115 年 國立臺北大學會計學系碩士班《成本與管理會計》

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第 1. 題25 分

Answer each of the following independent questions and show all relevant computations on the answer sheet.

(1) A company is looking to purchase and replace a fixed asset for 2,100,000.Itwillselltheassetthatwillbereplacedfor2,100,000. It will sell the asset that will be replaced for 410,000 but will incur a 10,000gainuponthatsale.Itmustalsocommit10,000 gain upon that sale. It must also commit 300,000 of working-capital to the investment. The firm's tax rate is 20%.

Required:
What is the amount of the relevant initial investment?

(2) The NTPU Company orders most of its items in lot sizes of 10 units. Average annual demand per side of beef is 720 units per year. Ordering costs are 25perorderwithanaveragepurchasingpriceof25 per order with an average purchasing price of 100. Annual inventory carrying costs are estimated to be 40% of the unit cost.

Required:
Determine the annual cost savings if NTPU Company changes its order size from 10 units to the economic order quantity.

(3) NTPU Corporation makes miniature statues of the Empire State Building from cast iron. Sales total 50,000 units a year. The statues are finished either rough or polished, with an average demand of 60% rough and 40% polished. Iron ingots, the direct material, costs 5perpound.Processingcostsare5 per pound. Processing costs are 300 to convert 30 pounds into 60 statues. Rough statues are sold for 17each,andpolishedstatuescanbesoldfor17 each, and polished statues can be sold for 19 or engraved for an additional cost of 5.Polishedstatuescanthenbesoldfor5. Polished statues can then be sold for 40.

Required:
Determine whether NTPU Company should sell the engraved statues. Why?

(4) NTPU Corp is committed to its quality program. It works with all areas of the company to establish sound quality programs within reasonable budget guidelines. For 2026, it has budgeted 1,000,000forpreventioncostsand1,000,000 for prevention costs and 900,000 for appraisal costs. Internal failure has a budget of 100perfaileditem,whileexternalfailurehasatotalbudgetof100 per failed item, while external failure has a total budget of 600,000. Product Testing has proposed to management a change in the 2026 budget for a new method of testing products. If management decides to implement the new method, 1.5perunitofappraisalcostswillbesaved,uptoalevelof150,000tests.Noadditionalsavingsareexpectedpastthe150,000level.Thenewmethodinvolves1.5 per unit of appraisal costs will be saved, up to a level of 150,000 tests. No additional savings are expected past the 150,000 level. The new method involves 95,000 in training costs and 65,000inyearlytestingsupplies.Traditionally,565,000 in yearly testing supplies. Traditionally, 5% of all completed items have to be reworked. External failure costs average 120 per failed unit. The company's average external failures are 1% of units sold. The company carries no ending inventories.

Required:
How much do internal failure costs change, assuming 500,000 units are tested under the new method and it reduces the amount of unacceptable units in the manufacturing process by 40%?

(5) LUKE is considering purchasing a new computer network for 82,000.Itwillrequireadditionalworkingcapitalof82,000. It will require additional working capital of 13,000. Its anticipated eight-year life will generate additional client revenue of 33,000annuallywithoperatingcosts,excludingdepreciation,of33,000 annually with operating costs, excluding depreciation, of 15,000. At the end of eight years, it will have a salvage value of 9,500andreturn9,500 and return 5,000 in working capital. Taxes are not considered. The company has a required rate of return of 14%.

Required:
What is the net present value of the proposed investment? What is the internal rate of return?

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這一題的完整詳解

（1）相關初始投資

核心觀念
更換資產的相關初始投資，等於新資產成本加上營運資金投入，再減去舊資產處分的稅後收入。舊資產出售所得須扣除出售利益所產生的稅額。

解題方法
舊資產出售收入為 $410,000，出售利益為 $10,000，因此應納稅額為：

10,000×20%=2,00010{,}000 \times 20\% = 2{,}000

舊資產處分稅後收入為 $410,000 − $2,000 = $408,000。相關初始投資為：

2,100,000+300,000−408,000=1,992,0002{,}100{,}000 + 300{,}000 - 408{,}000 = 1{,}992{,}000

解題技巧
若題目給的是出售價格與出售利益，應以出售利益計算處分稅額；不必另外以帳面價值計算，除非題目要求推算帳面價值。

**【答案】**相關初始投資為 $1,992,000。

（2）改採經濟訂購量的年成本節省

核心觀念
經濟訂購量（EOQ）使年度訂購成本與年度持有成本的總和最低：

EOQ=2DSHEOQ = \sqrt{\frac{2DS}{H}}

其中，DD 為年需求量、SS 為每次訂購成本、HH 為每單位年持有成本。採購成本在訂購量改變前後相同，因此比較訂購成本與持有成本即可。

解題方法
每單位年持有成本為：

H=100×40%=40H = 100 \times 40\% = 40

計算經濟訂購量：

EOQ=2×720×2540=900=30 單位EOQ = \sqrt{\frac{2 \times 720 \times 25}{40}} = \sqrt{900} = 30 \text{ 單位}

原訂購量為 10 單位，年度訂購與持有成本為：

72010×25+102×40=1,800+200=2,000\frac{720}{10} \times 25 + \frac{10}{2} \times 40 = 1{,}800 + 200 = 2{,}000

改採 30 單位後，年度訂購與持有成本為：

72030×25+302×40=600+600=1,200\frac{720}{30} \times 25 + \frac{30}{2} \times 40 = 600 + 600 = 1{,}200

因此年度成本節省為：

2,000−1,200=8002{,}000 - 1{,}200 = 800

解題技巧
平均存貨量以訂購量的一半計算；改變訂購量不會改變全年需求量，所以不必把採購成本納入節省額比較。

**【答案】**每年可節省 $800。

（3）是否應將拋光雕像刻字後出售

核心觀念
是否進一步加工，應比較加工後增加的收入與增加的成本。共同發生的材料與前段加工成本不因是否刻字而改變，屬於不相關成本。

解題方法
每年拋光雕像銷量為：

50,000×40%=20,000 個50{,}000 \times 40\% = 20{,}000 \text{ 個}

拋光雕像直接出售可得 $19；刻字後售價為 $40，刻字的增額收入為：

40−19=2140 - 19 = 21

每個雕像刻字需增加 $5 成本，因此每個刻字雕像增加的利益為：

21−5=1621 - 5 = 16

每年增額利益為：

20,000×16=320,00020{,}000 \times 16 = 320{,}000
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第 2. 題25 分

Answer each of the following independent questions and show all relevant computations on the answer sheet.

(1) NTPU Inc. manufactures only specific orders. It uses a standard cost system. During one large order for the airport authority, an unusual number of signs were spoiled. The normal spoilage rate is 10% of units started. The point of first inspection is half way through the process, the second is three-fourths through the process, and the final inspection is at the end of the process. Other information about the job is as follows:

Signs started: 3,000
Signs spoiled: 450
Direct materials put into process at beginning: 60,000Conversioncostsforjob:60,000 Conversion costs for job: 120,000
Standard direct material costs per sign: 27Standardconversioncostpersign:27 Standard conversion cost per sign: 54
Average point of spoilage is the 3/4 completion point
Average current disposal cost per spoiled sign: $15

Required:
Make necessary journal entries to record all spoilage.

(2) TSMC has budgeted construction overhead for August of 435,000forfixedcosts.Actualcostsforthemonthtotaledfor435,000 for fixed costs. Actual costs for the month totaled for 450,000 for fixed. Allocated fixed overhead totaled 430,000.Thecompanytrackseachiteminanoverheadcontrolaccountbeforeallocationsaremadetoindividualjobs.ThefixedoverheadspendingvarianceforAugustwas430,000. The company tracks each item in an overhead control account before allocations are made to individual jobs. The fixed overhead spending variance for August was 15,000 unfavorable for fixed.

Required:
Make journal entries to record the actual costs incurred as well as the variances for August.

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這一題的完整詳解

第 2 題

（1）異常損壞與正常損壞

核心觀念

本題考查製造過程中的正常損壞與異常損壞，以及標準成本制度下損壞品成本的計算。

  • 正常損壞數量：
正常損壞=3,000×10%=300 個\text{正常損壞}=3,000\times 10\%=300\text{ 個}
  • 異常損壞數量：
異常損壞=450−300=150 個\text{異常損壞}=450-300=150\text{ 個}

正常損壞屬於正常生產成本，應由該批良品吸收；異常損壞則應列為當期異常損失。

題目指出平均損壞點在製程完成度的四分之三處。直接材料一開始即投入，因此每個損壞品均已吸收完整直接材料成本；轉換成本則只發生至四分之三的程度。

損壞品的標準成本

每個損壞品的直接材料成本：

$27\$27

每個損壞品的轉換成本：

$54×34=$40.50\$54\times\frac{3}{4}=\$40.50

每個損壞品的標準成本：

$27+$40.50=$67.50\$27+\$40.50=\$67.50

正常損壞品成本：

300×$67.50=$20,250300\times\$67.50=\$20,250

異常損壞品成本：

150×$67.50=$10,125150\times\$67.50=\$10,125

損壞品總標準成本：

$20,250+$10,125=$30,375\$20,250+\$10,125=\$30,375

損壞處分成本

每個損壞品的處分成本為 $15，因此總處分成本為：

450×$15=$6,750450\times\$15=\$6,750

其中：

正常損壞的處分成本：

300×$15=$4,500300\times\$15=\$4,500

異常損壞的處分成本：

150×$15=$2,250150\times\$15=\$2,250

分錄

若直接材料與轉換成本尚未入帳，先記錄本批製造成本：

借：在製品—機場主管機關訂單       $180,000
    貸：原料                                $60,000
        各項製造成本                        $120,000

移除損壞品。正常損壞成本仍由本批良品吸收，異常損壞則列為異常損失：

借：在製品—機場主管機關訂單        $20,250
借：異常損壞損失                    $10,125
    貸：在製品—機場主管機關訂單               $30,375

記錄損壞品的處分成本：

借：在製品—機場主管機關訂單         $4,500
借：異常損壞損失                     $2,250
    貸：現金或應付帳款
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第 3. 題25 分

(3) MILKBOTTLE bought a 2,000-acre island for 10,000,000anddivideditinto200equalsizelots.Asthelotsaresold,theyareclearedatanaveragecostof10,000,000 and divided it into 200 equal size lots. As the lots are sold, they are cleared at an average cost of 5,000. Storm drains and driveways are installed at an average cost of 8,000persite.Salescommissionsare108,000 per site. Sales commissions are 10% of selling price. Administrative costs are 850,000 per year. The average selling price was 160,000perlotduring2025when50lotsweresold.During2026,thecompanyboughtanother2,000−acreislandanddevelopeditexactlythesameway.Lotsalesin2026totaled300withanaveragesellingpriceof160,000 per lot during 2025 when 50 lots were sold. During 2026, the company bought another 2,000-acre island and developed it exactly the same way. Lot sales in 2026 totaled 300 with an average selling price of 160,000. All costs were the same as in 2025.

Required:
Determine operating income for both years using both absorption costing and variable costing.

  1. Linda Company reaches its breakeven point at 2,000,000ofrevenues.Atpresent,itisselling60,000units.Theunitvariablecostis2,000,000 of revenues. At present, it is selling 60,000 units. The unit variable cost is 40 and the total fixed cost is $400,000.

Required:
(1) Compute the contribution margin ratio. (4%)
(2) Compute the unit price. (4%)
(3) Compute the margin of safety ratio and the degree of operating leverage. (8%)
(4) What is the relationship between profit ratio, contribution margin ratio and margin of safety ratio? (4%)

  1. Taipei Company produces a special toy. The various unit costs are as follows:
    Direct material 160Directlabor160 Direct labor 220
    Variable manufacturing overhead 100Fixedmanufacturingoverhead100 Fixed manufacturing overhead 160
    Variable marketing expense: 16% of the unit price

Suppose Taipei uses a 25% markup on the full unit cost. Compute the unit price of the toy. (10%)

  1. Agnetha division is an investment center of Abba Company. Agnetha collected the following information about its performance:
    Profits 200,000Investmentturnover5Residualincome200,000 Investment turnover 5 Residual income 100,000
    Abba's required rate of return is 10%.

Required:
(1) Compute the return on investment of Agnetha division. (10%)
(2) Compute the return on sales of Agnetha division. (10%)

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這一題的完整詳解

1.  MILKBOTTLE 兩年度營業利益之吸收成本法與變動成本法比較

核心觀念

  • 吸收成本法（Absorption Costing）：所有製造成本─包括變動製造成本與固定製造成本─均列為產品成本，期末存貨按全部成本計價。營業利益 = 銷貨收入 – 銷貨成本 – 期間費用。
  • 變動成本法（Variable Costing）：僅將變動製造成本列為產品成本，固定製造成本列為期間費用。營業利益 = 銷貨收入 – 變動製造成本 – 變動期間費用 – 固定期間費用。
  • 本題的「清理成本」與「基礎設施成本」均屬變動製造成本（每售出一塊地才發生），而 行政費用 $850,000/年 為固定期間費用。

解題步驟

(1) 先求每塊地之變動製造成本

  • 清理成本：5,0005,000
  • 基礎設施成本（排水＋道路）：8,0008,000
  • 單位變動製造成本 =  5,000+8,000=13,000=\;5,000+8,000=13,000

(2) 銷貨佣金

  • 佣金率 10% → 每塊銷售價格 160,000160,000 的佣金 =0.10×160,000=16,000=0.10 \times 160,000 = 16,000

(3) 2025 年資料

  • 銷售量 Q2025=50Q_{2025}=50 塊
  • 銷貨收入 R2025=50×160,000=8,000,000R_{2025}=50 \times 160,000 = 8,000,000
吸收成本法（2025）
  • 每塊地之 全部製造成本 = 變動製造成本 13,00013,000（本例無固定製造成本）
  • 銷貨成本 C2025Abs=50×13,000=650,000C_{2025}^{Abs}=50 \times 13,000 = 650,000
  • 期間變動費用（佣金） =50×16,000=800,000=50 \times 16,000 = 800,000
  • 固定期間費用 =850,000=850,000
= 8,000,000 - 650,000 - 800,000 - 850,000 = 5,700,000$$ ##### 變動成本法（2025） - 變動製造成本 $=650,000$（同上） - 變動期間費用 = 佣金 $800,000$ - 固定期間費用 $850,000$ $$\text{營業利益}_{2025}^{Var}= 8,000,000 - (650,000 + 800,000 + 850,000) = 5,700,000$$ > **觀察**：本題的固定製造成本為 $0$，因此兩種成本法於 2025 年得到相同營業利益。 #### (4) 2026 年資料 - 2026 年同樣取得另一 2,000‑acre 島，開發方式相同，固定行政費仍 $850,000$。 - 銷售量 $Q_{2026}=300$，每塊平均售價仍 $160,000$。 - 銷貨收入 $R_{2026}=300 \times 160,000 = 48,000,000$ - 變動製造成本 $C^{Var}_{2026}=300 \times 13,000 = 3,900,000$ - 佣金 $=300 \times 16,000 = 4,800,000$ ##### 吸收成本法（2026） $$\text{營業利益}_{2026}^{Abs}= 48,000,000 - 3,900,000 - 4,800,000 - 850,000 = 38,450,000$$ ##### 變動成本法（2026） $$\text{營業利益}_{2026}^{Var}= 48,000,000 - (3,900,000 + 4,800,000 + 850,000) = 38,450,000$$ > 同樣因無固定製造成本，兩法結果相同。 --- ### 【答案】 | 年度 | 吸收成本法營業利益 | 變動成本法營業利益 | |------|-------------------|-------------------| | 2025 | **$5,700,000** | **$5,700,000** | | 2026 | **$38,450,000** | **$38,450,000** | --- **2.  Linda Company 相關計算** --- ### 核心觀念 - **貢獻毛利（Contribution Margin, CM）**：單位銷售價格 $P$ 減去單位變動成本 $V$。 - **貢獻毛利率（CM Ratio）**：$CM/P$，亦即每單位收入能貢獻多少比例給固定成本與利潤。 - **安全邊際（Margin of Safety, MOS）**：實際銷售額減去盈虧平衡銷售額。 - **營業槓桿度（Degree of Operating Leverage, DOL）**：$ \displaystyle DOL = \frac{\text{貢獻毛利}}{\text{營業利益}}$，衡量營業利益對銷售變動的敏感度。 --- ### 已知條件 - 營收盈虧平衡點（BEP）$=2,000,000$ 元。 - 現行銷量 $Q=60,000$ 單位。 - 單位變動成本 $V=40$ 元。 - 總固定成本 $F=400,000$ 元。 --- #### (1) 計算 **貢獻毛利率** $$\text{BEP（單位）}= \frac{F}{CM/P}= \frac{F}{CM\ ratio}$$ 但亦可直接從盈虧平衡營收： $$CM\ ratio = \frac{F}{\text{BEP營收}} = \frac{400,000}{2,000,000}=0.20 = 20\%$$ > **答案**：貢獻毛利率 = **20%**。 #### (2) 計算 **單位售價 $P$** $$CM\ ratio = \frac{P-V}{P}=0.20$$ $$P - V = 0.20P \;\Rightarrow\; P(1-0.20)=V$$ $$0.80P = 40 \;\Rightarrow\; P = \frac{40}{0.80}=50$$ > **答案**：單位售價 $P = **\$50**$。 #### (3) 計算 **安全邊際率** 以及 **營業槓桿度** - 實際營收 $R = Q \times P = 60,000 \times 50 = 3,000,000$。 - 安全邊際（金額） $= R - \text{BEP營收}= 3,000,000 - 2,000,000 = 1,000,000
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第 3. 題

Linda Company reaches its breakeven point at 2,000,000ofrevenues.Atpresent,itisselling60,000units.Theunitvariablecostis2,000,000 of revenues. At present, it is selling 60,000 units. The unit variable cost is 40 and the total fixed cost is $400,000.

Required:
(1) Compute the contribution margin ratio. (4%)
(2) Compute the unit price. (4%)
(3) Compute the margin of safety ratio and the degree of operating leverage. (8%)
(4) What is the relationship between profit ratio, contribution margin ratio and margin of safety ratio? (4%)

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這一題的完整詳解

核心觀念

本題考查損益兩平分析（Cost-Volume-Profit Analysis, CVP）中的四項觀念：

  1. 邊際貢獻率（Contribution Margin Ratio, CMR）
  2. 單位售價與損益兩平點的推導
  3. 安全邊際率（Margin of Safety Ratio, MOS ratio）
  4. 營業槓桿程度（Degree of Operating Leverage, DOL）

基本公式如下：

邊際貢獻=銷貨收入−變動成本\text{邊際貢獻}=\text{銷貨收入}-\text{變動成本} 邊際貢獻率=邊際貢獻銷貨收入=單位售價−單位變動成本單位售價\text{邊際貢獻率} = \frac{\text{邊際貢獻}}{\text{銷貨收入}} = \frac{\text{單位售價}-\text{單位變動成本}}{\text{單位售價}} 損益兩平銷貨收入=固定成本邊際貢獻率\text{損益兩平銷貨收入} = \frac{\text{固定成本}}{\text{邊際貢獻率}} 安全邊際率=實際銷貨收入−損益兩平銷貨收入實際銷貨收入\text{安全邊際率} = \frac{\text{實際銷貨收入}-\text{損益兩平銷貨收入}} {\text{實際銷貨收入}} 營業槓桿程度=邊際貢獻營業利益\text{營業槓桿程度} = \frac{\text{邊際貢獻}}{\text{營業利益}}

解題方法與計算

（1）計算邊際貢獻率

在損益兩平點，營業利益為零，因此：

損益兩平點的邊際貢獻=固定成本=400,000\text{損益兩平點的邊際貢獻} = \text{固定成本} = 400,000

已知損益兩平銷貨收入為 $2,000,000，因此：

邊際貢獻率=400,0002,000,000=20%\text{邊際貢獻率} = \frac{400,000}{2,000,000} = 20\%

【答案】邊際貢獻率為 20%。

（2）計算單位售價

設單位售價為 PP。

根據邊際貢獻率公式：

P−40P=20%\frac{P-40}{P}=20\% P−40=0.2PP-40=0.2P 0.8P=400.8P=40 P=50P=50

因此，單位售價為 $50。

亦可利用損益兩平銷貨收入求損益兩平銷售量：

損益兩平銷售量=400,00050−40=40,000 單位\text{損益兩平銷售量} = \frac{400,000}{50-40} = 40,000\text{ 單位} 40,000 單位×$50=$2,000,00040,000 \text{ 單位}\times \$50 = \$2,000,000

與題目所給損益兩平銷貨收入相符。

【答案】單位售價為 $50。

（3）計算安全邊際率與營業槓桿程度

① 安全邊際率

目前銷售量為 60,000 單位，單位售價為 $50，因此目前銷貨收入為：

60,000×50=3,000,00060,000\times 50=3,000,000

安全邊際金額為：

安全邊際=3,000,000−2,000,000=1,000,000\text{安全邊際} = 3,000,000-2,000,000 = 1,000,000

安全邊際率為：

安全邊際率=1,000,0003,000,000=3313%\text{安全邊際率} = \frac{1,000,000}{3,000,000} = 33\frac{1}{3}\%

【答案】安全邊際率為 33.33%。

② 營業槓桿程度

單位邊際貢獻為：

50−40=1050-40=10

目前總邊際貢獻為：

60,000×10=600,00060,000\times 10=600,000

目前營業利益為：

600,000−400,000=200,000600,000-400,000=200,000

因此：

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第 4. 題10 分

Taipei Company produces a special toy. The various unit costs are as follows:
Direct material 160Directlabor160 Direct labor 220
Variable manufacturing overhead 100Fixedmanufacturingoverhead100 Fixed manufacturing overhead 160
Variable marketing expense: 16% of the unit price

Suppose Taipei uses a 25% markup on the full unit cost. Compute the unit price of the toy. (10%)

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這一題的完整詳解

此題考驗基於成本加成法的定價決策，需將所有相關成本納入考量，並正確計算加成金額與最終售價。

  • 已知資訊：

    • 單位成本：
      • 直接材料 (DM)：$160
      • 直接人工 (DL)：$220
      • 變動製造費用 (VOH)：$100
      • 固定製造費用 (FOH)：$160
      • 總單位製造成本 (Full Manufacturing Cost)： 160+160 + 220 + 100+100 + 160 = $640
    • 變動行銷費用 (Variable Marketing Expense, VME)：16% of unit price
    • 加成率 (Markup Rate)：25% on the full unit cost

  • 計算：

    1. 計算「全單價成本」(Full Unit Cost)：

      • 題目明確指出「full unit cost」，這通常指的是所有生產相關的單位成本。
      • Full Unit Cost = Direct Material + Direct Labor + Variable MOH + Fixed MOH
      • Full Unit Cost = 160+160 + 220 + 100+100 + 160 = $640

    2. 計算加成金額 (Markup Amount)：

      • 加成是基於「full unit cost」計算的。
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第 5. 題10 分

Agnetha division is an investment center of Abba Company. Agnetha collected the following information about its performance:
Profits 200,000Investmentturnover5Residualincome200,000 Investment turnover 5 Residual income 100,000
Abba's required rate of return is 10%.

Required:
(1) Compute the return on investment of Agnetha division. (10%)
(2) Compute the return on sales of Agnetha division. (10%)

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這一題的完整詳解

此題考驗績效衡量指標，包括投資報酬率 (ROI)、銷售報酬率 (ROS) 和剩餘所得 (RI)。

  • 已知資訊：

    • 利潤 (Profits) = $200,000
    • 投資週轉率 (Investment Turnover, IT) = 5
    • 剩餘所得 (Residual Income, RI) = $100,000
    • 要求報酬率 (Required Rate of Return, RRR) = 10%

  • 計算：

    • (1) 投資報酬率 (Return on Investment, ROI)
      • 核心公式：
        • ROI = Profits / Investment
        • Investment Turnover (IT) = Sales / Investment
        • Residual Income (RI) = Profits - (Investment × RRR)
      • 步驟 1：計算投資額 (Investment)。
        • 利用 RI 的公式：100,000=100,000 = 200,000 - (Investment × 10%)
        • 100,000=100,000 = 200,000 - 0.10 × Investment
        • 0.10 × Investment = 200,000−200,000 - 100,000
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其他考古題

臺北大學《成本與管理會計》其他年度

114 年113 年112 年111 年109 年108 年

其他學校的財金會計考古題

臺灣大學104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暨南國際大學13高雄大學6嘉義大學6臺北商業大學3