109 年 國立臺灣大學會計學系碩士班《成本與管理會計》

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第 1 題

Problem 1 [20%]

Renato Cosmetics purchases direct materials and processes them into perfume. From a certain mix of direct materials, a joint production process generates Luxury, a high-grade perfume, and Mystery, a medium-grade perfume.

In October, 480,000ofdirectmaterialswereprocessedatacostof480,000 of direct materials were processed at a cost of 720,000, resulting in 16,000 ounces of Luxury and 4,000 ounces of Mystery. Luxury sells for 35perounceandMysterysellsfor35 per ounce and Mystery sells for 60 per ounce. Management generally processes each of these perfumes further in separable processes to manufacture more refined products. Luxury is processed separately at a cost of 18perounce,withtheresultingproduct,LuxuryX.Mysteryisprocessedseparatelyatacostof18 per ounce, with the resulting product, LuxuryX. Mystery is processed separately at a cost of 24 per ounce, with the resulting product, MysteryX.

If both Luxury and Mystery are processed into refined products, the sales value of two final products totals 2,688,000.IfRenatousesthenet−realizable−valuemethodtoallocatejointproductioncosts,thejointproductioncostallocatedtoLuxuryis2,688,000. If Renato uses the net-realizable-value method to allocate joint production costs, the joint production cost allocated to Luxury is 750,000.

Required:

  1. If Renato uses the relative-sales-value method to allocate joint production costs, compute the costs allocated to Luxury and Mystery. (10%)
  2. If Renato uses the physical-units method to allocate joint production costs, from a profitability perspective, should Mystery be processed into MysteryX? Show your calculations. (10%)

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這一題的完整詳解

核心觀念

  1. 聯合成本分攤方法（Joint Cost Allocation Methods）：

    • 總聯合成本（Total Joint Costs）：包含分離點前發生的所有直接材料與聯合加工成本（轉化成本）。
    • 分離點相對售價法（Relative-Sales-Value Method / Sales Value at Splitoff Method）：以各聯產品在「分離點（Splitoff Point）」的總銷貨價值為權數，分攤總聯合成本。
    • 淨變現價值法（Net-Realizable-Value Method, NRV Method）：當產品在分離點後仍需加工時，以各產品之「最終預期銷貨價值」減去「分離後可分加工成本（Separable Costs）」計算出淨變現價值（NRV），並依 NRV 比例分攤聯合成本。

  2. 出售或進一步加工決策（Sell or Process Further Decision）與無關成本：

    • 決策原則：比較進一步加工所產生的「增額收入（Incremental Revenue）」與「增額可分成本（Incremental Separable Cost）」。若增額收入大於增額成本（即增額營業利益為正），則應進一步加工。
    • 無關成本觀念：聯合成本為分離點前已發生的沉沒成本（Sunk Cost），且無論採用何種分攤方法（實體數量法、售價法或 NRV 法），分攤金額皆屬於無關成本（Irrelevant Cost），絕不影響進一步加工之決策。

解題方法

步驟一：彙整基本資料與反推隱含數據

  1. 計算總聯合成本（Total Joint Cost）：
總聯合成本=直接材料+加工成本=480,000+720,000=1,200,000 元 \text{總聯合成本} = \text{直接材料} + \text{加工成本} = 480,000 + 720,000 = 1,200,000 \text{ 元}

  1. 計算各產品於分離點之銷貨價值：

    • Luxury：16,000×35=16,000 \times 35 = $560,000
    • Mystery：4,000×60=4,000 \times 60 = $240,000
    • 分離點總銷貨價值：$560,000+560,000 + $240,000=240,000 = $800,000

  2. 計算分離後可分加工成本（Separable Costs）：

    • LuxuryX：16,000×18=16,000 \times 18 = $288,000
    • MysteryX：4,000×24=4,000 \times 24 = $96,000
    • 總可分成本：$288,000+288,000 + $96,000=96,000 = $384,000

  3. 透過 NRV 法已知條件，反推 MysteryX 之最終售價：

    • 最終產品總銷貨價值（Total Final Sales Value）為 $2,688,000。
    • 兩項產品合計之總淨變現價值（Total NRV）：
Total NRV=2,688,000−384,000=2,304,000 元 \text{Total NRV} = 2,688,000 - 384,000 = 2,304,000 \text{ 元}
  • 已知採 NRV 法時，Luxury 分攤之聯合成本為 $750,000：
NRVLuxuryTotal NRV=750,0001,200,000=0.625 (62.5%) \frac{\text{NRV}_{\text{Luxury}}}{\text{Total NRV}} = \frac{750,000}{1,200,000} = 0.625 \ (62.5\%) NRVLuxury=2,304,000×62.5%=1,440,000 元 \text{NRV}_{\text{Luxury}} = 2,304,000 \times 62.5\% = 1,440,000 \text{ 元}
  • 故 MysteryX 之淨變現價值（NRVMystery\text{NRV}_{\text{Mystery}}）：
NRVMystery=2,304,000−1,440,000=864,000 元 \text{NRV}_{\text{Mystery}} = 2,304,000 - 1,440,000 = 864,000 \text{ 元}
  • 由此可得 MysteryX 之最終總銷貨價值（SMS_M）：
SM=NRVMystery+Mystery 可分成本=864,000+96,000=960,000 元 S_M = \text{NRV}_{\text{Mystery}} + \text{Mystery 可分成本} = 864,000 + 96,000 = 960,000 \text{ 元} 
 （即 MysteryX 單位售價為 \
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第 2 題

Problem 2 [20%]

Svenson Corporation manufactures two types of fishing rods, Basic and Deluxe. The Basic type requires 60 hours of labor and 24 machine-hours per unit. Deluxe type requires 102 labor-hours and 60 machine-hours per unit. Basic type has a unit contribution margin of 384,andDeluxetypehasaunitcontributionmarginof384, and Deluxe type has a unit contribution margin of 2,160.

The demand for Basic type exceeds Svenson's production capacity, which is limited by available machine-hours and direct manufacturing labor-hours. The maximum demand for Deluxe type is 240 per month. Direct manufacturing labor is limited to 4,800 hours per week and machine-hours are limited to 3,600 per week.

Management desires a product mix that will maximize the weekly contribution toward fixed costs and profits. The management uses a linear programming approach, where B represents Basic type and D represents Deluxe type.

Required:
Formulate the objective function (5%) and constraints (15%) necessary to determine the optimal product mix.

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這一題的完整詳解

本題考驗線性規劃在產銷組合決策的應用，重點在於建立正確的目標函數與限制式。

核心觀念：

  1. 線性規劃： 針對資源有限情況下，最大化（或最小化）某目標函數。
  2. 目標函數 (Objective Function)： 欲最大化或最小化的目標，在此為最大化總貢獻毛益。
  3. 限制式 (Constraints)： 資源的限制，在此為勞動工時、機器工時與市場需求。
  4. 貢獻毛益 (Contribution Margin)： 銷售收入減去變動成本。

題目分析：

  • 決策變數：

    • BB：Basic 型釣竿的生產數量（單位：支/週）
    • DD：Deluxe 型釣竿的生產數量（單位：支/週）

  • 資源限制：

    • 總勞動工時：每週 4,800 小時
    • 總機器工時：每週 3,600 小時

  • 產品資源需求：

    產品單位貢獻毛益勞動工時/單位機器工時/單位
    Basic (B)$3846024
    Deluxe (D)$2,16010260

  • 市場需求限制：

    • Deluxe 型最大需求：240 支/月。由於題目給的資源是每週限制，我們需要將月需求轉換為週需求。假設每月有 4 週，則 Deluxe 型每週最大需求為 240 / 4 = 60 支。
    • Basic 型需求：題目說明 Basic 型的需求超過生產能力，因此 Basic 型本身不受最大需求限制，僅受資源限制。

目標函數 (Objective Function)：

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第 3 題

Problem 3 [20%]

In 2019, Clark Corporation starts its operation and prepares the accounting information as follows:

Direct materials used $ 360,000
Direct labor 192,000
Variable manufacturing overhead 72,000
Fixed manufacturing overhead 240,000
Variable selling and administrative costs 122,400
Fixed selling and administrative costs 144,000
Sales revenues 1,500,000

In 2019, the gross profit ratio derived from 2019 throughput costing income statement is 85%.

Required:

  1. Compute the net income that would be reported on a variable-costing income statement. (10%)
  2. Compute the cost of the company's year-end inventory if Clark adopts an absorption costing. (10%)

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這一題的完整詳解

核心觀念

  1. 變動成本法 (Variable‑Costing)：製造成本僅計入變動製造費用（直接材料、直接人工、變動製造間接費），所有固定製造間接費列為期間費用。變動銷管費亦列為期間費用。
  2. 完全吸收成本法 (Absorption‑Costing)：製造成本包括全部製造費用（變動＋固定），期末存貨會含有固定製造間接費的分攤。
  3. 毛利率 (Gross‑Profit Ratio)：毛利率 = 毛利 ÷ 銷售收入 = (Sales – Cost‑of‑Goods‑Sold) / Sales。題目給予的 85% 為吸收成本下的毛利率，可用來推算本期已銷貨的成本，進而求得期末存貨成本。

解題方法與計算步驟

1. 變動成本法之淨利

項目金額 (USD)
銷貨收入 (Sales)1,500,000
直接材料 (DM)360,000
直接人工 (DL)192,000
變動製造間接費 (Variable MOH)72,000
變動銷管費 (Variable S&A)122,400
  1. 變動製造成本

Variable Manufacturing Cost=DM+DL+Variable  MOH=360,000+192,000+72,000=624,000\text{Variable Manufacturing Cost}=DM+DL+Variable\;MOH = 360,000+192,000+72,000 = 624,000

  1. 變動營業貢獻

Contribution Margin=Sales−Variable Manufacturing Cost−Variable S&A=1,500,000−624,000−122,400=753,600\text{Contribution Margin}=Sales-\text{Variable Manufacturing Cost}-\text{Variable S\&A}=1,500,000-624,000-122,400 = 753,600

  1. 扣除固定期間費用
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第 4 題

Problem 4 [20%]

FootLove Corporation manufactures quality walking shoes and uses a weighted average process costing system. All direct materials are introduced at the start of the process, and conversion cost is incurred evenly throughout manufacturing.

An examination of the company's Work-in-Process account for September revealed the following selected information:

Debit side—
September 1 balance: 2,100 units, 40% complete. Direct material cost of 105,000anddirectmanufacturinglaborcostof105,000 and direct manufacturing labor cost of 20,440.
Production started: 6,300 units
Direct materials used during August: $315,000

Credit side—
Production completed: 4,900 units
Costs of transferred-out unit: $392,000

Conversations with manufacturing personnel revealed that the ending work in process was 80% complete. Accounting personnel cannot disclose the information of conversion costs added in September, but manufacturing overhead is applied by 150% of direct manufacturing labor costs.

Required: (Round cost per equivalent unit to the nearest hundredth)

  1. If FootLove uses a FIFO process costing system, calculate the cost of goods completed during September. (10%)
  2. If FootLove uses a FIFO process costing system, determine the cost of the September 30 work-in-process inventory. (10%)

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這一題的完整詳解

核心觀念

本題的核心考點在於**分步成本制（Process Costing）下加權平均法（Weighted-Average Method）與先進先出法（FIFO Method）**的雙軌整合應用與逆向推導：

  1. 客觀投入成本的不變性：無論企業採用加權平均法或先進先出法，本期實際發生的直接材料與加工成本總額均為客觀事實。本題給定加權平均法下的轉出成本，需藉此「逆向推導（Back-calculate）」出本期投入的加工成本總額。
  2. 加工成本之組成：加工成本（Conversion Costs, CC）包含直接人工（Direct Labor, DL）與製造費用（Manufacturing Overhead, MOH）。題目明確指出製造費用按直接人工成本的 150% 分攤，故加工成本總額為直接人工的 2.5 倍：
    CC=DL+MOH=DL+1.5×DL=2.5×DLCC = DL + MOH = DL + 1.5 \times DL = 2.5 \times DL
  3. 約當產量（Equivalent Units of Production, EUP）：
    • 加權平均法：混合期初與本期產出，不區分完工程度之來源。
    • 先進先出法（FIFO）：嚴格區分「期初在製品本期完工」、「本期投產並完工（Started & Completed）」及「期末在製品」之本期投入約當產量。

解題方法

第一階段：實體數量流程與期初成本整理

  1. 實體數量平衡分析：
    期初在製品數量+本期投入數量=完工轉出數量+期末在製品數量\text{期初在製品數量} + \text{本期投入數量} = \text{完工轉出數量} + \text{期末在製品數量}
    2,100+6,300=4,900+期末在製品數量2,100 + 6,300 = 4,900 + \text{期末在製品數量}
    期末在製品數量=8,400−4,900=3,500 單位（完工程度 80%）\text{期末在製品數量} = 8,400 - 4,900 = 3,500\text{ 單位（完工程度 } 80\% \text{）}

  2. 期初在製品（9 月 1 日）成本還原：

    • 直接材料（DM）：$105,000
    • 直接人工（DL）：$20,440
    • 製造費用（MOH）：$20,440×150%=20,440 \times 150\% = $30,660
    • 期初加工成本（CC）：$20,440+20,440 + $30,660=30,660 = $51,100
    • 期初在製品總成本：$105,000+105,000 + $51,100=51,100 = $156,100

第二階段：利用加權平均法逆向推導「本期投入加工成本」

  1. 加權平均法約當產量（EUPWAEUP_{\text{WA}}）：

    • 直接材料（製程開始投入）：
      EUPDM, WA=4,900+(3,500×100%)=8,400 單位EUP_{\text{DM, WA}} = 4,900 + (3,500 \times 100\%) = 8,400\text{ 單位}
    • 加工成本（製程均勻發生）：
      EUPCC, WA=4,900+(3,500×80%)=4,900+2,800=7,700 單位EUP_{\text{CC, WA}} = 4,900 + (3,500 \times 80\%) = 4,900 + 2,800 = 7,700\text{ 單位}

  2. 加權平均法單位約當成本：

    • 直接材料單位成本：
      材料加權單位成本=期初材料+本期投入材料EUPDM, WA=$105,000+$315,0008,400=$420,0008,400=$50.00\text{材料加權單位成本} = \frac{\text{期初材料} + \text{本期投入材料}}{EUP_{\text{DM, WA}}} = \frac{\$105,000 + \$315,000}{8,400} = \frac{\$420,000}{8,400} = \$50.00
    • 完工轉出產品每單位成本（題目給定總轉出成本為 $392,000）：
      每單位總成本=$392,0004,900=$80.00\text{每單位總成本} = \frac{\$392,000}{4,900} = \$80.00
    • 加工成本單位成本：
      加工加權單位成本=每單位總成本−材料加權單位成本=$80.00−$50.00=$30.00\text{加工加權單位成本} = \text{每單位總成本} - \text{材料加權單位成本} = \$80.00 - \$50.00 = \$30.00

  3. **推算本期投入之加工成本（$\text{CC}_{\text{current}}

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第 5 題

Problem 5 [20%]

Sanchez Corporation is a manufacturing company that processes direct materials A and B into two products: X and Y. Although the X and Y are a matching set, they are sold individually and so the sales mix is not 1:1. Sanchez is planning annual budget for fiscal year 2020. Here is information for 2020:

Input Prices
Direct materials
A 1.8perpoundB1.8 per pound B 0.72 per pound
Direct manufacturing labor $ 54 per direct manufacturing labor-hour

Input Quantities per Unit of Output
X Y
Direct materials
A 16 pounds 8 pounds
B 5 pounds 8 pounds
Direct manufacturing labor 0.04 hours 0.16 hours
Machine-hours (MH) 0.06 ΜΗ 0.24 ΜΗ

Direct Materials Inventory Information
A B
Beginning inventory 1,820 pounds 1,600 pounds
Target ending inventory 2,272 pounds 1,766 pounds
Cost of beginning inventory 3,4063,406 1,095

Sanchez accounts for direct materials using a FIFO cost flow.
Sales and Inventory Information, Finished Goods
X Y
Expected sales in units 12,000 14,000
Selling price 21.621.6 72
Target ending inventory in units 1,200 1,400
Beginning inventory in units 600 1,200
Beginning inventory in dollars 6,4806,48065,232

Sanchez uses a FIFO cost flow assumption for finished goods inventory. X is manufactured in batches of 200, and Y is manufactured in batches of 100. It takes 20 minutes to set up for a batch of X and 1 hour to set up for a batch of Y. Sanchez uses activity-based costing and has classified all overhead costs into activity cost pools as shown in the following table.
Activity Type Overhead Costs Cost Driver/Allocation Base
Manufacturing
Materials handling 95,364NumberofouncesofBusedSetup64,548Setup−hoursProcessing99,936Machine−hoursInspection28,944NumberofunitsproducedNonmanufacturingMarketing95,364 Number of ounces of B used Setup 64,548 Setup-hours Processing 99,936 Machine-hours Inspection 28,944 Number of units produced Nonmanufacturing Marketing266,760 Sales revenue
Distribution 2,808 Number of deliveries*
*Delivery trucks transport units sold in delivery sizes of 1,000 Xs or 1,000 Ys.

Required:

  1. Compute the budgeted purchasing costs of direct material A (5%) and B (5%) on the direct material purchases budget for the year 2020.
  2. Determine the budgeted net income (ignore income taxes) for the year 2020. (10%)

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這一題的完整詳解

核心觀念

  • 直接材料購買預算：依需求量＋期初庫存－期末庫存＝本期購買量，然後乘以單價與（5%）的附加費用。
  • FIFO 成本流：期初存貨先銷售，其成本以期初單位成本計算，餘下之需求以本期製造成本計算。
  • ABC 法分配製造與非製造間接費：先求各活動之費率（總成本 ÷ 總驅動基礎），再依單位使用量分配至產品。
  • 製造批次與設定時間：批次大小決定每批設定成本，必須先算批次數再分配至單位。
  • 營業淨利：

淨利=營業收入−銷貨成本\text{淨利}= \text{營業收入} - \text{銷貨成本}

（不考慮所得稅，營業成本已含製造與行銷、配送間接費）。

1️⃣ 直接材料購買成本（含 5% 附加費）

需求量計算

X 單位需求:12,000+1,200−600=12,600Y 單位需求:14,000+1,400−1,200=14,200\begin{aligned} \text{X 單位需求} &: 12{,}000+1{,}200-600 = 12{,}600 \\ \text{Y 單位需求} &: 14{,}000+1{,}400-1{,}200 = 14{,}200 \end{aligned} A 總需求 (磅)=16(12,600)+8(14,200)=315,200B 總需求 (磅)=5(12,600)+8(14,200)=176,600\begin{aligned} \text{A 總需求 (磅)} &= 16(12{,}600)+8(14{,}200)=315{,}200\\ \text{B 總需求 (磅)} &= 5(12{,}600)+8(14{,}200)=176{,}600 \end{aligned}

計算購買量

A 購買量=315,200+2,272−1,820=315,652 磅B 購買量=176,600+1,766−1,600=176,766 磅\begin{aligned} \text{A 購買量} &= 315{,}200 + 2{,}272 - 1{,}820 = 315{,}652\ \text{磅}\\ \text{B 購買量} &= 176{,}600 + 1{,}766 - 1{,}600 = 176{,}766\ \text{磅} \end{aligned}

成本 (含 5% 追加)

A 成本=315,652×1.80×1.05=596,582.28B 成本=176,766×0.72×1.05=133,632.00\begin{aligned} \text{A 成本} &= 315{,}652 \times 1.80 \times 1.05 = \boxed{596{,}582.28}\\[4pt] \text{B 成本} &= 176{,}766 \times 0.72 \times 1.05 = \boxed{133{,}632.00} \end{aligned}

答案：直接材料 A 購買成本 596,582.28，直接材料B購買成本596,582.28，直接材料 B 購買成本 133,632.00（均已含 5% 附加費）。

2️⃣ 預算淨利（不計所得稅）

(1) 銷售收入

RX=12,000×21.6=259,200RY=14,000×72=1,008,000總收入=1,267,200\begin{aligned} R_X &= 12{,}000 \times 21.6 = 259{,}200\\ R_Y &= 14{,}000 \times 72 = 1{,}008{,}000\\ \text{總收入} &= \boxed{1{,}267{,}200} \end{aligned}

(2) 生產量與批次

X 批次=12,600200=63Y 批次=14,200100=142\begin{aligned} \text{X 批次} &= \frac{12{,}600}{200}=63\\ \text{Y 批次} &= \frac{14{,}200}{100}=142 \end{aligned}

(3) 直接成本（每單位）

成本項目XY
材料 A16×1.80=28.8016 \times 1.80=28.808×1.80=14.408 \times 1.80=14.40
材料 B5×0.72=3.605 \times 0.72=3.608×0.72=5.768 \times 0.72=5.76
直接人工0.04×54=2.160.04 \times 54=2.160.16×54=8.640.16 \times 54=8.64
直接成本合計$34.56$28.80

(4) ABC 製造間接費率

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第 Problem 2 題

Problem 2 [20%]

Svenson Corporation manufactures two types of fishing rods, Basic and Deluxe. The Basic type requires 60 hours of labor and 24 machine-hours per unit. Deluxe type requires 102 labor-hours and 60 machine-hours per unit. Basic type has a unit contribution margin of 384,andDeluxetypehasaunitcontributionmarginof384, and Deluxe type has a unit contribution margin of 2,160.

The demand for Basic type exceeds Svenson's production capacity, which is limited by available machine-hours and direct manufacturing labor-hours. The maximum demand for Deluxe type is 240 per month. Direct manufacturing labor is limited to 4,800 hours per week and machine-hours are limited to 3,600 per week.

Management desires a product mix that will maximize the weekly contribution toward fixed costs and profits. The management uses a linear programming approach, where B represents Basic type and D represents Deluxe type.

Required:
Formulate the objective function (5%) and constraints (15%) necessary to determine the optimal product mix.

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這一題的完整詳解

本題考驗線性規劃在產銷組合決策的應用，重點在於建立正確的目標函數與限制式。

核心觀念：

  1. 線性規劃： 針對資源有限情況下，最大化（或最小化）某目標函數。
  2. 目標函數 (Objective Function)： 欲最大化或最小化的目標，在此為最大化總貢獻毛益。
  3. 限制式 (Constraints)： 資源的限制，在此為勞動工時、機器工時與市場需求。
  4. 貢獻毛益 (Contribution Margin)： 銷售收入減去變動成本。

題目分析：

  • 決策變數：

    • BB：Basic 型釣竿的生產數量（單位：支/週）
    • DD：Deluxe 型釣竿的生產數量（單位：支/週）

  • 資源限制：

    • 總勞動工時：每週 4,800 小時
    • 總機器工時：每週 3,600 小時

  • 產品資源需求：

    產品單位貢獻毛益勞動工時/單位機器工時/單位
    Basic (B)$3846024
    Deluxe (D)$2,16010260

  • 市場需求限制：

    • Deluxe 型最大需求：240 支/月。由於題目給的資源是每週限制，我們需要將月需求轉換為週需求。假設每月有 4 週，則 Deluxe 型每週最大需求為 240 / 4 = 60 支。
    • Basic 型需求：題目說明 Basic 型的需求超過生產能力，因此 Basic 型本身不受最大需求限制，僅受資源限制。

目標函數 (Objective Function)：

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第 Problem 3 題

Problem 3 [20%]

In 2019, Clark Corporation starts its operation and prepares the accounting information as follows:

Direct materials used $ 360,000
Direct labor 192,000
Variable manufacturing overhead 72,000
Fixed manufacturing overhead 240,000
Variable selling and administrative costs 122,400
Fixed selling and administrative costs 144,000
Sales revenues 1,500,000

In 2019, the gross profit ratio derived from 2019 throughput costing income statement is 85%.

Required:

  1. Compute the net income that would be reported on a variable-costing income statement. (10%)
  2. Compute the cost of the company's year-end inventory if Clark adopts an absorption costing. (10%)

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這一題的完整詳解

核心觀念

  1. 變動成本法 (Variable‑Costing)：製造成本僅計入變動製造費用（直接材料、直接人工、變動製造間接費），所有固定製造間接費列為期間費用。變動銷管費亦列為期間費用。
  2. 完全吸收成本法 (Absorption‑Costing)：製造成本包括全部製造費用（變動＋固定），期末存貨會含有固定製造間接費的分攤。
  3. 毛利率 (Gross‑Profit Ratio)：毛利率 = 毛利 ÷ 銷售收入 = (Sales – Cost‑of‑Goods‑Sold) / Sales。題目給予的 85% 為吸收成本下的毛利率，可用來推算本期已銷貨的成本，進而求得期末存貨成本。

解題方法與計算步驟

1. 變動成本法之淨利

項目金額 (USD)
銷貨收入 (Sales)1,500,000
直接材料 (DM)360,000
直接人工 (DL)192,000
變動製造間接費 (Variable MOH)72,000
變動銷管費 (Variable S&A)122,400
  1. 變動製造成本

Variable Manufacturing Cost=DM+DL+Variable  MOH=360,000+192,000+72,000=624,000\text{Variable Manufacturing Cost}=DM+DL+Variable\;MOH = 360,000+192,000+72,000 = 624,000

  1. 變動營業貢獻

Contribution Margin=Sales−Variable Manufacturing Cost−Variable S&A=1,500,000−624,000−122,400=753,600\text{Contribution Margin}=Sales-\text{Variable Manufacturing Cost}-\text{Variable S\&A}=1,500,000-624,000-122,400 = 753,600

  1. 扣除固定期間費用
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第 4 題

Problem 4 [20%]

FootLove Corporation manufactures quality walking shoes and uses a weighted average process costing system. All direct materials are introduced at the start of the process, and conversion cost is incurred evenly throughout manufacturing.

An examination of the company's Work-in-Process account for September revealed the following selected information:

Debit side—
September 1 balance: 2,100 units, 40% complete. Direct material cost of 105,000anddirectmanufacturinglaborcostof105,000 and direct manufacturing labor cost of 20,440.
Production started: 6,300 units
Direct materials used during August: $315,000

Credit side—
Production completed: 4,900 units
Costs of transferred-out unit: $392,000

Conversations with manufacturing personnel revealed that the ending work in process was 80% complete. Accounting personnel cannot disclose the information of conversion costs added in September, but manufacturing overhead is applied by 150% of direct manufacturing labor costs.

Required: (Round cost per equivalent unit to the nearest hundredth)

  1. If FootLove uses a FIFO process costing system, calculate the cost of goods completed during September. (10%)
  2. If FootLove uses a FIFO process costing system, determine the cost of the September 30 work-in-process inventory. (10%)

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這一題的完整詳解

核心觀念

本題的核心考點在於**分步成本制（Process Costing）下加權平均法（Weighted-Average Method）與先進先出法（FIFO Method）**的雙軌整合應用與逆向推導：

  1. 客觀投入成本的不變性：無論企業採用加權平均法或先進先出法，本期實際發生的直接材料與加工成本總額均為客觀事實。本題給定加權平均法下的轉出成本，需藉此「逆向推導（Back-calculate）」出本期投入的加工成本總額。
  2. 加工成本之組成：加工成本（Conversion Costs, CC）包含直接人工（Direct Labor, DL）與製造費用（Manufacturing Overhead, MOH）。題目明確指出製造費用按直接人工成本的 150% 分攤，故加工成本總額為直接人工的 2.5 倍：
    CC=DL+MOH=DL+1.5×DL=2.5×DLCC = DL + MOH = DL + 1.5 \times DL = 2.5 \times DL
  3. 約當產量（Equivalent Units of Production, EUP）：
    • 加權平均法：混合期初與本期產出，不區分完工程度之來源。
    • 先進先出法（FIFO）：嚴格區分「期初在製品本期完工」、「本期投產並完工（Started & Completed）」及「期末在製品」之本期投入約當產量。

解題方法

第一階段：實體數量流程與期初成本整理

  1. 實體數量平衡分析：
    期初在製品數量+本期投入數量=完工轉出數量+期末在製品數量\text{期初在製品數量} + \text{本期投入數量} = \text{完工轉出數量} + \text{期末在製品數量}
    2,100+6,300=4,900+期末在製品數量2,100 + 6,300 = 4,900 + \text{期末在製品數量}
    期末在製品數量=8,400−4,900=3,500 單位（完工程度 80%）\text{期末在製品數量} = 8,400 - 4,900 = 3,500\text{ 單位（完工程度 } 80\% \text{）}

  2. 期初在製品（9 月 1 日）成本還原：

    • 直接材料（DM）：$105,000
    • 直接人工（DL）：$20,440
    • 製造費用（MOH）：$20,440×150%=20,440 \times 150\% = $30,660
    • 期初加工成本（CC）：$20,440+20,440 + $30,660=30,660 = $51,100
    • 期初在製品總成本：$105,000+105,000 + $51,100=51,100 = $156,100

第二階段：利用加權平均法逆向推導「本期投入加工成本」

  1. 加權平均法約當產量（EUPWAEUP_{\text{WA}}）：

    • 直接材料（製程開始投入）：
      EUPDM, WA=4,900+(3,500×100%)=8,400 單位EUP_{\text{DM, WA}} = 4,900 + (3,500 \times 100\%) = 8,400\text{ 單位}
    • 加工成本（製程均勻發生）：
      EUPCC, WA=4,900+(3,500×80%)=4,900+2,800=7,700 單位EUP_{\text{CC, WA}} = 4,900 + (3,500 \times 80\%) = 4,900 + 2,800 = 7,700\text{ 單位}

  2. 加權平均法單位約當成本：

    • 直接材料單位成本：
      材料加權單位成本=期初材料+本期投入材料EUPDM, WA=$105,000+$315,0008,400=$420,0008,400=$50.00\text{材料加權單位成本} = \frac{\text{期初材料} + \text{本期投入材料}}{EUP_{\text{DM, WA}}} = \frac{\$105,000 + \$315,000}{8,400} = \frac{\$420,000}{8,400} = \$50.00
    • 完工轉出產品每單位成本（題目給定總轉出成本為 $392,000）：
      每單位總成本=$392,0004,900=$80.00\text{每單位總成本} = \frac{\$392,000}{4,900} = \$80.00
    • 加工成本單位成本：
      加工加權單位成本=每單位總成本−材料加權單位成本=$80.00−$50.00=$30.00\text{加工加權單位成本} = \text{每單位總成本} - \text{材料加權單位成本} = \$80.00 - \$50.00 = \$30.00

  3. **推算本期投入之加工成本（$\text{CC}_{\text{current}}

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第 5 題

Problem 5 [20%]

Sanchez Corporation is a manufacturing company that processes direct materials A and B into two products: X and Y. Although the X and Y are a matching set, they are sold individually and so the sales mix is not 1:1. Sanchez is planning annual budget for fiscal year 2020. Here is information for 2020:

Input Prices
Direct materials
A 1.8perpoundB1.8 per pound B 0.72 per pound
Direct manufacturing labor $ 54 per direct manufacturing labor-hour

Input Quantities per Unit of Output
X Y
Direct materials
A 16 pounds 8 pounds
B 5 pounds 8 pounds
Direct manufacturing labor 0.04 hours 0.16 hours
Machine-hours (MH) 0.06 ΜΗ 0.24 ΜΗ

Direct Materials Inventory Information
A B
Beginning inventory 1,820 pounds 1,600 pounds
Target ending inventory 2,272 pounds 1,766 pounds
Cost of beginning inventory 3,4063,406 1,095

Sanchez accounts for direct materials using a FIFO cost flow.
Sales and Inventory Information, Finished Goods
X Y
Expected sales in units 12,000 14,000
Selling price 21.621.6 72
Target ending inventory in units 1,200 1,400
Beginning inventory in units 600 1,200
Beginning inventory in dollars 6,4806,48065,232

Sanchez uses a FIFO cost flow assumption for finished goods inventory. X is manufactured in batches of 200, and Y is manufactured in batches of 100. It takes 20 minutes to set up for a batch of X and 1 hour to set up for a batch of Y. Sanchez uses activity-based costing and has classified all overhead costs into activity cost pools as shown in the following table.
Activity Type Overhead Costs Cost Driver/Allocation Base
Manufacturing
Materials handling 95,364NumberofouncesofBusedSetup64,548Setup−hoursProcessing99,936Machine−hoursInspection28,944NumberofunitsproducedNonmanufacturingMarketing95,364 Number of ounces of B used Setup 64,548 Setup-hours Processing 99,936 Machine-hours Inspection 28,944 Number of units produced Nonmanufacturing Marketing266,760 Sales revenue
Distribution 2,808 Number of deliveries*
*Delivery trucks transport units sold in delivery sizes of 1,000 Xs or 1,000 Ys.

Required:

  1. Compute the budgeted purchasing costs of direct material A (5%) and B (5%) on the direct material purchases budget for the year 2020.
  2. Determine the budgeted net income (ignore income taxes) for the year 2020. (10%)

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這一題的完整詳解

核心觀念

  • 直接材料購買預算：依需求量＋期初庫存－期末庫存＝本期購買量，然後乘以單價與（5%）的附加費用。
  • FIFO 成本流：期初存貨先銷售，其成本以期初單位成本計算，餘下之需求以本期製造成本計算。
  • ABC 法分配製造與非製造間接費：先求各活動之費率（總成本 ÷ 總驅動基礎），再依單位使用量分配至產品。
  • 製造批次與設定時間：批次大小決定每批設定成本，必須先算批次數再分配至單位。
  • 營業淨利：

淨利=營業收入−銷貨成本\text{淨利}= \text{營業收入} - \text{銷貨成本}

（不考慮所得稅，營業成本已含製造與行銷、配送間接費）。

1️⃣ 直接材料購買成本（含 5% 附加費）

需求量計算

X 單位需求:12,000+1,200−600=12,600Y 單位需求:14,000+1,400−1,200=14,200\begin{aligned} \text{X 單位需求} &: 12{,}000+1{,}200-600 = 12{,}600 \\ \text{Y 單位需求} &: 14{,}000+1{,}400-1{,}200 = 14{,}200 \end{aligned} A 總需求 (磅)=16(12,600)+8(14,200)=315,200B 總需求 (磅)=5(12,600)+8(14,200)=176,600\begin{aligned} \text{A 總需求 (磅)} &= 16(12{,}600)+8(14{,}200)=315{,}200\\ \text{B 總需求 (磅)} &= 5(12{,}600)+8(14{,}200)=176{,}600 \end{aligned}

計算購買量

A 購買量=315,200+2,272−1,820=315,652 磅B 購買量=176,600+1,766−1,600=176,766 磅\begin{aligned} \text{A 購買量} &= 315{,}200 + 2{,}272 - 1{,}820 = 315{,}652\ \text{磅}\\ \text{B 購買量} &= 176{,}600 + 1{,}766 - 1{,}600 = 176{,}766\ \text{磅} \end{aligned}

成本 (含 5% 追加)

A 成本=315,652×1.80×1.05=596,582.28B 成本=176,766×0.72×1.05=133,632.00\begin{aligned} \text{A 成本} &= 315{,}652 \times 1.80 \times 1.05 = \boxed{596{,}582.28}\\[4pt] \text{B 成本} &= 176{,}766 \times 0.72 \times 1.05 = \boxed{133{,}632.00} \end{aligned}

答案：直接材料 A 購買成本 596,582.28，直接材料B購買成本596,582.28，直接材料 B 購買成本 133,632.00（均已含 5% 附加費）。

2️⃣ 預算淨利（不計所得稅）

(1) 銷售收入

RX=12,000×21.6=259,200RY=14,000×72=1,008,000總收入=1,267,200\begin{aligned} R_X &= 12{,}000 \times 21.6 = 259{,}200\\ R_Y &= 14{,}000 \times 72 = 1{,}008{,}000\\ \text{總收入} &= \boxed{1{,}267{,}200} \end{aligned}

(2) 生產量與批次

X 批次=12,600200=63Y 批次=14,200100=142\begin{aligned} \text{X 批次} &= \frac{12{,}600}{200}=63\\ \text{Y 批次} &= \frac{14{,}200}{100}=142 \end{aligned}

(3) 直接成本（每單位）

成本項目XY
材料 A16×1.80=28.8016 \times 1.80=28.808×1.80=14.408 \times 1.80=14.40
材料 B5×0.72=3.605 \times 0.72=3.608×0.72=5.768 \times 0.72=5.76
直接人工0.04×54=2.160.04 \times 54=2.160.16×54=8.640.16 \times 54=8.64
直接成本合計$34.56$28.80

(4) ABC 製造間接費率

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其他考古題

臺灣大學《成本與管理會計》其他年度

115 年114 年113 年112 年111 年108 年

其他學校的財金會計考古題

清華大學33成功大學62政治大學68中央大學5中正大學32中山大學8臺北大學48暨南國際大學13高雄大學6嘉義大學6臺北商業大學3