Practice gce model questions vol1 commerce 2024 Past Questions

Question 1 View Details

A company plans an advertising campaign using two media: TV and online. Each TV spot costs $\£2000$ and reaches 5000 viewers. Due to diminishing returns, each additional TV spot reaches only 80% of the viewers reached by the previous spot. Each viewer has a 0.1% chance of making a purchase. Online advertising costs $\£0.10$ per click, and each click converts to a sale with probability 2%. The profit per unit sold is $\£25$. The company currently sells 800 units per month with a profit of $\£6000$. It wants to increase its monthly profit by at least $\£4000$. Determine the minimum number of TV spots (an integer $t\ge 1$) and the minimum number of online clicks (an integer $c$) required to achieve this profit increase. Show all reasoning steps.

A. 1 TV spot and 15 000 online clicks

Correct B. 1 TV spot and 14 688 online clicks

C. 2 TV spots and 13 500 online clicks

D. 3 TV spots and 12 000 online clicks

Correct Answer: B

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Question 2 View Details

A retailer buys 200 units of a product. The purchase price (excluding freight) is $\£P$. Freight adds 5% of $\£P$. The retailer marks the product up by 30% on the purchase price (excluding freight) to obtain the full selling price. A seasonal discount of 12% is offered on the selling price, and a trade‑in allowance of $\£15$ per unit is given to customers who return an old appliance (the allowance is added to the revenue). The profit per unit sold at the full price is therefore $\£0.25P/200$. The retailer wants a total profit of $\£3000$ from this batch. Assuming the purchase price is $\£10\,000$, what is the minimum number of units that must be sold at the discounted price (with the trade‑in allowance) in order to reach the profit target? Show all steps.

A. 80 units

B. 75 units

C. 60 units

Correct D. 70 units

Correct Answer: D

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Question 3 View Details

A warehouse stocks a product whose daily demand is normally distributed with mean $120$ units and standard deviation $30$ units. The company can choose between two lead‑time options: - **Option A**: Lead time $L=5$ days, no extra cost. - **Option B**: Lead time $L=3$ days, but an additional cost of $\£200$ is incurred for each order placed. Holding cost is $\£0.25$ per unit per day. The profit per unit sold is $\£0.25$ per unit (i.e., the contribution margin). The company uses a continuous‑review system and orders a fixed quantity $Q$ each cycle, equal to the expected demand over the lead time. It wishes to maintain a 95 % service level (i.e., the probability of no stock‑out during lead time). Determine which lead‑time option minimises the total expected monthly cost (30 days) and give the corresponding order quantity $Q$. Show all calculations.

A. Lead‑time 3 days, order quantity 360 units

B. Lead‑time 3 days, order quantity 600 units

Correct C. Lead‑time 5 days, order quantity 600 units

D. Lead‑time 5 days, order quantity 550 units

Correct Answer: C

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Question 4 View Details

A customer borrows $\£5000$ from a bank. The bank adds a flat arrangement fee of $\£150$ to the loan amount and then requires the customer to make equal monthly repayments of $\£150$ for 36 months. Using the cash‑flow method, calculate the Annual Percentage Rate (APR) of this loan, expressed as a percentage to two decimal places. Show the steps required to obtain the APR.

Correct A. 7.45%

B. 9.15%

C. 6.80%

D. 8.20%

Correct Answer: A

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Question 5 View Details

An importer in the UK must pay a US supplier $\$12\,000$ for goods. The bank offers two ways to obtain the pounds needed: - **Spot transaction**: exchange rate $\£0.78$ per $\$1$, a commission of 0.5 % on the dollar amount, and a flat fee of $\£30$. - **Forward contract**: exchange rate $\£0.80$ per $\$1$, no commission, but a flat fee of $\£20$. The importer expects to sell the goods in the UK for $\£10\,500$. Which option gives the higher profit, and what is that profit (to two decimal places)? Show all reasoning steps.

A. Spot transaction; profit = £1,000.00

Correct B. Spot transaction; profit = £1,063.20

C. Forward contract; profit = £880.00

D. Forward contract; profit = £1,050.00

Correct Answer: B

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Question 6 View Details

A consumer purchases a washing machine advertised as having an average annual electricity cost of $£120$. After one year of use the actual electricity cost is $£180$ per year. The machine comes with a 2‑year warranty, but it fails after 18 months and the seller refuses repair, offering instead a repair service that would cost the consumer $£200$. The consumer wishes to claim compensation for (i) the difference in electricity cost for the remaining warranty period and (ii) the repair cost. Calculate the total amount the consumer can claim.

A. 120

B. 260

Correct C. 230

D. 190

Correct Answer: C

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Question 7 View Details

A motor insurance policy has a base premium of $£500$. The driver has a 3‑year no‑claims record, giving a discount of 20% for each claim‑free year, up to a maximum of 5 years. Because the driver is under 25, a surcharge of 15% is added to the discounted premium. The driver also opts for optional fire coverage, which adds 12% of the premium after the surcharge. What is the final annual premium the driver must pay?

A. 329.73

B. 224.00

C. 230.00

Correct D. 257.60

Correct Answer: D

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Question 8 View Details

A company can raise £100,000 by issuing debentures that pay an 8% annual coupon and are issued at 98% of face value. Alternatively, it can obtain a bank loan of £95,000 at a nominal rate of 7% per annum payable semi‑annually. Calculate the effective annual cost of each option and state which financing method is cheaper.

A. Debentures, 8.16%

B. Debentures, 7.85%

Correct C. Bank loan, 7.12%

D. Bank loan, 6.95%

Correct Answer: C

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Question 9 View Details

A health insurance policy has an annual premium of $£1,200$. In a particular year the policyholder incurs medical expenses of $£5,000$. The policy applies a deductible of $£200$ per claim and a co‑payment of 20% on the amount exceeding the deductible. How much will the insurer reimburse for that year?

A. 4200

B. 3520

C. 4000

Correct D. 3840

Correct Answer: D

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Question 10 View Details

A firm's capital structure consists of 60% equity and 40% debt. The cost of equity is 12% per annum. The pre‑tax cost of debt is 8% per annum and the corporate tax rate is 30%. Calculate the firm's weighted average cost of capital (WACC).

A. 10.24

Correct B. 9.44

C. 8.80

D. 7.20

Correct Answer: B

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Question 11 View Details

A retailer purchases 500 identical units of a product at an unknown cost price per unit. He marks each unit up by $30\%$ to set the list price. During a promotional period he offers a discount of $11.5\%$ on the list price and, for each unit sold, includes a free accessory whose cost to him equals $5\%$ of the list price. After the promotion his total profit on the batch is ₦40,000. What was the original cost price per unit (in naira, to 2 decimal places)?

Correct A. 935.09

B. 912.34

C. 1020.75

D. 960.50

Correct Answer: A

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Question 12 View Details

A company's shares are currently trading at ₦1,200. It announces a 1‑for‑4 rights issue at a subscription price that is $20\%$ lower than the current market price. Existing shareholders receive one right per share and need four rights to subscribe for one new share. The rights can be sold on the market at their theoretical value. After the rights issue the share price adjusts to the theoretical ex‑rights price. The company also declares a dividend equal to $5\%$ of the new market price per share. An investor holds 200 shares before the rights issue and subscribes to all the rights he is entitled to. Calculate (a) the total cash outlay the investor must pay to acquire the new shares, and (b) the dividend income he will receive after the rights issue, assuming the market price stabilises at the theoretical ex‑rights price.

Correct A. Cash outlay = ₦48,000; Dividend income = ₦14,400

B. Cash outlay = ₦47,200; Dividend income = ₦14,000

C. Cash outlay = ₦50,000; Dividend income = ₦15,200

D. Cash outlay = ₦45,000; Dividend income = ₦13,500

Correct Answer: A

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Question 13 View Details

A wholesaler buys a product from a manufacturer at a cost of ₦800 per unit. He adds a markup of $25\%$ on the cost price and then adds a commission equal to $12\%$ of the final selling price to cover his services. For orders of 100 units or more he offers a bulk discount of $6\%$ on the final selling price (after commission). A retailer purchases 150 units. Determine (a) the total amount the retailer must pay, and (b) the wholesaler's total profit on this transaction. Give answers to two decimal places.

Correct A. Total amount = 160,077.27; Profit = 40,077.27

B. Total amount = 158,500.00; Profit = 38,500.00

C. Total amount = 159,900.12; Profit = 39,900.12

D. Total amount = 162,300.45; Profit = 42,300.45

Correct Answer: A

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Question 14 View Details

Three partners A, B and C start a partnership with capital contributions of ₦120,000, ₦80,000 and ₦100,000 respectively. The partnership agreement provides that (i) interest on capital at $5\%$ per annum is to be paid to each partner, (ii) partner A receives a fixed salary of ₦30,000 per year for managerial duties, and (iii) the remaining profit for the year is to be divided in the ratio of their capital contributions. If the total profit of the partnership before any deductions is ₦250,000, calculate the amount each partner receives after interest and salary are accounted for. Give your answers to the nearest naira.

A. A: 115,000; B: 60,000; C: 75,000

Correct B. A: 118,000; B: 58,667; C: 73,333

C. A: 117,500; B: 59,500; C: 73,000

D. A: 120,000; B: 55,000; C: 75,000

Correct Answer: B

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Question 15 View Details

A home‑based baker prepares a batch of 40 cupcakes. The total cost of ingredients and utilities for the batch is ₦12,000. She sells each cupcake at a price that includes a $15\%$ sales tax, and the final selling price per cupcake (including tax) is ₦500. How much profit does she make on the whole batch before tax is removed? Give your answer to two decimal places.

A. 7,400.00

B. 5,000.00

C. 8,000.00

Correct D. 5,391.30

Correct Answer: D

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Question 16 View Details

An entrepreneur wishes to discount a 180‑day bill of exchange with a face value of $\text{₦}10{,}000$. The bank offers a discount rate of 20% per annum calculated on a discount basis (i.e., Discount = rate $\times$ face value $\times$ $t/365$). The entrepreneur requires that the amount he receives after discount be at least $\text{₦}9{,}500$.\n\n(a) What is the greatest number of days, $t$, for which the bill can be discounted while still meeting his requirement?\n\n(b) For that discount period, calculate the effective annual interest rate that the bank is earning on the amount actually received.

A. Maximum discount period = 85 days; Effective annual interest rate ≈ 19.8%

Correct B. Maximum discount period = 91 days; Effective annual interest rate ≈ 21.1%

C. Maximum discount period = 95 days; Effective annual interest rate ≈ 22.4%

D. Maximum discount period = 100 days; Effective annual interest rate ≈ 24.0%

Correct Answer: B

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Question 17 View Details

A trader imports goods costing $\$8{,}000$. He pays freight equal to 5% of the cost and insurance equal to 2% of the sum of cost and freight. He also pays customs duty of 12% on the total of cost, freight and insurance. What is the total landed cost of the goods?

A. ₦9,800.25

B. ₦9,450.00

C. ₦9,300.50

Correct D. ₦9,596.16

Correct Answer: D

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Question 18 View Details

A wholesaler purchases a product at $\text{₦}150$ per unit and sells to retailers at a list price of $\text{₦}250$ per unit. He offers a 10% discount on the list price for orders of at least 200 units. His monthly fixed costs are $\text{₦}30{,}000$ and his only variable cost is the purchase price. The wholesaler wants to earn a profit of at least $\text{₦}20{,}000$ in a month. What is the minimum number of units he must sell (including any discount) to achieve this target?

A. 700 units

B. 660 units

Correct C. 667 units

D. 650 units

Correct Answer: C

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Question 19 View Details

Three partners A, B and C start a partnership with capital contributions of $\text{₦}120{,}000$, $\text{₦}80{,}000$ and $\text{₦}100{,}000$ respectively. The partnership agreement provides each partner a monthly salary of $\text{₦}5{,}000$ and interest on capital at 8% per annum (simple). At the end of the year the partnership records a net profit of $\text{₦}300{,}000$ before salaries and interest are paid. Determine the total amount each partner receives (salary + interest + share of remaining profit).

A. A: ₦110,000; B: ₦92,000; C: ₦98,000

Correct B. A: ₦108,000; B: ₦92,000; C: ₦100,000

C. A: ₦108,000; B: ₦90,000; C: ₦102,000

D. A: ₦107,000; B: ₦93,000; C: ₦100,000

Correct Answer: B

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Question 20 View Details

A retailer stores a product in a warehouse. Annual demand is 12,000 units, uniformly distributed throughout the year. The ordering cost is $\text{₦}2{,}000$ per order. Holding cost is 25% of the unit cost per year; the unit cost is $\text{₦}150$. Lead time is 10 days. The retailer wants a 95% service level, and demand during lead time follows a normal distribution with mean equal to the average demand during lead time and standard deviation equal to 10% of that mean. Determine:\n\n(a) the Economic Order Quantity (EOQ);\n(b) the safety stock required for the 95% service level;\n(c) the reorder point (ROP) in units;\n(d) the total annual inventory cost (ordering + holding + safety‑stock holding cost).

Correct A. EOQ ≈ 1,131 units; Safety stock ≈ 54 units; ROP ≈ 383 units; Total annual inventory cost ≈ ₦44,464

B. EOQ ≈ 1,200 units; Safety stock ≈ 60 units; ROP ≈ 420 units; Total annual inventory cost ≈ ₦45,800

C. EOQ ≈ 1,050 units; Safety stock ≈ 45 units; ROP ≈ 350 units; Total annual inventory cost ≈ ₦43,200

D. EOQ ≈ 1,300 units; Safety stock ≈ 70 units; ROP ≈ 470 units; Total annual inventory cost ≈ ₦47,600

Correct Answer: A

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Question 21 View Details

An electronics firm plans to sell (5{,}000) units of a new product. It can advertise by TV spots or by a social‑media campaign. • Each 30‑second TV spot costs ₦150,000, reaches 20,000 viewers and has a conversion rate of 2 % (i.e. each viewer buys the product with probability 0.02). • The social‑media campaign requires a set‑up fee of ₦2,000,000 and a cost of ₦500 per click. Each click converts at 5 % (probability 0.05). The firm can run at most (8) TV spots because of scheduling limits. Determine the number of TV spots and the number of social‑media clicks that will achieve the sales target at the minimum total advertising cost. State the total cost.

A. 8 TV spots and 30,000 social‑media clicks; total cost ₦20,500,000

B. 9 TV spots and 35,000 social‑media clicks; total cost ₦22,300,000

Correct C. 8 TV spots and 36,000 social‑media clicks; total cost ₦21,200,000

D. 7 TV spots and 38,000 social‑media clicks; total cost ₦20,800,000

Correct Answer: C

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Question 22 View Details

An investor purchases shares of XYZ Ltd. as follows: • Day 1: 1,200 shares at ₦45 each, commission 0.5 % of the transaction value. • Day 2: 800 shares at ₦48 each, commission 0.5 % of the transaction value. Later the investor sells 1,500 shares at ₦52 each, paying a commission of 0.5 % of the sale value and a securities transaction tax (STT) of 0.1 % of the sale value. Calculate the investor's overall profit (or loss) on the shares sold, rounded to the nearest naira.

A. ₦8,120 profit

Correct B. ₦7,886 profit

C. ₦6,450 profit

D. ₦7,100 loss

Correct Answer: B

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Question 23 View Details

ABC Ltd needs ₦10 million for a new project. It can obtain the funds by either: Option A - a bank loan of ₦10 million at 12 % per annum payable annually. An arrangement fee of 2 % of the loan amount is charged at the start, and the loan is to be repaid in equal annual instalments over 5 years. Option B - issuing 10‑year debentures of ₦10 million at 10 % per annum payable semi‑annually. An issue cost of 1.5 % of the amount is payable at issuance, and only interest is paid each half‑year; the principal is repaid at the end of 10 years. Which option results in the lower total cash outflow during the first 5 years? State the total cash outflow for the preferred option.

A. Option B, total cash outflow ₦5,250,000

B. Option A, total cash outflow ₦5,100,000

Correct C. Option B, total cash outflow ₦5,150,000

D. Option A, total cash outflow ₦5,300,000

Correct Answer: C

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Question 24 View Details

A retailer stocks two products, A and B. Annual demand: $D_A = 12{,}000$ units, $D_B = 8{,}000$ units. Holding cost per unit per year: $h_A = ₦2$, $h_B = ₦3$. The ordering cost for a combined order (which may contain both products) is $S = ₦5{,}000$. Because of limited space, the average total inventory ( $\frac{Q_A}{2} + \frac{Q_B}{2}$ ) cannot exceed 5,000 units. Assuming the retailer orders the two items together so that the order cycle is the same for both products, determine the order quantities $Q_A$ and $Q_B$ that minimise the total annual cost (ordering plus holding) while satisfying the space constraint. Give the quantities to the nearest whole unit.

A. Q_A ≈ 5,200 units, Q_B ≈ 4,000 units

Correct B. Q_A ≈ 5,477 units, Q_B ≈ 3,651 units

C. Q_A ≈ 5,300 units, Q_B ≈ 3,800 units

D. Q_A ≈ 5,600 units, Q_B ≈ 3,400 units

Correct Answer: B

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Question 25 View Details

A company must move (1{,}200) tonnes of raw material from Port X to Factory Y. Two transport modes are available: • Rail: fixed cost per trip ₦150,000, variable cost ₦30 per tonne, maximum load 400 tonnes per trip. • Road: fixed cost per trip ₦80,000, variable cost ₦45 per tonne, maximum load 200 tonnes per trip. Because of rail‑track maintenance, at most two rail trips can be scheduled. Determine the number of rail trips and road trips (whole trips only) that will meet the required quantity at minimum total cost, and state that minimum cost.

A. 0 rail trips and 6 road trips; total cost ₦534,000

Correct B. 2 rail trips and 2 road trips; total cost ₦502,000

C. 1 rail trip and 3 road trips; total cost ₦429,000

D. 2 rail trips and 1 road trip; total cost ₦413,000

Correct Answer: B

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