Replacement Analysis Questions and Answers

Answer: C

Correct answer: 65 000, the market value plus the repair

Keeping the machine costs two things: the 40,000 that must be spent on it, and the 25,000 that could have been had by selling it instead. Together those are the investment in retention. The 100,000 paid five years ago is sunk and identical whichever course is chosen, so it plays no part.

Answer: D

Correct answer: 224 700

\[ 200{,}000 \times 1.06^2 = 200{,}000 \times 1.1236 = 224{,}720. \] Note this is compounding rather than simple addition: two years at six per cent is 12.36 per cent, not 12. Over longer deferrals the difference grows and the rising challenger price becomes a real argument against waiting.

Answer: A

Correct answer: 1-Q, 2-P, 3-R

The three figures have quite different standing. The market value is the investment forgone by keeping the asset, and it is the defender’s first cost for the purposes of the study. The original first cost is sunk and irrelevant. And the book value matters only because it fixes the taxable gain or loss on disposal.

Answer: B

Correct answer: 1-Q, 2-P, 3-R

Two opposing trends and their resultant. Capital recovery falls as the investment is spread over more years; operating and maintenance costs rise as the asset ages; and their sum, falling at first and rising later, passes through a minimum. That minimum is the economic service life.

Answer: C

Correct answer: 2, 3, 1, 4

Establish what keeping the defender actually costs by finding its market value; establish the best the challenger can do by finding its minimum annual cost; compare the defender’s marginal cost for the next year with that figure; and decide. Reversing the first two steps is harmless, but comparing before either is established is not.

Answer: D

Correct answer: 1 and 2 only are correct

Statements 1 and 2 are correct: the original first cost is sunk, and the economic service life is where the total annual cost is least. Statement 3 confuses accounting with economics - depreciation is a bookkeeping allocation, and an asset fully written down may still be the cheapest way to do the job.

Answer: A

Correct answer: the market value of the existing asset

Only the market value is relevant, because only it represents money that a decision now can affect: keeping the asset forgoes the proceeds a sale would bring. The purchase price, the depreciation charged and the interest already paid are all history, identical under either course.

Answer: B

Correct answer: the asset has become fully depreciated

Full depreciation is an accounting state, not an economic one: the asset may run perfectly well and cost less than anything that could replace it. The other three are genuine reasons - changed requirements, rising operating costs and the availability of something better are precisely what replacement analysis exists to evaluate.

Answer: C

Correct answer: sunk and identical whichever course is taken

The 400,000 has gone and cannot be recovered by either decision, so it cannot distinguish between them. Keeping an uneconomic machine to avoid admitting the loss simply adds the excess running costs to that loss. The relevant figures are the machine’s market value now and the costs of the two courses from here on.

Answer: D

Correct answer: may give the wrong answer and the full annual cost comparison is needed

The one-more-year rule assumes the marginal cost rises steadily, so that the first year it exceeds the challenger’s figure is the right year to replace. A cost that falls again in year 4 breaks that assumption: replacing at the first crossing could forgo a cheaper later period, so the defender’s annual cost must be evaluated over each possible retention period instead.