A machine has a market value of 30 000, will be worth 22 000 in a year, will cost 9000 to run and the rate is 10 per cent. Its marginal cost for the year is
Answer: A
Lost interest on the 30 000 of market value is 3000, the fall in that value over the year is 8000, and operating cost adds 9000, giving 20 000 in all. That figure is what one more year of the old machine actually costs the firm.
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If the challenger's minimum equivalent uniform annual cost is 18 000, that defender should be
Answer: B
Correct answer: replaced now, its marginal cost being higher
The defender’s marginal cost for the coming year works out at 20,000 - 8,000 of value lost, 3,000 of interest on the 30,000 tied up, and 9,000 to run it. Against a challenger able to provide the service for 18,000 a year, keeping the defender costs 2,000 more, so it should be replaced now.
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If instead the challenger's minimum annual cost were 24 000, that defender should be
Answer: C
The defender's 20 000 for another year is cheaper than the challenger's 24 000, so retention is right for now and the test is simply repeated next year. The decision is revisited annually rather than settled once and for all.
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An asset costing 60 000 with a salvage of 20 000 after 3 years has, at 10 per cent, a capital recovery cost of about
Answer: D
Taking the first cost less salvage times the capital recovery factor and adding interest on the salvage gives 40 000 times 0.40211 plus 2000, that is 18 084. The equivalent form, 60 000 times 0.40211 less 20 000 times 0.30211, gives 18 085, which is the check.
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A defender's equivalent annual cost over its economic life is 22 000 and the challenger's is 22 200. The defender should be
Answer: A
Correct answer: kept, though the margin is within estimating error
On the figures the defender is marginally cheaper, so it is kept - but 200 in 22,000 is under one per cent, far inside the accuracy of any forecast of future maintenance or salvage. The honest report says the two are effectively equal and lets non-economic factors, such as reliability or capacity, settle it.
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An asset with a first cost of 50 000 and no salvage has capital recovery at 10 per cent over 2 years of about
Answer: B
Correct answer: 28 810
\[ A = 50{,}000 \times (A/P, 10\%, 2) = 50{,}000 \times 0.5762 = 28{,}810. \] Spreading the cost over only two years leaves each year carrying more than half the purchase price, which is why capital recovery dominates the total annual cost of a young asset.
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For that same asset over 5 years the capital recovery is about
Answer: C
Correct answer: 13 190
\[ A = 50{,}000 \times (A/P, 10\%, 5) = 50{,}000 \times 0.2638 = 13{,}190. \] Extending the life from two years to five cuts the capital recovery by more than half. That steep fall is what makes keeping an asset attractive, and it is only checked when maintenance costs rise fast enough to overtake it.
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An asset's annual costs are 19 000 at a 3-year life, 17 500 at 4 years, 17 200 at 5 years and 17 800 at 6 years. Its economic service life is
Answer: D
Correct answer: 5 years
The annual costs fall from 19,000 to 17,500 to 17,200 and then rise to 17,800, so the minimum is at five years. Note the shape: the curve is quite flat near the bottom, only 300 separating four years from five, which means the exact life matters much less than being somewhere near it.
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A defender's market value is 40 000 and its book value 55 000. Selling it at a 30 per cent tax rate gives net proceeds of
Answer: A
Correct answer: 44 500
The asset sells for less than its book value, giving a loss of \( 55{,}000 - 40{,}000 = 15{,}000 \) and a tax saving of \( 0.30 \times 15{,}000 = 4{,}500 \). Net proceeds are therefore \[ 40{,}000 + 4{,}500 = 44{,}500. \] A loss on disposal is worth having in cash terms, since it shelters other income from tax.
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Had that same defender's book value been 28 000 rather than 55 000, the net proceeds of sale would have been
Answer: B
A book value below the market value turns the disposal into a taxable gain of 12 000, costing 3600, instead of a deductible loss worth 4500. The same asset at the same price therefore yields 8100 less in cash purely because of its depreciation history.
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