111 年 國立政治大學會計研究所會計組《成本與管理會計》

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第 第一題 題10 分

Beta Corp. is planning the 2022 operating budget. Average operating assets of 1,800,000willbeusedduringtheyearandunitsellingpricesareexpectedtoaverage1,800,000 will be used during the year and unit selling prices are expected to average 100 each. Variable costs of the division are budgeted at 40perunit,whilefixedcostsaresetat40 per unit, while fixed costs are set at 300,000. The company's required rate of return is 18%.

Required:
(A) The division manager receives a bonus of 50% of residual income. What is his anticipated bonus for 2022, assuming he achieves the 20% ROI from sales? (5%)
(B) If there is another branch company to jointly utilize one-third of Beta's operating assets in 2022, Beta' sales volume will decrease to 3,000 units. What is the new ROI for joint utilization of operating assets? (5%)

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這一題的完整詳解

核心觀念

本題評量分權化組織（Decentralized Organization）下的責任會計與績效評估（Performance Measurement），涵蓋以下關鍵觀念與公式：

  1. 投資報酬率（Return on Investment, ROI）：
    衡量投資中心利用營業資產產生營業利益之效率：
    ROI=營業利益（Operating Income）平均營業資產（Average Operating Assets）\text{ROI} = \frac{\text{營業利益（Operating Income）}}{\text{平均營業資產（Average Operating Assets）}}

  2. 剩餘利益（Residual Income, RI）：
    衡量投資中心創造超過資金成本（最低要求報酬）之超額利潤，能有效減緩 ROI 導致的次最佳化（Sub-optimization）問題：
    RI=營業利益−(平均營業資產×要求報酬率)\text{RI} = \text{營業利益} - (\text{平均營業資產} \times \text{要求報酬率})

  3. 經理人獎金制度（Managerial Bonus）：
    預期獎金=剩餘利益 (RI)×獎金比例\text{預期獎金} = \text{剩餘利益 (RI)} \times \text{獎金比例}

  4. 本量利分析（CVP Analysis）損益計算：
    單位邊際貢獻 (Unit CM)=單位售價−單位變動成本\text{單位邊際貢獻 (Unit CM)} = \text{單位售價} - \text{單位變動成本}
    營業利益=(銷售量×單位邊際貢獻)−固定成本\text{營業利益} = (\text{銷售量} \times \text{單位邊際貢獻}) - \text{固定成本}

解題方法與詳細推導

(A) 計算 2022 年部門經理之預期獎金

  1. 推算目標營業利益：
    題目設定部門達成 20% 之 ROI，已知平均營業資產為 $1,800,000：
    營業利益=平均營業資產×ROI=$1,800,000×20%=$360,000\text{營業利益} = \text{平均營業資產} \times \text{ROI} = \$1,800,000 \times 20\% = \$360,000

  2. 計算資本成本（最低要求報酬）：
    公司之必要報酬率（Required Rate of Return）為 18%：
    最低要求報酬=平均營業資產×必要報酬率=$1,800,000×18%=$324,000\text{最低要求報酬} = \text{平均營業資產} \times \text{必要報酬率} = \$1,800,000 \times 18\% = \$324,000

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第 第二題 題24 分

Robert Inc. desires to buy a new foundry equipment for newly developed models which are required for their R&D staffs. They have received three proposals from suppliers. These three proposals have same costs for initial investment in equipment. However, the purchasing department struggles to find a supplier willing to offer a 10% discount for initial investment in equipment of proposal C. Other information on each proposal is as follows:

Proposal AProposal BProposal C
Initial investment in equipment$90,000$90,000?
Annual cash increase in operations:
Year 180,00045,00090,000
Year 245,00010,00045,000
Year 345,00045,0000
Salvage value000
Estimated life3 years3 years1 year

The company uses straight-line depreciation for all capital assets.

Required:
(A) Compute the payback period, net present value, and accrual accounting rate of return with initial investment, for each proposal. Use a required rate of return of 14%. (15%)
(B) Rank each proposal 1, 2, and 3 using each method separately. Which proposal is best? Why? (5%)
(C) Accountant Mary argues that we should consider original cost of an old equipment, initial working capital investment, and depreciation cost, as well as after-tax cash flow from operations when evaluating component of net-initial-investment cash flows for proposals. Do you agree her opinion? Why? (4%)

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這一題的完整詳解

本題主要考查資本預算決策中的三個常用評估方法：回收期法 (Payback Period)、淨現值法 (Net Present Value, NPV) 及會計報酬率法 (Accrual Accounting Rate of Return, AARR)，並要求進行方案排序與說明。

核心觀念：

  • 回收期法：衡量投資回收原始投資金額所需的時間。
  • 淨現值法：將未來現金流量折現至現值，並減去原始投資，若 NPV > 0 則投資可行。
  • 會計報酬率法：衡量投資的平均稅後淨利相對於平均投資的報酬率。

解題步驟：

首先，處理題目給予的資訊與計算基礎。

  1. 初始投資金額 (Initial Investment)：

    • Proposal A: $90,000
    • Proposal B: $90,000
    • Proposal C: 題目提到「purchasing department struggles to find a supplier willing to offer a 10% discount for initial investment in equipment of proposal C」。這表示 Proposal C 的初始投資金額是基於某個價格，但可以獲得 10% 的折扣。然而，題目並未提供 Proposal C 的原始標價，因此我們無法計算出確切的折扣後的初始投資。
    • 此處假設題目意圖是 Proposal C 的初始投資額與 A、B 相同，但可以取得 10% 的折扣，故其初始投資為 90,000×(1−10%)=90,000 \times (1-10\%) = $81,000。 如果題目意圖是提供一個原始標價，則此題無法計算。基於後續的計算，此假設是最合理的。
    • 修正： 題目說「These three proposals have same costs for initial investment in equipment. However, the purchasing department struggles to find a supplier willing to offer a 10% discount for initial investment in equipment of proposal C.」這句話非常矛盾。
      • 第一句：三個方案初始投資相同。
      • 第二句：C 方案可以獲得 10% 折扣。
      • 這意味著 C 方案的「相同」初始投資金額，在折扣後會比 A、B 方案低。
      • 最合理的理解是： 原始標價相同，假設為 X。A、B 方案的初始投資就是 X。C 方案的初始投資是 X 乘以 (1-10%)。但題目又說「These three proposals have same costs for initial investment in equipment.」
      • 另一種理解： A 和 B 的初始投資是 90,000。C方案的「相同」初始投資是指其「標價」與A、B相同，但可以獲得折扣。如果C的「標價」也是90,000。C 方案的「相同」初始投資是指其「標價」與 A、B 相同，但可以獲得折扣。如果 C 的「標價」也是 90,000，那麼折扣後就是 $81,000。
      • 最直接的理解： A 和 B 的初始投資是 90,000。C方案的初始投資額是「？」但可以獲得1090,000。C 方案的初始投資額是「？」但可以獲得 10% 折扣。如果「相同」是指「標價」相同，那麼 C 的標價是 90,000，折扣後是 $81,000。
      • 最後一種解讀： 題目可能想表達，A 和 B 的初始投資為 90,000。C方案的「標價」是90,000。C 方案的「標價」是 90,000，但若能談到折扣，則初始投資會低於 90,000。如果我們假設A和B的初始投資是90,000。如果我們假設 A 和 B 的初始投資是 90,000，而 C 方案的「標價」也是 90,000，但能以9折成交，則C的初始投資為90,000，但能以 9 折成交，則 C 的初始投資為 81,000。
      • 本題最常見的處理方式是：A 和 B 初始投資 90,000；C方案標價90,000；C 方案標價 90,000，可獲 10% 折扣，故初始投資為 90,000×0.9=90,000 \times 0.9 = $81,000。 我們將以此假設進行計算。

  2. 折舊計算 (Depreciation)：
    公司使用直線法折舊。

    • Proposal A & B (Estimated life: 3 years)
      每年折舊 = (初始投資 - 殘值) / estimated life
      每年折舊 = (($90,000−90,000 - $0)/3=0) / 3 = $30,000。
    • Proposal C (Estimated life: 1 year)
      每年折舊 = (($81,000−81,000 - $0)/1=0) / 1 = $81,000。

  3. 稅前淨收益計算 (Pre-tax Net Income)：
    題目給的是「Annual cash increase in operations」。這通常指稅前現金流入。
    會計報酬率需要稅後淨收益。由於題目未給稅率，我們假設稅率為 0%，即稅前淨收益等於稅後淨收益。
    稅前淨收益 = 年度現金流入 - 年度折舊

(A) 各方案的回收期、淨現值、會計報酬率計算

Proposal A

  • 初始投資 = $90,000

  • 年度現金流入：Year 1: 80,000;Year2:80,000; Year 2: 45,000; Year 3: $45,000

  • 折舊：$30,000/年

  • 要求報酬率 = 14%

    • 回收期 (Payback Period)：

      • Year 1 結束時累積現金流入 = $80,000。
      • 剩餘未回收金額 = 90,000−90,000 - 80,000 = $10,000。
      • Year 2 的現金流入 = $45,000。
      • 回收期 = 1年 + (10,000/10,000 / 45,000) = 1 + 0.2222 = 1.22 年。

    • 淨現值 (Net Present Value, NPV)：

      • 折現因子 (PVF) at 14%:
        • Year 1: 1/(1.14)1=0.87721 / (1.14)^1 = 0.8772
        • Year 2: 1/(1.14)2=0.76951 / (1.14)^2 = 0.7695
        • Year 3: 1/(1.14)3=0.67501 / (1.14)^3 = 0.6750
      • NPV = ( $80,000×0.8772+80,000 \times 0.8772 + $45,000×0.7695+45,000 \times 0.7695 + $45,000×0.6750)−45,000 \times 0.6750) - $90,000
      • NPV = (($70,176+70,176 + $34,627.5+34,627.5 + $30,375)−30,375) - $90,000
      • NPV = $135,178.5−135,178.5 - $90,000=90,000 = $45,178.5。

    • 會計報酬率 (Accrual Accounting Rate of Return, AARR)：

      • 總稅後淨收益 = 總稅前現金流入 - 總折舊
      • 總稅前現金流入 = 80,000+45,000+45,000=80,000 + 45,000 + 45,000 = $170,000
      • 總折舊 = 30,000×3=30,000 \times 3 = $90,000
      • 總稅後淨收益 = $170,000−170,000 - $90,000=90,000 = $80,000。
      • 平均稅後淨收益 = $80,000/3=80,000 / 3 = $26,666.67。
      • 平均投資 = (初始投資 + 期末殘值) / 2 = (($90,000+90,000 + $0)/2=0) / 2 = $45,000。
      • AARR = 平均稅後淨收益 / 平均投資
      • AARR = $26,666.67/26,666.67 / $45,000=0.592645,000 = 0.5926 或 59.26%。
      • 另一種 AARR 計算方式 (基於期初投資)：
        AARR = 平均稅後淨收益 / 期初投資
        AARR = $26,666.67/26,666.67 / $90,000=0.296390,000 = 0.2963 或 29.63%。
        通常題目會指明使用哪種方法，若未指明，平均投資法較常見。我們使用平均投資法。

Proposal B

  • 初始投資 = $90,000

  • 年度現金流入：Year 1: 45,000;Year2:45,000; Year 2: 10,000; Year 3: $45,000

  • 折舊：$30,000/年

  • 要求報酬率 = 14%

    • 回收期 (Payback Period)：

      • Year 1 結束時累積現金流入 = $45,000。
      • 剩餘未回收金額 = 90,000−90,000 - 45,000 = $45,000。
      • Year 2 的現金流入 = $10,000。
      • Year 3 的現金流入 = $45,000。
      • 回收期 = 2年 + (45,000−45,000 - 10,000) / 45,000=2年+45,000 = 2年 + 35,000 / $45,000 = 2 + 0.7778 = 2.78 年。

    • 淨現值 (Net Present Value, NPV)：

      • NPV = ( $45,000×0.8772+45,000 \times 0.8772 + $10,000×0.7695+10,000 \times 0.7695 + $45,000×0.6750)−45,000 \times 0.6750) - $90,000
      • NPV = (($39,474+39,474 + $7,695+7,695 + $30,375)−30,375) - $90,000
      • NPV = $77,544−77,544 - $90,000=−90,000 = -$12,456。

    • 會計報酬率 (Accrual Accounting Rate of Return, AARR)：

      • 總稅前現金流入 = 45,000+10,000+45,000=45,000 + 10,000 + 45,000 = $100,000
      • 總折舊 = 30,000×3=30,000 \times 3 = $90,000
      • 總稅後淨收益 = $100,000−100,000 - $90,000=90,000 = $10,000。
      • 平均稅後淨收益 = $10,000/3=10,000 / 3 = $3,333.33。
      • 平均投資 = (($90,000+90,000 + $0)/2=0) / 2 = $45,000。
      • AARR = $3,333.33/3,333.33 / $45,000=0.074145,000 = 0.0741 或 7.41%。

Proposal C

  • 初始投資 = 81,000(假設為81,000 (假設為 90,000 \times 0.9$)

  • 年度現金流入：Year 1: 90,000;Year2:90,000; Year 2: 45,000; Year 3: $0

  • 折舊：$81,000/年

  • 要求報酬率 = 14%

    • 回收期 (Payback Period)：

      • Year 1 結束時累積現金流入 = $90,000。
      • 回收期 = 81,000/81,000 / 90,000 = 0.90 年。

    • 淨現值 (Net Present Value, NPV)：

      • 折現因子 at 14%:
        • Year 1: 0.8772
        • Year 2: 0.7695
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第 第三題 題15 分

The XYZ Company produces four products – XX, YY, ZZ, and BB by a joint production process. During October, joint costs of production totaled 400,000.ThecompanytreatsproductBBasabyproductthatcanbesoldfor400,000. The company treats product BB as a byproduct that can be sold for 6 per unit at split-off point by incurring disposal costs of $1 per unit. No joint cost is to be allocated to the byproduct. There were 100 units of BB on October 1. In October, 2,000 units of byproduct BB were produced and 800 units were sold. Products XX, YY, and ZZ are further refined and then sold. XYZ uses the FIFO inventory flow assumption to cost the products. Assume no beginning or ending work-in-process inventory. Data related to October are as follows:

XXYYZZ
Beginning inventory200400500
Units sold1,8004,0006,300
Units produced2,0004,0006,000
Separable processing$50,000$80,000$150,000
Selling price per unit$100$80$60

Required: (Consider each situation independently.)
(A) If XYZ Company allocates the joint costs to main products using the NRV (net realizable value) method and accounts for the byproduct using the production method, what is the ending inventory cost for product YY?
(B) If each product could be sold immediately at the split-off point for the following selling price: XX, 70;YY,70; YY, 65; and ZZ, 36.Theunitsproducedremainunchangedwhetherthecompanyprocessestheproductsfurtherbeyondthesplit−offpointornot.Pleaseignoretheunitssoldabove.NomatterwhetherthecompanysellsproductXX,YY,andZZatthesplit−offpointorafterfurtherprocessing,alloftheoutputcouldbesold.(1)WhichofthemainproductsshouldXYZCompanysellatthesplit−offpointtomaximizeoperatingincome?Supportyouranswerwithcomputations.(2)Supposethe36. The units produced remain unchanged whether the company processes the products further beyond the split-off point or not. Please ignore the units sold above. No matter whether the company sells product XX, YY, and ZZ at the split-off point or after further processing, all of the output could be sold. (1) Which of the main products should XYZ Company sell at the split-off point to maximize operating income? Support your answer with computations. (2) Suppose the 150,000 cost of ZZ's separable processing includes 38,000ofallocatedfixedcosts,andthefacilitiesthatwouldbeusedtofurtherprocessZZhaveanalternativeusetogeneraterevenuesof38,000 of allocated fixed costs, and the facilities that would be used to further process ZZ have an alternative use to generate revenues of 20,000 and variable costs of $5,000. What effect would selling product ZZ at the split-off point have on the company's operating income instead of selling it after further processing?

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這一題的完整詳解

核心觀念

  • 共同成本（Joint Costs）：在同一生產過程中同時產生，須在主要產品間分配。
  • 淨可實現價值（NRV）分配法：以各產品在分割點（split‑off point）之「銷售價格 – 繼續加工成本」的總額比例分配共同成本。
  • 副產品（By‑product）之生產法：副產品不分配共同成本，僅認列其銷售淨收入（銷售價格 – 處置成本）作為期間收入。
  • FIFO 存貨流動假設：先銷售期初存貨，餘下的期末存貨皆為本期製造之產品。

(A) 以 NRV 法分配共同成本、以生產法處理副產品 BB，求 YY 之期末存貨成本

  1. 計算每單位的可再加工成本（Separable processing）
XX: 50,0002,000=25 元/件YY: 80,0004,000=20 元/件ZZ: 150,0006,000=25 元/件\begin{aligned} \text{XX: } & \frac{50{,}000}{2{,}000}=25\ \text{元/件}\\ \text{YY: } & \frac{80{,}000}{4{,}000}=20\ \text{元/件}\\ \text{ZZ: } & \frac{150{,}000}{6{,}000}=25\ \text{元/件} \end{aligned}
  1. 取得分割點之 NRV（每單位）
XX: 100−25=75YY: 80−20=60ZZ: 60−25=35\begin{aligned} \text{XX: } & 100-25 = 75\\ \text{YY: } & 80-20 = 60\\ \text{ZZ: } & 60-25 = 35 \end{aligned}
  1. 計算各產品的總 NRV（僅以本期產出計）
XX: 2,000×75=150,000YY: 4,000×60=240,000ZZ: 6,000×35=210,000合計: 600,000\begin{aligned} \text{XX: } & 2{,}000 \times 75 = 150{,}000\\ \text{YY: } & 4{,}000 \times 60 = 240{,}000\\ \text{ZZ: } & 6{,}000 \times 35 = 210{,}000\\ \text{合計: } & 600{,}000 \end{aligned}
  1. 以 NRV 比例分配共同成本 400,000400,000
XX: 400,000×150,000600,000=100,000YY: 400,000×240,000600,000=160,000ZZ: 400,000×210,000600,000=140,000\begin{aligned} \text{XX: } & 400{,}000 \times \frac{150{,}000}{600{,}000}=100{,}000\\ \text{YY: } & 400{,}000 \times \frac{240{,}000}{600{,}000}=160{,}000\\ \text{ZZ: } & 400{,}000 \times \frac{210{,}000}{600{,}000}=140{,}000 \end{aligned}
  1. YY 的單位成本
單位共同成本=160,0004,000=40 元單位可再加工成本=20 元單位總成本=40+20=60 元\text{單位共同成本}= \frac{160{,}000}{4{,}000}=40\ \text{元} \\ \text{單位可再加工成本}=20\ \text{元} \\ \boxed{\text{單位總成本}=40+20=60\ \text{元}}
  1. FIFO 計算期末存貨
  • 期初存貨 400 件（已在前期成本化）
  • 本期製造 4,000 件
  • 銷售 4,000 件，先以 FIFO 銷售期初 400 件，餘下 3,600 件來自本期製造。

因此期末存貨 = 本期製造剩餘 400 件，成本：

400×60=24,000 元\boxed{400 \times 60 = 24{,}000\ \text{元}}

【答案】 YY 之期末存貨成本為 24,000 元。

(B‑1) 以分割點價格決定應於何時銷售，以最大化營業利益

產品分割點價格 PsoP_{so}完全加工後價格 PfP_f可再加工成本 CsepC_{sep}Pf−CsepP_f-C_{sep} (加工後 NRV)差額 = (Pf−Csep)−Pso=\,(P_f-C_{sep})-P_{so}
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第 第四題 題18 分

The Nature Corporation produces a wide variety of fruit vinegars. One of its popular products is FV-ABC, a mixture of direct materials - Fruit A, Fruit B, and Fruit C. The standard mix for producing a single batch of FV-ABC is as follows:

FruitStandard quantityStandard unit cost
A90$ 10
B270$ 8
C140$ 6

Work-in-process inventories are insignificant and can be ignored. Changing the standard mix of direct material quantities does not significantly affect the overall end product. The total direct materials yield variance for January is $19,500 unfavorable. The actual quantities and costs of the materials purchased and placed in production during January were as follows (There was no beginning direct materials inventory.):

FruitActual quantity purchased and usedActual cost
A38,000$ 402,800
B102,000$ 775,200
C60,000$ 354,000

Required:
(A) How many batches of FV-ABC were produced during January? (5%)
(B) Compute the total direct materials mix variance for January, indicating whether the variance is favorable or unfavorable. (5%)
(C) According to your analysis, comment on the results of variance analysis and recommend possible ways for the company's future improvement. (8%)

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這一題的完整詳解

核心觀念

本題的核心為**直接材料差異分析（Direct Materials Variance Analysis）中，將「材料數量差異（效率差異）」進一步細分為材料配比差異（Direct Materials Mix Variance）與材料產出差異（Direct Materials Yield Variance）**之進階應用。

  1. 基本定義與符號：

    • AQiAQ_i：第 ii 種材料的實際使用數量（Actual Quantity）。
    • TAQ=∑AQiTAQ = \sum AQ_i：全部材料的實際總投入量（Total Actual Quantity）。
    • SMiSM_i：第 ii 種材料在標準配方中的標準配比（Standard Mix Percentage）。
    • SPiSP_i：第 ii 種材料的標準單價（Standard Price）。
    • SP‾\overline{SP}：標準配比下的加權平均標準單價（Weighted-Average Standard Price）。
    • TSQTSQ：實際產量下，允許投入的標準材料總數量（Total Standard Quantity allowed for actual output）。

  2. 核心公式：

    • 標準配比加權平均單價： SP‾=∑(SMi×SPi)=單批標準材料總成本單批標準材料總投入量\overline{SP} = \sum (SM_i \times SP_i) = \frac{\text{單批標準材料總成本}}{\text{單批標準材料總投入量}}
    • 材料產出差異（Direct Materials Yield Variance）：衡量「總投入量」是否偏離「標準總投入量」所造成的成本差異。 Yield Variance=(TAQ−TSQ)×SP‾=∑(TAQ×SMi−SQi)×SPi\text{Yield Variance} = (TAQ - TSQ) \times \overline{SP} = \sum (TAQ \times SM_i - SQ_i) \times SP_i
      • 若 TAQ>TSQTAQ > TSQ，表示投入過多材料，產生不利差異（Unfavorable, UU）。
      • 若 TAQ<TSQTAQ < TSQ，表示材料耗用節約，產生有利差異（Favorable, FF）。
    • 材料配比差異（Direct Materials Mix Variance）：衡量材料投入的「實際配比」偏離「標準配比」所造成的成本差異。 Mix Variance=∑(AQi−TAQ×SMi)×SPi\text{Mix Variance} = \sum (AQ_i - TAQ \times SM_i) \times SP_i
      • 亦可簡化為：Mix Variance=∑(AQi×SPi)−(TAQ×SP‾)\text{Mix Variance} = \sum (AQ_i \times SP_i) - (TAQ \times \overline{SP})。

解題方法與步驟推導

基礎資料整理

  1. 單批（Single Batch）標準投入與標準成本：

    • Fruit A：90 單位×90\text{ 單位} \times $10=10 = $900
    • Fruit B：270 單位×270\text{ 單位} \times $8=8 = $2,160
    • Fruit C：140 單位×140\text{ 單位} \times $6=6 = $840
    • 每批標準總投入量：90+270+140=500 單位90 + 270 + 140 = 500\text{ 單位}
    • 每批標準總成本：$900+900 + $2,160+2,160 + $840=840 = $3,900

  2. 標準配比（SMSM）與加權平均標準單價（SP‾\overline{SP}）：

    • SMA=90500=18%SM_A = \frac{90}{500} = 18\%
    • SMB=270500=54%SM_B = \frac{270}{500} = 54\%
    • SMC=140500=28%SM_C = \frac{140}{500} = 28\%
    • \overline{SP} = \frac{$3,900}{500} = $7.80 / 單位7.80\text{ / 單位}

  3. 1 月份實際投入總量（TAQTAQ）：

    TAQ=38,000+102,000+60,000=200,000 單位TAQ = 38,000 + 102,000 + 60,000 = 200,000\text{ 單位}

(A) 計算 1 月份生產批數（Batches Produced）

利用題目給定的材料產出差異 Yield Variance=\text{Yield Variance} = $19,500 (U)19,500\text{ }(U) 反推實際產出對應之標準總投入量（TSQTSQ）：

Yield Variance=(TAQ−TSQ)×SP‾\text{Yield Variance} = (TAQ - TSQ) \times \overline{SP}

代入已知數值：

19,500=(200,000−TSQ)×7.8019,500 = (200,000 - TSQ) \times 7.80 200,000−TSQ=19,5007.80=2,500 單位200,000 - TSQ = \frac{19,500}{7.80} = 2,500\text{ 單位} TSQ=200,000−2,500=197,500 單位TSQ = 200,000 - 2,500 = 197,500\text{ 單位}

由於生產每批 FV-ABC 需標準投入 500 單位500\text{ 單位} 材料：

實際生產批數=TSQ每批標準投入量=197,500500=395 批\text{實際生產批數} = \frac{TSQ}{\text{每批標準投入量}} = \frac{197,500}{500} = 395\text{ 批}

(B) 計算 1 月份材料配比總差異（Total Direct Materials Mix Variance）

按實際總投入量 TAQ=200,000 單位TAQ = 200,000\text{ 單位}，計算各材料在標準配比下應有的投入量（TAQ×SMiTAQ \times SM_i），並與實際投入量（AQiAQ_i）比較：

  1. 各材料在實際總量下的標準配比投入量：

    • Fruit A：200,000×18%=36,000 單位200,000 \times 18\% = 36,000\text{ 單位}
    • Fruit B：200,000×54%=108,000 單位200,000 \times 54\% = 108,000\text{ 單位}
    • Fruit C：200,000×28%=56,000 單位200,000 \times 28\% = 56,000\text{ 單位}

  2. 各材料配比差異計算：

    • Fruit A：(38,000−36,000)×(38,000 - 36,000) \times $10=+2,000×10 = +2,000 \times $10=10 = $20,000 (U)20,000\text{ }(U)
    • Fruit B：(102,000−108,000)×(102,000 - 108,000) \times $8=−6,000×8 = -6,000 \times $8=8 = $48,000 (F)48,000\text{ }(F)
    • Fruit C：(60,000−56,000)×(60,000 - 56,000) \times $6=+4,000×6 = +4,000 \times $6=6 = $24,000 (U)24,000\text{ }(U)
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第 第五題 題33 分

Tech Toys produces electronic toys for children and young adults. Chips are crucial components for toys that feature light, sound, and motion. However, the global chip shortage after the Covid-19 pandemic causes concern for numerous products and business, including the toy industry, and has been squeezing supply from electronics to white goods to toys. The situation is compounded by competition for the limited supply between electronics manufactures and automakers. 91% of chip manufacturing is based in Asia, mostly in Taiwan and South Korea. With the bulk of chip production concentrated in a handful of suppliers, analysts warn that the shortage is likely to last throughout 2022 and even into 2023 as production problem continue to bite. Unfortunately, it seems likely that toy companies will be at the back of the queue when it comes to sourcing chips, behind tech giants like Apple and car manufacturers, partly because they can't compete on price and partly because they lack their collective clout when it comes to securing supplies. For example, one of the world's biggest chipmakers - Taiwan Semiconductor Manufacturing Company - has prioritized Apple and cars.

Tech Toys manufactures the products in a factory located in China and ships the products to the retailers in the U.S. and Europe. The company has run just in time from sourcing, production, to delivering for almost two decades. The production process of Tech Toys consists of two basic operations. In the first operation, plastic pieces are molded in the plastics department. These pieces are then transferred to the assembly department, where direct materials are added after some assembly has been done. For example, plastic pieces of the toy are put together, then the electronic parts are added, and finally some details are painted on the sides and back. The direct materials, including chips, are added in the assembly department when the process is 75% complete.

Data for the assembly department for January 2022 are as follows. Beginning inventory is 80% complete and ending inventory is 25% complete.

Beginning inventory costs (in thousands) for the assembly department:

Transferred inDirect materialsConversion costsTotal cost
$4,000$2,000$1,600$7,600

Costs (in thousands) incurred in the assembly department during current period:

Transferred inDirect materialsConversion costsTotal cost
$36,000$18,000$16,000$70,000

Physical units in the assembly department:

Units in beginning inventoryUnits started this monthTotal units completed and transferred outNormal spoilageAbnormal spoilage
2,00018,00014,8001,000 (100% complete)1,000 (100% complete)

Required:
(A) Choose a process costing method for the assembly department. Explain your choice and describe its pros and cons. Prepare journal entries for the work of January 2022 using the method you choose. (23%)
(B) Jerry Wang is the founder of Tech Toys and is now the chairman of the board. He is concerned about the global chip shortage and wondering why the chipmakers can't make more and why there aren't more chipmakers as there is a huge demand for chips in the foreseeable future. He also would like to know how to deal with the chip shortage and other global issues facing companies like Tech Toys in 2022. Write a memo to Jerry Wang discussing the issues he is concerned and would like to know, together with your recommendations and suggested actions to the top management (in bullet points or numbered lists). You are encouraged to provide real-life business examples anywhere appropriate in the memo. (10%)

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這一題的完整詳解

一、核心觀念

  1. 製程成本法（Process Costing）：適用於大量同質產品的連續製造流程。每個部門的成本以「等效單位」(equivalent units) 分攤。
  2. 等效單位：將未完成商品的部分完成度（%）化為完整單位，以便與完整商品同等計算成本。
  3. 正常損耗 vs. 異常損耗
    • 正常損耗：視同已完成的單位，計入每單位成本。
    • 異常損耗：以實際發生成本列為損失，不列入單位成本。
  4. 加權平均法（Weighted‑Average） vs FIFO 法
    • 加權平均法把期初在製與本期成本合併計算，計算簡單，適合期初在製成本佔比不大或決策者較關心本期平均成本。
    • FIFO 法分別列示期初在製成本與本期新發生成本，能較真實反映本期生產效率，但計算較繁瑣。

二、解題方法
本題要求先選擇一種製程成本法，再列示 2022 年 1 月的會計分錄。因為題目未特別要求顯示期初成本的分別，且涉及正常與異常損耗，採用 加權平均法 為較佳選擇，理由如下：

方法優點缺點
加權平均法1. 計算步驟少；<br>2. 期初在製成本與本期成本合併，簡化等效單位與成本/單位的計算；<br>3. 方便快速報表製作。1. 無法分辨期初在製成本與本期成本的差異，若期初在製成本佔比較大，會掩蓋本期效率變化。
FIFO 法1. 期初在製成本保留原始金額，能觀察本期成本變動；<br>2. 更符合成本控制需求。1. 計算較繁雜，需要分別列示期初與本期等效單位；<br>2. 若題目僅要求「說明方法」而非比較期初成本變化，使用上較不必要。

因此本解答 採用加權平均法，並依下列步驟計算：

  1. 確定實際物量

    • 期初在製：2,000 單位 (80% 完成)
    • 本期投入：18,000 單位
    • 完工轉出：14,800 單位
    • 正常損耗：1,000 單位 (100% 完成)
    • 異常損耗：1,000 單位 (100% 完成)
    • 期末在製 = 20,000 – (14,800+1,000+1,000) = 3,200 單位，完成度 25%

  2. 等效單位（加權平均）

    • 轉入成本 (Transfer‑in) ：全部 20,000 單位均已全額計入 → 20,000 EU
    • 直接材料：材料於加工 75% 時才加入，故未完成的期末在製尚未收到材料 →
      EUDM=14,800+1,000+1,000=16,800EU_{DM}=14,800+1,000+1,000=16,800
    • 轉換成本 (Conversion)：依實際完成度計算 →
      EUCC=14,800+1,000+1,000+3,200×0.25=17,600EU_{CC}=14,800+1,000+1,000+3,200\times0.25=17,600

  3. 每等效單位成本

Transfer‑in  cost/unit=40,00020,000=2.00  (千)Direct  materials  cost/unit=20,00016,800=1.190476  (千)Conversion  cost/unit=17,60017,600=1.00  (千)\begin{aligned} \text{Transfer‑in\;cost/unit}&=\frac{40,000}{20,000}=2.00\;(千)\\[2mm] \text{Direct\;materials\;cost/unit}&=\frac{20,000}{16,800}=1.190476\;(千)\\[2mm] \text{Conversion\;cost/unit}&=\frac{17,600}{17,600}=1.00\;(千) \end{aligned}
  1. 成本分配
分配對象單位數轉入成本直接材料轉換成本合計成本 (千)
完工並轉出 (含正常損耗)15,800 (14,800 完工 + 1,000 正常損耗)$31,600$18,809.5$15,800$66,209.5
期末在製3,200$6,400$0$800$7,200
異常損耗1,000$2,000$1,190.5$1,000$4,190.5

※ 以上成本之和 = 66,209.5+66,209.5 + 7,200 + 4,190.5=4,190.5 = 77,600，與本期總成本相符。

  1. 會計分錄（金額均以千元計）
日期/說明借方貸方
1. 本期發生成本Work‑in‑Process – Assembly　$70,000Materials‑Inventory　18,000<br>∗∗Conversion‑Costs∗∗　18,000<br>**Conversion‑Costs**　16,000<br>Transfer‑in (from Plastics)　$36,000
2. 完工與正常損耗轉出Finished‑Goods (或下一部門 WIP)　$66,209.5Work‑in‑Process – Assembly　$66,209.5
3. 記錄異常損耗Abnormal‑Spoilage Expense　$4,190.5Work‑in‑Process – Assembly　$4,190.5
4. 期末在製餘額 (留在資產帳)Work‑in‑Process – Assembly
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