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Give step-by-step solution with explanation and final answer:Decision on whether to launch a new product A company is currently manufacturing at only 60% of full practical capacity, in each of its two production departments, due 10 a reduction in market share. The company is secking to launch a new product which it is hoped will recover some lost sales. The estimated direct costs of the new product, Product X, are to be established from the following information: Direct materials: Every 100 units of the product will require 30 kilos net of Material A. Losses of 10% of materials input are to be expected. Material A costs £5.40 per kilo before discount. A quantity discount of 5% is given on all purchases if the monthly purchase quantity exceeds 25,000 kilos, Other materials are expected to cost £1.34 per unit of Product X. Direct labour (per hundred units): Department 1: 40 hours at £12.00 per hour. Department 2: 15 hours at £13.00 per hour. Scparate overhead absorption rates arc established for cach production department. Department | overheads are absorbed at 130% of direct wages, which is based upon the expected overhead costs and usage of capacity if Product X is launched. The rate in Department 2 is to be established as a rate per direct labour hour also based on expected usage of capacity. The following annual figures for Department 2 are based on full practical capacity: Overhead: £5,424,000 Direct labour hours: 2,200,000 Variable overheads in Department | are assessed at 40% of direct wages and in Department 2 are £1,980,000 (at full practical capacity). Variable overheads in Department | are assessed at 40% of direct wages and in Department 2 are £1,980,000 (at full practical capacity). Non-production overheads are estimated as follows (per unit of Product X) Variable: £0.70 Fixed: £1.95 The selling price for Product X is expected to be £16 per unit, with annual sales of 2,400,000 units. Required: (a) Determine the estimated cost per unit of Product X. (13 marks) (b) Comment on the viability of Product X. (7 marks) (¢) Market research indicates that an alternative selling price for Product X could be £15.50 per unit, at which price annual sales would be expected to be 2,900,000 units. Determine, and comment briefly upon, the optimum selling price & marks)

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Give step-by-step solution with explanation and final answer:Uploaded ImageUploaded ImageDecision on whether to launch a new product A company is currently manufacturing at only 60% of full practical capacity, in each of its two production departments, due 10 a reduction in market share. The company is secking to launch a new product which it is hoped will recover some lost sales. The estimated direct costs of the new product, Product X, are to be established from the following information: Direct materials: Every 100 units of the product will require 30 kilos net of Material A. Losses of 10% of materials input are to be expected. Material A costs £5.40 per kilo before discount. A quantity discount of 5% is given on all purchases if the monthly purchase quantity exceeds 25,000 kilos, Other materials are expected to cost £1.34 per unit of Product X. Direct labour (per hundred units): Department 1: 40 hours at £12.00 per hour. Department 2: 15 hours at £13.00 per hour. Scparate overhead absorption rates arc established for cach production department. Department | overheads are absorbed at 130% of direct wages, which is based upon the expected overhead costs and usage of capacity if Product X is launched. The rate in Department 2 is to be established as a rate per direct labour hour also based on expected usage of capacity. The following annual figures for Department 2 are based on full practical capacity: Overhead: £5,424,000 Direct labour hours: 2,200,000 Variable overheads in Department | are assessed at 40% of direct wages and in Department 2 are £1,980,000 (at full practical capacity). Variable overheads in Department | are assessed at 40% of direct wages and in Department 2 are £1,980,000 (at full practical capacity). Non-production overheads are estimated as follows (per unit of Product X) Variable: £0.70 Fixed: £1.95 The selling price for Product X is expected to be £16 per unit, with annual sales of 2,400,000 units. Required: (a) Determine the estimated cost per unit of Product X. (13 marks) (b) Comment on the viability of Product X. (7 marks) (¢) Market research indicates that an alternative selling price for Product X could be £15.50 per unit, at which price annual sales would be expected to be 2,900,000 units. Determine, and comment briefly upon, the optimum selling price & marks)

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Asked by: Nishant Saini
Created at: 2025-09-27 10:34:05

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Let's break down the solution step-by-step as required: --- # (a) Estimated Cost per Unit of Product X ## **1. Direct Materials Costs** ### **Material A:** - Every 100 units require **30 kg net**. - 10% loss → Input required = 30 / (1 - .10) = **33.33 kg per 100 units** - Per unit: 33.33 kg / 100 = **.3333 kg per unit** #### **Material A Cost Calculation:** - Cost per kg before discount = £5.40 - Monthly purchase > 25,000 kg ⇒ 5% discount - Discounted price = £5.40 × .95 = **£5.13 per kg** - Cost per unit = .3333 × £5.13 = **£1.71** ### **Other Materials:** - Cost per unit = **£1.34** ### **Total Direct Materials per unit:** - £1.71 (Material A) + £1.34 (Other) = **£3.05** --- ## **2. Direct Labour** ### **Department 1:** - 40 hours per 100 units = .40 hours/unit - Rate: £12/hour - Cost per unit = .40 × £12 = **£4.80** ### **Department 2:** - 15 hours per 100 units = .15 hours/unit - Rate: £13/hour - Cost per unit = .15 × £13 = **£1.95** ### **Total Direct Labour per unit:** - £4.80 + £1.95 = **£6.75** --- ## **3. Production Overheads** ### **Department 1:** - 130% of direct wages - Dept 1 direct wages/unit = .40 × £12 = £4.80 - Overheads/unit = 130% × £4.80 = **£6.24** ### **Department 2:** - Overhead rate = Total overheads / Total DLH = £5,424,000 / 2,200,000 = **£2.465/hour** - DLH per unit = .15 - Overheads/unit = .15 × £2.465 = **£.37** ### **Total Production Overheads per unit:** - £6.24 + £.37 = **£6.61** --- ## **4. Variable Overheads** ### **Department 1:** - 40% of direct wages - Dept 1 direct wages = £4.80 - Variable overhead = 40% × £4.80 = **£1.92** ### **Department 2:** - Total variable OH: £1,980,000 for 2,200,000 hours = £.90/hour - Hours per unit = .15 - Overhead per unit = .15 × £.90 = **£.135** ### **Total Variable Overheads per unit:** - £1.92 + £.135 = **£2.06** --- ## **5. Non-Production Overheads** - Variable: £.70 per unit - Fixed: £1.95 per unit --- ## **6. Total Cost per Unit** | Cost Component | £ per unit | |--------------------------|------------| | Direct Materials | 3.05 | | Direct Labour | 6.75 | | Production Overheads | 6.61 | | Variable Overheads | 2.06 | | Non-production Variable | .70 | | Non-production Fixed | 1.95 | | **Total** | **21.12** | --- # (b) Comment on Viability **Selling Price = £16.00** **Cost per unit = £21.12** **Loss per unit = £5.12** Since the cost per unit (£21.12) exceeds the selling price (£16.00), Product X would generate a loss of £5.12 per unit. For expected annual sales (2,400,000 units), the total annual loss would be: - Annual Loss = 2,400,000 × £5.12 = **£12,288,000** **Conclusion:** Product X is **not viable** at the proposed cost and selling price. --- # (c) Alternative Selling Price Analysis - **New price:** £15.50 per unit - **Expected annual sales:** 2,900,000 units - **Cost per unit (from above):** £21.12 **Loss per unit = £21.12 - £15.50 = £5.62** - Total loss = 2,900,000 × £5.62 = **£16,298,000** At this lower price, the loss is **even higher**. ## **Optimum Price** **The optimum price, based on the given costs, is the highest possible selling price.** Neither £16.00 nor £15.50 per unit covers the cost, so the project is not financially viable **unless costs can be reduced** or the selling price increased above £21.12 per unit. --- ## **Summary Table** | Price | Units Sold | Profit/(Loss) per unit | Total Profit/(Loss) | |---------|------------|-----------------------|---------------------| | £16.00 | 2,400,000 | £(5.12) | £(12,288,000) | | £15.50 | 2,900,000 | £(5.62) | £(16,298,000) | --- ## **Final Answers** ### **(a)** Estimated cost per unit: **£21.12** ### **(b)** Product X is **not viable** at either selling price based on current costs. ### **(c)** The optimum price is **the highest possible**; both £16.00 and £15.50 result in substantial losses. --- If you need **detailed step-by-step calculations for any cost component** or a more concise summary, just ask!

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