111 年 國立臺灣大學會計學系碩士班《成本與管理會計》
第 1 題10 分
Princess Corporation grows, processes, packages, and sells three apple products: slices, applesauce, and apple juice. The outside skin of the apple, which is removed in the cutting department and processed as animal feed, is treated as a by-product. Princess uses the net realizable value method to assign costs of the joint process to its main products. The apple skin by-product net realizable value is used to reduce the joint production costs prior to allocation to the main products. Details of Princess' production process follow:
- The cutting department washes the apples and removes the outside skin. The department then cores and trims the apples for slicing. At this point, each of the three main products and the by-product are recognizable. Each product is then transferred to the next department for final processing.
- The slicing department receives the trimmed apples and slices and freezes them. Any juice generated during the slicing operation is frozen with the slices.
- The crushing department trims pieces of apple and processes them into applesauce. The juice generated during this operation is used in the applesauce.
- The juicing department pulverizes the core and any surplus apple from the cutting department into a liquid. This department experiences a loss equal to 8 percent of the weight of the good output produced.
A total of 270,000 pounds of apples entered the cutting department during November. The following information shows the costs incurred in each department, the proportion by weight (based on pounds) transferred to the four final processing departments, and the selling price of each end product. Assume no beginning or ending inventory of apple slices, applesauce, or juice.
| Department | Costs Incurred | Proportion of Product by Weight Transferred to Departments | Selling Price per Pound of Final Product |
|---|---|---|---|
| Cutting | $ 60,000 | ||
| Slicing | 11,280 | 33% | $ 0.80 |
| Crushing | 8,550 | 30% | 0.55 |
| Juicing | 3,000 | 27% | 0.40 |
| Feed | 700 | 10% | 0.10 |
| Total | $ 83,530 | 100% |
Required:
Calculate the gross margin in dollars for apple juice. (10%)
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核心觀念
- 聯合加工成本:多種產品於同一生產階段共同產生成本,需以合適方法分配。
- 淨可變現價法 (Net Realizable Value, NRV):先計算每項產品的 銷售收入 - 直接變現成本,再以各產品的 NRV 比例分配除副產品外的聯合成本。
- 副產品的處理:副產品的 NRV 先從總聯合成本中扣除,剩餘成本才分配給主要產品。
- 實際產出重量:如有加工損失,必須以 實際產出重量 乘以單位售價計算收入、NRV。
解題方法
- 計算各產品與副產品的投入重量
- 考慮 Juicing 部門的 8% 重量損失
- 計算每項產品的銷售收入(即 NRV,因題目未提其他變現成本)
- 總聯合成本
第 2 題
Outback Corporation manufactures tactical LED flashlights in Brisbane, Australia. The firm uses an absorption costing system for internal reporting purposes; however, the company is considering using variable costing. Data regarding Outback's planned and actual operations for 20x1 follow:
| Item | Budgeted Costs Per Unit | Budgeted Costs Total | Actual Costs Total |
|---|---|---|---|
| Direct material | $ 12.70 | $1,689,100 | $1,562,100 |
| Direct labor | 9.30 | 1,236,900 | 1,143,900 |
| Variable manufacturing overhead | 5.10 | 678,300 | 627,300 |
| Fixed manufacturing overhead | 4.80 | 638,400 | 648,400 |
| Variable selling expenses | 7.80 | 1,037,400 | 881,400 |
| Fixed selling expenses | 7.90 | 1,050,700 | 1,050,700 |
| Variable administrative expenses | 2.80 | 372,400 | 316,400 |
| Fixed administrative expenses | 2.10 | 279,300 | 286,300 |
| Total | $ 52.50 | $6,982,500 | $6,516,500 |
Additional information:
| Planned Activity | Actual Activity | |
|---|---|---|
| Beginning finished-goods inventory in units | 38,000 | 38,000 |
| Sales in units | 133,000 | 113,000 |
| Production in units | 133,000 | 123,000 |
The budgeted per-unit cost figures were based on Outback producing and selling 133,000 units in 20x1. Outback uses a predetermined overhead rate for applying manufacturing overhead to its product. A total manufacturing overhead rate of 71.70 per unit.
Required:
(1) Determine the overapplied or underapplied manufacturing overhead. (5%)
(2) Using the actual data, calculate the operating income under variable costing. (5%)
(3) Using the actual data, calculate the operating leverage under absorption costing. Round your answer to the second decimal place. (5%)
(4) Calculate the breakeven point in units under absorption costing. (5%)
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核心觀念
本題綜合考查:
- 製造費用的預定分攤與過度/不足分攤。
- 變動成本法下的營業利益。
- 吸收成本法下的營業利益與營業槓桿。
- 損益兩平點的計算。
重要成本資料如下:
- 單位變動製造成本:
- 單位吸收成本製造成本:
- 單位變動成本總額:
- 單位邊際貢獻:
期末存貨單位數為:
(1)製造費用過度或不足分攤
① 實際製造費用
實際變動製造費用:
實際固定製造費用:
因此,實際製造費用為:
② 已分攤製造費用
預定製造費用分攤率為每單位 $9.90,實際生產量為 123,000 單位:
③ 判斷過度或不足分攤
實際製造費用高於已分攤製造費用,因此為不足分攤,且期末應借記銷貨成本 $58,000。
(2)變動成本法下的營業利益
變動成本法將固定製造費用視為期間成本,不列入產品存貨成本。
① 銷貨收入
② 變動銷貨成本
變動成本法下,每銷售一單位的變動製造成本為 $27.10:
③ 變動銷售與管理費用
變動銷售費用:
變動管理費用:
④ 邊際貢獻
⑤ 固定成本
固定製造費用:
固定銷售費用:
固定管理費用:
固定成本合計:
⑥ 營業利益
(3)吸收成本法下的營業槓桿
營業槓桿通常以「邊際貢獻 ÷ 營業利益」計算:
第 3 題
Redtop Co. uses a standard cost system and flexible budgets. The following flexible budget was prepared at the 80% operating level for the year:
| Value | |
|---|---|
| Standard direct labor hours (DLHs) | 28,800 |
| Budgeted variable manufacturing overhead cost | $149,760 |
| Total manufacturing overhead rate per DLH | $18.70 |
| Standard DLHs per unit of output | 4.0 |
| Excess of actual manufacturing overhead cost incurred over the flexible budget for total overhead based on units produced during the period | $12,000 |
| Excess of actual fixed overhead cost over budgeted fixed overhead cost for the period | $5,000 |
For purposes of calculating the standard fixed overhead application rate, the company defined the "denominator volume" as the 90% capacity level. During the year, Redtop worked 33,600 DLHs to manufacture 8,500 units. The actual manufacturing overhead cost incurred was 5,000 was due to fixed overhead.
Required:
(1) Determine the fixed overhead production-volume variance. (10%)
(2) Determine the variable overhead spending variance. (10%)
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核心觀念
本題考核彈性預算下的製造費用差異分析,重點區分:
- 固定製造費用產能差異(production-volume variance)
固定製造費用是以「分母產能」建立標準分攤率;實際產量所吸收的固定製造費用若少於預算固定製造費用,即形成不利產能差異。
- 變動製造費用支出差異(spending variance)
比較實際變動製造費用與按實際直接人工小時計算的彈性預算變動製造費用:
其中,本題給的 $12,000 總製造費用超支中,有 $5,000 屬固定製造費用超支,因此其餘 $7,000 屬變動製造費用超支。
解題方法
一、拆出預算固定與變動製造費用
80% 營運水準下,標準直接人工小時為 28,800 小時,總製造費用率為每 DLH $18.70。
該水準下的總預算製造費用為:
已知變動製造費用預算為 $149,760,因此預算固定製造費用為:
標準變動製造費用率為:
因此,固定製造費用標準分攤率為:
亦可由分母產能計算驗證:80% 水準為 28,800 DLHs,所以 90% 分母產能為:
固定製造費用標準分攤率:
第 4 題10 分
Cramer Company produces smartphone components. In Cramer, regular components are manufactured to meet forecasted orders, and specialized components are made after an order is received. With the recent downturn in the smartphone industry, Cramer's financial performance has suffered. This month, Cramer received from Easecom Company an order inquiry, in which Easecom offers to purchase 6,900 units of XYZ, one type of specialized components, from Cramer. XYZ component has the following manufacturing cost structure:
| Item | Details | Unit Cost |
|---|---|---|
| Direct materials | $103.5 | |
| Direct labor | 2 hours at $34.5 per hour | $69 |
| Manufacturing overhead | 2 hours at $80.5 per hour | $161 |
The normal selling price of XYZ components is 215 because of the large quantity it is willing to purchase.
Easecom's special order requires a design modification that will allow a 20,010 in additional set-up costs and will have to purchase a $7,590 special device to manufacture these units. The device will be discarded once the special order is completed.
Total manufacturing overhead costs are applied to production at the rate of 3,300,960 and planned production activity of 55,200 labor hours. Cramer currently uses 34,500 labor hours. Cramer will allocate $15,000 of existing fixed administrative costs (resources to maintain the headquarter operations) to this order.
Required:
Should Cramer accept or reject Easecom's special order? Show calculations to support your answer. (10%)
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一、核心觀念
- 相關成本概念:在特別訂單決策中,只考慮增量(incremental)或可避免成本,即若接受訂單而額外發生的成本;固定成本、已分配的行政費用等屬於沉沒成本,於決策無關。
- 貢獻邊際(Contribution Margin):
若貢獻邊際乘以訂單數量能覆蓋所有額外固定成本,則接受訂單。 - 容量限制:若有閒置產能(本題 34,500 小時 < 計畫 55,200 小時),固定製造間接費不因多產而變動,故不列入相關成本。
二、解題方法
-
列出全部增量成本
- 直接材料(已因設計變更降低):
- 直接人工:
- 變動製造間接費:(依每勞工時的費率計算,視為與產量同增)
- 設備一次性購買費 (訂單完成即棄置)
- 設定成本 (一次性)
- 不列入:已分配之 行政固定費、預算中包含的固定製造間接費(因產能閒置而不變動)。
-
計算單位變動成本
- 計算整體增量成本
- 變動成本總額:
第 5 題
The VanCooper Company is an equipment parts supplier that uses computer numerical control (CNC) machine to automatically manufacture precision parts from copper bars. VanCooper's required rate of return on investment is 25% per year. VanCooper's budgeted income statement for the year ending December 31, 20X2 (in thousands) is as follows:
| Value | |
|---|---|
| Revenues (1,260,000 units) | $ 15,120 |
| Cost of goods sold | |
| Variable costs | $ 5,670 |
| Fixed costs | 2,030 |
| Total costs of goods sold | 7,700 |
| Gross margin | 7,420 |
| Marketing and distribution costs | |
| Variable costs | $ 1,260 |
| Fixed costs | 2,100 |
| Total marketing and distribution costs | 3,360 |
| Operating income | $ 4,060 |
VanCooper's inventory of raw copper averages 800 per order, is willing to supply copper in smaller lots at no additional charge. VanCooper identifies the following effects of adopting a JIT purchasing program to virtually eliminate copper inventory:
- Without scheduling any overtime, lost sales due to stockouts would increase by 49,000 units per year. However, by incurring overtime premiums of $56,000 per year, the increase in lost sales could be reduced to 28,000 units per year. This would be the maximum amount of overtime that would be feasible for VanCooper.
- Two warehouses currently used for copper bar storage would no longer be needed. VanCooper rents one warehouse from another company under a cancelable leasing arrangement at an annual cost of 2.10 per square foot per year. Insurance and property tax costs totaling $19,600 per year would be eliminated.
Required:
(1) Before deciding whether to adopt the JIT purchasing program, use EOQ model to compute the relevant total costs at optimal order quantity for raw copper. (10%)
(2) Should VanCooper adopt the JIT purchasing program? Show calculations to support your answer. (10%)
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核心觀念
-
經濟訂貨量 (EOQ) 模型:在已知年需求量 、單位訂購成本 (ordering cost)以及單位持有成本 (holding cost)時,求使總成本最小的訂購量 。
總成本(TC)=購買成本(與決策無關)+訂購成本+持有成本
-
持有成本的計算:持有成本 = (平均庫存價值) × (持有率)。在此題中持有率=必要報酬率 25%(即資金機會成本)。
-
JIT(Just‑In‑Time):減少或消除庫存,會影響持有成本、租金、保險、稅金等固定費用,同時可能因缺貨而失銷,需衡量加班成本與減少失銷的效益。
解題方法
(1) EOQ 之最適訂購量與相關總成本
-
年需求量
需求單位:1,260,000 件
單位售價:$12(僅供參考,算 EOQ 時不需)
因題目僅給出「單位」需求,直接以件數作為需求量:
-
單位訂購成本
題目說明「供應商每次訂購收取 $800」:
-
單位持有成本
- 平均庫存價值 =
但 EOQ 中持有成本直接以「單位金額」乘以持有率。 - 年平均庫存金額已給:(以金額計算)。
- 持有率 = 必要報酬率 25%
因此每美元庫存的年持有成本為 ,故
但 EOQ 需要「每單位(件)持有成本」。先算每件的成本:
在 EOQ 模型中,平均庫存件數 = 。為求 ,以年平均庫存金額直接作持有成本基礎:
這是當 實際平均庫存 為 時的持有成本。
在 EOQ 的成本式 中, 必須是「每件每年持有成本」。令
為了在求 時不致循環,我直接使用 金額方式 的 EOQ 變形:
事實上上述化簡回到同樣的持有成本 ,表示持有成本與 無關(因庫存金額固定),此情形下 EOQ 模型失效。
正確做法:把持有成本視為 每美元庫存的機會成本,而庫存金額隨 成比例: - 每次訂購 件,平均庫存件數 = 。
- 每件的單位成本 = $0.6667。
因此每件的持有成本
- 平均庫存價值 =
第 6 題
The Hiro Corporation is a manufacturer of wine glasses. It produces all of its products in one department. The FIFO process costing method is used. Direct materials are added at the beginning of the process. Factory overhead is applied at a rate equal to 37.5% of direct manufacturing labor. All spoilage is normal and is detected at the end of the process. Spoilage is recognized.
The information for June is as follows:
| Value | |
|---|---|
| Beginning work-in-process | 60,000 units |
| Units started | 88,000 units |
| Units completed and transferred out | 12,000 units |
| Ending work-in-process | 23,200 units |
| Spoilage | 4,800 units |
| Beginning work-in-process direct materials | $40,000 |
| Beginning work-in-process conversion | $16,000 |
| Direct materials added during month | $182,000 |
| Direct manufacturing labor during month | $64,032 |
Beginning work-in-process was 25% complete as to conversion. The ending work-in-process shows its completion rate as a missing information on record.
The information for July is as follows:
| Value | |
|---|---|
| Beginning work-in-process | 23,200 units |
| Units started | 49,000 units |
| Units completed and transferred out | 60,000 units |
| Ending work in process | 9,600 units |
| Spoilage | 2,600 units |
| Beginning work-in-process direct materials | $47,982 |
| Beginning work-in-process conversion | $10,931 |
| Direct materials added during month | $72,000 |
| Direct manufacturing labor during month | $26,182 |
Ending work-in-process was 55% complete as to conversion.
Required:
(1) Determine the costs for spoilage units during June. (10%)
(2) Prepare journal entry for transferring out units to the finished goods during July. (10%)
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一、核心觀念
- FIFO 流程成本法:
- 只把本期加入的直接材料、直接人工與製造間接費列入本期的等價單位計算。
- 期初在製存貨的已發生成本先全部計入期初存貨,期末在製存貨只列入本期尚未完成的等價單位。
- 等價單位 (Equivalent Units):
- 直接材料:本期開始即全部加入,故每個加工單位的材料等價單位皆為 1。
- 製造轉換成本(直接人工+製造費用):以完成度乘以單位數求得等價單位。
- 正常損耗:在期末偵測,視同已完成之單位,全部列入等價單位,並分配與正常製造單位相同的單位成本。
- 製造費用的分配:
(1) 6 月正常損耗之成本
1. 計算本期等價單位
| 項目 | 單位數 | 完成度 | 等價單位 (材料) | 等價單位 (轉換) |
|---|---|---|---|---|
| 期初在製 (60,000) | 60,000 | 材料 100%<br>轉換 25% (已完成 25%) | — | |
| 本期開始之單位 (88,000) | 88,000 | 材料 100%<br>轉換 100% | 88,000 | 88,000 |
| 正常損耗 (4,800) | 4,800 | 材料 100%<br>轉換 100% (期末偵測) | 4,800 | 4,800 |
| 期末在製 (23,200) | 23,200 | 材料 100%<br>轉換 55%(題目缺失,依 7 月已給 55% 推斷) | 23,200 |
2. 計算單位成本
- 材料成本
- 轉換成本
3. 計算正常損耗之成本
損耗單位已全部完成,故每單位成本 = 材料成本 + 轉換成本
【答案】 6 月正常損耗的成本為 **