📚 Worksheet Answers – Chapter 31: Budgets and Variance Analysis | 第31章练习题答案 – 预算与差异分析
This comprehensive answer guide walks through a typical Cambridge A-Level Business worksheet on budgets and variance analysis. Every numerical question is broken down with clear steps, followed by a detailed discussion of the managerial implications. Work through these solutions to strengthen your understanding of budgeting techniques, cash planning and performance measurement.
这套全面的答案指南讲解了一份典型的剑桥A-Level商务预算与差异分析练习题。每道计算题都配有清晰的步骤拆解，并深入讨论了管理层面的含义。通过研读这些答案解析，你可以强化对预算编制方法、现金规划和业绩衡量知识的掌握。
1. Sales Budget Calculation | 销售预算计算
A firm expects to sell 500 units in January, 600 units in February and 700 units in March. The selling price is held constant at $80 per unit. Prepare the sales budget for the first quarter.
一家企业预计1月销售500件，2月销售600件，3月销售700件。售价保持在每件80美元不变。请编制第一季度的销售预算。
The sales budget translates the sales forecast into expected revenue. Multiply each month's volume by the unit price. January: 500 × $80 = $40,000. February: 600 × $80 = $48,000. March: 700 × $80 = $56,000.
销售预算将销售预测转化为预期收入。用每个月的销量乘以单价。1月：500 × 80 = 40,000美元。2月：600 × 80 = 48,000美元。3月：700 × 80 = 56,000美元。
The quarterly sales budget is the sum of the three months, giving a total of $144,000. This figure feeds into the cash budget and the master budget, and it is also used to set sales targets for the team.
第一季度销售预算是这三个月之和，总计144,000美元。这个数字将汇入现金预算和总预算，同时也会被用来为销售团队设定目标。
| Month | Volume (units) | Price per unit | Sales revenue |
|---|---|---|---|
| January | 500 | $80 | $40,000 |
| February | 600 | $80 | $48,000 |
| March | 700 | $80 | $56,000 |
| Total Q1 | 1,800 | $144,000 |
2. Production Budget in Units | 产量预算（单位）
Using the sales forecast from Question 1, the company holds an opening inventory of 50 units on 1 January. Its policy is to maintain a closing inventory equal to 20% of the next month's sales. Calculate the production budget in units for January, February and March. Assume April sales are forecast at 800 units.
沿用第1题的销售预测，公司在1月1日持有期初存货50件。公司政策是保持期末存货为下月销售量的20%。请计算1月、2月和3月的生产预算（以件数计）。假设4月的销售预测为800件。
he required production formula is: Production = budgeted sales + desired closing inventory – ntory. Closing inventory for a month becomes the opening inventory of the following month.
所需产量的计算公式为：生产量 = 预算销量 + 目标期末存货 – 期初存货。某月的期末存货即成为下月的期初存货。
January: sales 500, closing inventory 20% × 600 = 120, opening inventory 50. Production = 500 + 120 − 50 = 570 units.
1月：销量500，期末存货 20% × 600 = 120，期初存货50。产量 = 500 + 120 – 50 = 570件。
February: sales 600, closing inventory 20% × 700 = 140, opening inventory 120. Production = 600 + 140 − 120 = 620 units.
2月：销量600，期末存货 20% × 700 = 140，期初存货120。产量 = 600 + 140 – 120 = 620件。
March: sales 700, closing inventory 20% × 800 = 160, opening inventory 140. Production = 700 + 160 − 140 = 720 units.
3月：销量700，期末存货 20% × 800 = 160，期初存货140。产量 = 700 + 160 – 140 = 720件。
The production budget ensures the factory can meet forecast demand while maintaining adequate buffer stock, avoiding lost sales due to stock-outs.
生产预算确保工厂既能满足预测需求，又能维持足够的缓冲库存，从而避免因缺货而失去销售机会。
3. Direct Materials Usage Budget | 直接材料用量预算
Each unit requires 2 kg of raw material, which costs $5 per kg. The company wishes to hold closing material inventory equal to 10% of the following month's material usage. Opening raw material inventory on 1 January is 120 kg. Using the production units from Question 2, prepare the materials purchases budget (in kg and $) for January and February. March data: assume April material usage is 1,600 kg.
每件产品需要2公斤原材料，原材料成本为每公斤5美元。公司希望保持期末原料库存为下月材料用量的10%。1月1日期初原料库存为120公斤。请利用第2题的产量数据，编制1月和2月的材料采购预算（分别以公斤和美元计）。3月数据：假设4月的材料用量为1,600公斤。
: 570 × 2 = 1,140 kg. February usage: 620 × 2 = 1,240 kg. March usage: 720 × 2 = 1,440 kg.
先计算每月材料用量：产量 × 2公斤。1月用量：570 × 2 = 1,140公斤。2月用量：620 × 2 = 1,240公斤。3月用量：720 × 2 = 1,440公斤。
Desired closing inventory for January is 10% of February usage = 10% × 1,240 = 124 kg. February closing inventory = 10% × 1,440 = 144 kg.
1月的目标期末库存为2月用量的10% = 10% × 1,240 = 124公斤。2月期末库存 = 10% × 1,440 = 144公斤。
inventory. January: 1,140 + 124 − 120 = 1,144 kg. February: 1,240 + 144 − 124 = 1,260 kg.
采购量（公斤） = 用量 + 期末库存 – 期初库存。1月：1,140 + 124 – 120 = 1,144公斤。2月：1,240 + 144 – 124 = 1,260公斤。
Cost of purchases: January 1,144 × $5 = $5,720; February 1,260 × $5 = $6,300.
采购成本：1月 1,144 × 5 = 5,720美元；2月 1,260 × 5 = 6,300美元。
This materials budget helps the procurement department plan orders and ensures the business does not tie up too much cash in excessive raw material stocks.
这份材料预算有助于采购部门规划订单，并确保企业不会在过多的原材料库存中积压过多资金。
4. Direct Labour Budget | 直接人工预算
Each unit requires 0.5 direct labour hours, and the hourly wage rate is $15. Using the production budget from Question 2, calculate the direct labour hours needed and the total labour cost for the quarter.
每件产品需要0.5个直接人工小时，小时工资率为15美元。请利用第2题的生产预算，计算本季度所需的直接人工小时数和总人工成本。
0 units. Labour hours required = 1,910 × 0.5 = 955 hours. Total direct labour cost = 955 × $15 = $14,325.
本季度总产量 = 570 + 620 + 720 = 1,910件。所需人工小时 = 1,910 × 0.5 = 955小时。直接人工总成本 = 955 × 15 = 14,325美元。
Monthly breakdown: January 570 × 0.5 = 285 hours, cost $4,275; February 620 × 0.5 = 310 hours, cost $4,650; March 720 × 0.5 = 360 hours, cost $ elps the HR department to arrange appropriate staffing levels and control labour spending.
月度明细：1月 570 × 0.5 = 285小时，成本4,275美元；2月 620 × 0.5 = 310小时，成本4,650美元；3月 720 × 0.5 = 360小时，成本5,400美元。这份时间安排有助于人力资源部门调配适当的人员配备水平并控制人工支出。
5. Cash Budget Preparation | 现金预算编制
From the budgets above and additional information, prepare a simple cash budget for January. Assume 60% of sales revenue is received in the month of sale, and 40% in the following month. December sales were $32,000. Material purchases are paid for in the month after purchase; December purchases were $4,800. Labour costs are paid in the month they are incurred. Overhead payments are $9,000 per month. The opening cash balance on 1 January is $5,000.
根据上述预算及其他资料，编制一份简明的1月现金预算。假设60%的销售收入在销售当月收到，40%在下月收到。12月销售额为32,000美元。材料采购在采购发生后的次月支付；12月采购额为4,800美元。人工成本在发生的当月支付。每月管理费用支出为9,000美元。1月1日的期初现金余额为5,000美元。
Cash inflows: From January sales: 60% × $40,000 = $24,000; from December sales: 40% × $32,000 = $12,800. Total inflows = $36,800.
现金流入：来自1月销售：60% × 40,000 = 24,000美元；来自12月销售：40% × 32,000 = 12,800美元。流入总额 = 36,800美元。
Cash outflows: Payment for December materials = $4,800; January labour = $4,275; overheads = $9,000. Total outflows = $4,800 + $4,275 + $9,000 = $18,075.
现金流出：支付12月材料款 = 4,800美元；1月人工 = 4,275美元；管理费用 = 9,000美元。流出总额 = 4,800 + 4,275 + 9,000 = 18,075美元。
Closing cash balance = opening $5,000 + inflows $36,800 − outflows $18,075 = $ thy liquidity for the month, though future months must be monitored for any seasonal dips.
期末现金余额 = 期初5,000 + 流入36,800 – 流出18,075 = 23,725美元。期末余额为正值，显示本月流动性良好，但仍需监控后续月份是否存在季节性下降。
6. Material Cost Variance | 材料成本差异
After the first quarter, the company examines actual performance. In March, actual output was 700 units. The standard material cost is 2 kg per unit at $5 per kg. Actual material used was 1,450 kg, costing $7,685 in total. Calculate the total material variance, material price variance and material usage variance.
在第一季度结束后，公司检查了实际业绩。3月实际产量为700件。标准材料成本为每件2公斤，每公斤5美元。实际耗用材料1,450公斤，总成本为7,685美元。请计算总材料差异、材料价格差异和材料用量差异。
First, obtain actual price per kg: $7,685 ÷ 1,450 kg = $5.30 per kg. Standard quantity for actual output = 700 units × 2 kg = 1,400 kg.
首先，计算每公斤实际价格：7,685 ÷ 1,450 = 5.30美元/公斤。实际产量下的标准用量 = 700 × 2 = 1,400公斤。
Material price variance = (Actual price − Standard price) × Actual quantity = ($5.30 − $5.00) × 1,450 = $435 adverse.
材料价格差异 = (实际价格 – 标准价格) × 实际用量 = (5.30 – 5.00) × 1,450 = 435美元 不利差异。
sage variance = (Actual quantity − Standard quantity) × Standard price = (1,450 − 1,400) × $5 = $250 adverse.
材料用量差异 = (实际用量 – 标准用量) × 标准价格 = (1,450 – 1,400) × 5 = 250美元 不利差异。
Total material variance = $435 + $250 = $685 adverse (which can also be checked by actual cost $7,685 − standard cost 1,400 × $5 = $7,685 − $7,000 = $ sing may have faced price rises and production may have experienced waste or inefficiency.
总材料差异 = 435 + 250 = 685美元 不利差异（也可通过实际成本7,685 – 标准成本1,400×5=7,000来验证，结果为685美元不利）。两项差异均为不利差异，表明采购可能遇到了价格上涨，生产环节可能存在浪费或效率低下的问题。
7. Labour Cost Variance | 人工成本差异
For the same output of 700 units, the standard labour time is 0.5 hours per unit at $15 per hour. Actual hours worked were 330 hours at a total cost of $5,445. Calculate the labour rate variance, labour efficiency variance and total labour variance.
同样针对700件的产量，标准工时为每件0.5小时，标准工资率每小时15美元。实际耗用工时为330小时，实际总成本为5,445美元。请计算人工工资率差异、人工效率差异和总人工差异。
Actual hourly rate = $5,445 ÷ 330 = $16.50 per hour. Standard hours for actual output = 700 × 0.5 = 350 hours.
实际小时工资率 = 5,445 ÷ 330 = 16.50美元/小时。实际产量下的标准工时 = 700 × 0.5 = 350小时。
Labour rate variance = (Actual rate − Standard rate) × Actual hours = ($16.50 − $15.00) × 330 = $495 adverse.
人工工资率差异 = (实际工资率 – 标准工资率) × 实际工时 = (16.50 – 15.00) × 330 = 495美元 不利差异。
bour efficiency variance = (Actual hours − Standard hours) × Standard rate = (330 − 350) × $15 = −$300, i.e. $300 favourable.
人工效率差异 = (实际工时 – 标准工时) × 标准工资率 = (330 – 350) × 15 = –300美元，即300美元有利差异。
Total labour variance = $495 adverse + $300 favourable = $195 adverse (check: actual cost $5,445 − standard cost 350 × $15 = $5,445 − $5,250 = $ variance is favourable, indicating workers produced the output in less time than standard.
总人工差异 = 495不利 + 300有利 = 195美元不利差异（验证：实际成本5,445 – 标准成本350×15=5,250，差异195不利）。工资率差异为不利差异，可能是因为支付了加班费或聘用了技能水平更高的工人；而效率差异为有利差异，表明工人用比标准更少的工时完成了产出。
8. Interpreting Variances for Decision-Making | 为决策解读差异
Published by TutorHao | A-Level 商务 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图