銷貨薪資與佣金是$10,000，而銷售120,000單位時，銷貨薪資與佣金則是$14,000，採用高低點法之情況下，銷貨薪資與佣金之變動部分為何？ a. $0.08 /單位 b. $0.10 /單位 c. $0.12 /單位 d. $0.125 /單位 See if you can apply what we have just discussed to determine the variable portion of sales salaries and commissions for this company.

5-42 隨堂測驗  銷售80,000單位時，銷貨薪資與佣金是$10,000，而銷售120,000單位時，銷貨薪資與佣金則是$14,000，採用高低點法之情況下，銷貨薪資與佣金之變動部分為何？ a. $0.08 /單位 b. $0.10 /單位 c. $0.12 /單位 d. $0.125 /單位 $4,000 ÷ 40,000 單位 = $0.10 /單位 The correct answer is 10 cents per unit.

5-43 隨堂測驗  銷售80,000單位時，銷貨薪資與佣金是$10,000，而銷售120,000單位時，銷貨薪資與佣金則是$14,000，採用高低點法之情況下，銷貨薪資與佣金之固定部分為何？ a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Using the same data, calculate the total fixed cost portion of sales salaries and commissions.

5-44 隨堂測驗  銷售80,000單位時，銷貨薪資與佣金是$10,000，而銷售120,000單位時，銷貨薪資與佣金則是$14,000，採用高低點法之情況下，銷貨薪資與佣金之固定部分為何？ a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 The calculation of the answer is a bit more complex, but we see that total fixed cost equals $2,000.

如果散佈圖顯示變數 X 與 Y 之間有近似線性的關係，這時可使用最小平方迴歸法來分析混合成本。 5-45 最小平方迴歸法 如果散佈圖顯示變數 X 與 Y 之間有近似線性的關係，這時可使用最小平方迴歸法來分析混合成本。 此方法使用所有的 資料點 來估計混合成本中的 固定與變動成本 此方法的目標：找到一條 配適所有資料點且迴歸 誤差平方和最小的直線。 The least-squares regression method is a more sophisticated approach to isolating the fixed and variable portion of a mixed cost. This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. This method is superior to the scattergraph plot method that relies upon only one data point and the high-low method that uses only two data points to estimate the fixed and variable cost components of a mixed cost. The basic goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors. The regression errors are the vertical deviations from the data points to the regression line.

最小平方迴歸會提供一個統計值，稱為 R2，可 衡量迴歸線對於所有資料點的配適程度。 5-46 最小平方迴歸法 可以使用軟體來找到一條最適所有資料點之迴歸線。 成本分析目標同樣是以下列等式表達成本： Y = a + bX The formulas that are used for least-squares regression are complex. Fortunately, computer software can perform the calculations, quickly. The observed values of the X and Y variables are entered into the computer program and all necessary calculations are made. In the appendix to this chapter, we show you how to use Microsoft Excel to complete a least-squares regression analysis. Output from the regression analysis can be used to create the equation that enables us to estimate total costs at any activity level. The key statistic to examine when evaluating regression results is called R squared, which is a measure of the goodness of fit. 最小平方迴歸會提供一個統計值，稱為 R2，可 衡量迴歸線對於所有資料點的配適程度。

* * * * * * * * * * 最小平方迴歸法 R2即總成本變異可由作業量解釋的比例。 Y 20 總成本 10 5-47 最小平方迴歸法 R2即總成本變異可由作業量解釋的比例。 Y 20 * * * * * * * * * * 總成本 10 The R square value can range from 0% to 100%. The higher the percentage, the better the fit. R2 介於 0% 與 100% 之間， 比例越高，配適程度越佳。 X 0 1 2 3 4 作業量

最小平方迴歸法所提供的估計數最精確，因為此法使用所有的資料點。 5-48 比較三種方法 三種方法所提供的固定成本與 單位變動成本估計數稍稍不同。 因為每一種方法所使用的資料量 不同，所以此種結果是意料之中。 最小平方迴歸法所提供的估計數最精確，因為此法使用所有的資料點。 The three methods we discussed for isolating the fixed and variable portions of a mixed cost yield slightly different results. The most accurate estimate is provided by the least-squared regression method. Less accurate results are usually associated with the scattergraph. The high-low method provides results that fall somewhere in the middle of the other two methods.

5-49 學習目標 4 利用貢獻格式編製損益表 Learning objective number 4 is to prepare an income statement using the contribution format.

讓我們利用成本習性方面的知識來編製貢獻式損益表吧！ 5-50 貢獻格式 讓我們利用成本習性方面的知識來編製貢獻式損益表吧！ The contribution approach provides an income statement format geared directly to cost behavior, which has been the focus of discussion in this chapter.

貢獻格式 貢獻格式強調成本習性。邊際貢獻在 回收固定成本後產生利潤。 5-51 貢獻格式 貢獻格式強調成本習性。邊際貢獻在 回收固定成本後產生利潤。 The contribution approach separates costs into fixed and variable. Sales minus variable costs equals contribution margin. The contribution margin minus fixed costs equals net operating income.

貢獻格式損益表用於內部規劃與決策，貢獻格式損益表將用於: 5-52 貢獻格式的用途 貢獻格式損益表用於內部規劃與決策，貢獻格式損益表將用於: 成本-數量-利潤分析(第6章). 編列預算 (第9章). 部門的利潤資料報告(第12章). 如定價與租或買分析之類的特別決策(第13章). This approach is used as an internal planning and decision-making tool, and will be discussed further in the chapters shown on your screen.

貢獻格式 主要用於外部報告 主要用於內部管理 5-53 貢獻格式 The contribution format allocates costs based on cost behavior. The contribution approach differs from the traditional approach covered in Chapter 2. The traditional approach organizes costs in a functional format. Costs relating to production, administration and sales are grouped together without regard to their cost behavior. The traditional approach is used primarily for external reporting purposes. 主要用於外部報告 主要用於內部管理

5-54 利用微軟Excel跑 最小平方迴歸 附錄 5A In this appendix, we will show you how to use Microsoft Excel to determine the key variable necessary for least-squares regression. As you have seen, we need three pieces of information: the estimated variable cost per unit (the slope of the line), the estimated fixed cost (the intercept), and R squared. Let’s get started. I think you will find that using Microsoft Excel is quite easy.

5-55 學習目標 5 利用最小平方迴歸法 分析混合成本 Learning objective number 5 is to analyze a mixed cost using the least-squares regression method.

舉例說明簡單迴歸分析 Matrix, Inc. 想要知道它的固定成本與單位變動成本。 5-56 舉例說明簡單迴歸分析 Matrix, Inc. 想要知道它的固定成本與單位變動成本。 根據右側資料，讓我們利用微軟Excel來做最小平方迴歸分析。 Matrix, Inc. has gathered 15 month’s of information concerning the number of meals prepared and the total cost of preparing them each month. We will use this data in our least-squares regression model. Using Microsoft Excel, we will estimate the variable and fixed cost components of the total meals cost.

利用Excel跑簡單迴歸 單位估計變動成本(直線斜率) 估計固定成本(直線截距) 配適程度 R2 5-57 利用Excel跑簡單迴歸 你需要從迴歸分析中取得三項資料，分別為: 單位估計變動成本(直線斜率) 估計固定成本(直線截距) 配適程度 R2 為取得這三項資料，我們將需要使用三種不同的Excel 函數： LINEST, INTERCEPT 與 RSQ To gather the three pieces of information we need, we will use three special functions in Excel. These functions are named LINEST, INTERCEPT, and RSQ. LINEST provides us with the slope of the line, INTERCEPT gives us the fixed cost intercept, and RSQ yields the R squared value. Load Excel on your computer and enter the data shown in the table on the right side of your screen. Start with the headings in cell B3, C3, and D3. Enter the months in column B, the total cost in column C, and the number of meals in column D. When finished entering this data, go to the next screen.

將游標停在欄位F4 ，然後輸入 = ， 接著選取適當函數。 5-58 利用Excel跑簡單迴歸 將游標停在欄位F4 ，然後輸入 = ， 接著選取適當函數。 We will place the slope of the line in cell F4, so place your cursor in cell F4 and press the equal key. Look to the left of your screen and you will see the special functions drop-down menu. Click on the down arrow to the right of the special functions tab and scroll down to select more functions.

找到 “統計”類別函數後，點選 “SLOPE”函數 5-59 利用Excel跑簡單迴歸 找到 “統計”類別函數後，點選 “SLOPE”函數 Use the Or select a category option to select statistical. Once statistical is selected, move to the select a function window and scroll down until you find SLOPE. Click on SLOPE.

利用Excel跑簡單迴歸 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 5-60 利用Excel跑簡單迴歸 The Function Arguments window will pop-up for SLOPE. The first blank space is for Known underscore y’s. We want to enter the total cost for each month in this space. To do this, click on cell C4, hold down the mouse button and drag down to cell C19. Now, release the mouse button and C4 colon C19 will appear in the first space. We have now entered the total cost. Move your cursor down to the second space named Known underscore x’s. We want to enter the number of meals prepared in this space. Click on cell D4, hold down the mouse button and drag down to cell D19. Release the mouse button and you have entered the number of meals. 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 2. 在 Known_x’s 欄位裡，輸入資料範圍 D4:D19

利用Excel跑簡單迴歸 此為直線斜率的估計數 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 5-61 利用Excel跑簡單迴歸 此為直線斜率的估計數 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 2. 在 Known_x’s 欄位裡，輸入資料範圍 D4:D19 Look at the bottom of your screen to locate the 2.77. This is the estimate of the slope of the line. Now look at your cell F4 and make sure it looks just like the cell contents on this screen. If you have 2.77 and your cell F4 looks like the one on your screen, press the enter key. You have calculated the slope of the line, which is the first piece of vital information.

將游標停在欄位F5 ，然後輸入 = ， 然後選統計函數，接著點選 INTERCEPT 函數。 5-62 利用Excel跑簡單迴歸 將游標停在欄位F5 ，然後輸入 = ， 然後選統計函數，接著點選 INTERCEPT 函數。 Move your cursor to cell F5 and press the equal key. Return to the special functions area and click on the down arrow. The statistical function should now be selected. Scroll the select a function window until you find INTERCEPT. Click on INTERCEPT to select this function.

利用Excel跑簡單迴歸 此為固定成本 的估計數 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 5-63 利用Excel跑簡單迴歸 此為固定成本 的估計數 Part I Once again, we are asked to enter the Known underscore y’s and x’s. Follow the same procedures we used earlier to enter the total cost values in the Known underscore y’s and the number of meals in the Known underscore x’s spaces. Part II Notice that Excel has already calculated the estimated fixed costs at $2,618.72. If you find this amount and your cell F5 looks like the one on the screen, press the enter key. You have just determined the fixed cost intercept, which is the second piece of information needed. 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 2. 在 Known_x’s 欄位裡，輸入資料範圍 D4:D19

最後，我們將利用RSQ函數，求出“配適程度”( 或 R2)。 5-64 利用Excel跑簡單迴歸 最後，我們將利用RSQ函數，求出“配適程度”( 或 R2)。 Move your cursor to cell F6, press the equal key, and select the special functions section of Excel. You are already in statistical, so scroll until you find the special function RSQ (or R squared). Click on RSQ and you are ready to enter the necessary data.

利用Excel跑簡單迴歸 此為R2的估計 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 5-65 利用Excel跑簡單迴歸 此為R2的估計 Part I Once again, the function arguments window asks you to enter the Known underscore y’s and x’s. Follow the same procedure to enter total cost in the Known underscore y’s and the number of meals in the Known underscore x’s. Part II Look in the arguments window and notice that the R squared is equal to 93.3%. That is an excellent R squared. If you calculated this value for R squared and your cell F6 looks like the one on your screen, press the enter key. You have now completed gathering all the information necessary. Using Excel to solve a least-squares regression problem is very easy. It is very important that you understand the output from these special functions. 1. 在 Known_y’s 欄位裡，輸入資料範圍 C4:C19 2. 在 Known_x’s 欄位裡，輸入資料範圍 D4:D19

5-66 第五章結束 End of chapter 5.