Delivered equipment costing 3 million with a Lang factor of 4.7 gives a total installed cost of about
Answer: C
Multiplying the equipment cost by the factor gives 14.1 million, the balance covering piping, instruments, structures, erection and engineering. It is a budget-class figure and should be quoted with an accuracy of the order of plus or minus thirty per cent.
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On an 80 per cent learning curve with a first unit taking 100 hours, the second unit takes
Answer: D
Correct answer: 80 hours
\[ 100 \times 0.80 = 80\ \mathrm{hours}. \] The percentage applies each time cumulative output doubles, and the second unit is the first doubling. It applies to the doubling rather than to each successive unit, which is what the next item makes clear.
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On that same curve the fourth unit takes
Answer: A
Correct answer: 64 hours
The fourth unit is the second doubling, so the factor is applied twice: \[ 100 \times 0.80^2 = 64\ \mathrm{hours}. \] Doublings come at 1, 2, 4, 8 and 16, so improvement is rapid at first and then slows - the eighth unit takes 51.2 hours and the sixteenth 41.
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Between the fourth and the eighth unit on that curve the time saved per unit is
Answer: B
The fourth unit takes 64 hours and the eighth 51.2, a difference of 12.8, whereas the first doubling saved 20 hours. The proportional reduction at each doubling is unchanged, but the absolute saving shrinks as the base falls, which is why late learning is worth less.
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Direct material is 40, direct labour 25 and direct expenses 5. The prime cost is
Answer: C
Correct answer: 70
\[ 40 + 25 + 5 = 70. \] All three are direct costs traceable to the job, and nothing else enters prime cost. This figure is the base of the build-up that the following items continue.
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With factory overhead at 60 per cent of direct labour, the works cost on that prime cost of 70 is
Answer: D
Correct answer: 85
Factory overhead is 60 per cent of the direct labour, not of the prime cost: \[ 70 + 0.60 \times 25 = 70 + 15 = 85. \] Applying the percentage to the prime cost instead gives 112, which is offered here and is the usual slip in this calculation.
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With administration overhead at 10 per cent of works cost, the cost of production on that works cost of 85 is
Answer: A
Correct answer: 93.5
\[ 85 \times 1.10 = 93.5. \] Administration overhead is taken on works cost, so the base changes at each stage of the build-up - direct labour for the factory overhead, works cost for the administration overhead. Reading which base applies is the substance of the exercise.
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Adding selling and distribution of 5 to that cost of production of 93.5 gives a total cost of
Answer: B
Correct answer: 98.5
\[ 93.5 + 5 = 98.5. \] Selling and distribution is given as an absolute figure here rather than a percentage, and adding it to the cost of production completes the total cost. Nothing further is added before the profit.
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Adding a profit of 20 per cent of total cost to that 98.5 gives a selling price of about
Answer: C
Correct answer: 118.2
\[ 98.5 \times 1.20 = 118.2. \] The profit is stated as a percentage of total cost, so it is added to it. Had it been quoted as a margin on the selling price the arithmetic would differ - 98.5 divided by 0.8 gives 123.1, which is offered here and is what that alternative reading produces.
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Overhead of 480 000 absorbed over 24 000 labour hours gives an absorption rate of
Answer: D
Correct answer: 20 per hour
\[ \frac{480{,}000}{24{,}000} = 20\ \mathrm{per\ hour}. \] The absorption rate spreads the overhead over the chosen base, so each job is charged 20 for every direct labour hour it consumes. The choice of base - labour hours, machine hours, material cost - determines how the overhead is distributed among jobs.
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