Rate of Return Analysis Questions and Answers

Answer: C

Correct answer: 6 years

The receipts must now cover the interest as well, so \( 10{,}000 \times (P/A, 10\%, n) \) must reach 40,000. At five years the factor is 3.791, giving 37,910 - not enough; at six years it is 4.355, giving 43,553. Recovery therefore falls in the sixth year, two years later than the simple calculation suggested.

Answer: D

Correct answer: the dearer alternative, the increment earning above 10 per cent

The individual rates of 22 and 16 per cent are not the criterion. The question is whether the extra money spent on the dearer alternative earns its keep, and at 13 per cent against a requirement of 10 it does. The dearer alternative is chosen even though its own rate of return is the lower of the two.

Answer: A

Correct answer: the cheaper alternative, the increment failing the test

Nothing about the projects has changed - only the required rate. The increment earning 13 per cent no longer clears a 15 per cent hurdle, so the extra investment is not justified and the cheaper alternative wins. Both remain acceptable in themselves, since 22 and 16 per cent both exceed 15; it is the increment between them that fails.

Answer: B

Correct answer: 20 per cent

For a perpetuity the present worth is \( A/i \), so setting it equal to the outlay gives \[ i = \frac{A}{P} = \frac{20{,}000}{100{,}000} = 0.20. \] The absence of any terminal date makes this the simplest of all rate of return calculations, and it is a useful approximation for a very long-lived asset.

Answer: C

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

Every discounting method carries a reinvestment assumption, stated or not. Present worth assumes intermediate receipts earn the minimum attractive rate, which is usually reasonable. The internal rate assumes they earn the computed rate itself, which for a project returning 60 per cent is optimistic. The modified rate exists precisely to make that assumption explicit and defensible.

Answer: D

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

Three situations, three correct responses. Two sign changes threaten multiple roots, so present worth or a modified rate is the safe course. Mutually exclusive alternatives of different scale require incremental analysis in order of first cost. And a single conventional investment can simply have its internal rate compared with the required rate, since the root is unique.

Answer: A

Correct answer: 2, 4, 1, 3

Order by first cost, take the cheapest acceptable alternative as the defender, then test each increment upward against the required rate, replacing the defender whenever an increment passes. Whatever is left standing at the end is the choice. Testing increments before the ordering is established gives increments that mean nothing.

Answer: B

Correct answer: 1 and 3 only are correct

Statements 1 and 3 are correct: the internal rate carries an implicit reinvestment assumption at its own value, and Descartes’ rule allows at most two positive roots for two sign changes. Statement 2 is the central error of the method - a rate is a ratio and ignores scale, so the highest rate need not identify the best alternative.

Answer: C

Correct answer: choosing whichever root exceeds the required rate

The other three are legitimate: computing a modified rate, compounding the positives forward at a stated rate (which is how the modified rate is formed), and falling back on present worth all give a defensible answer. Picking whichever root happens to clear the hurdle is not analysis but selection of a convenient number, since no root is the project’s return.

Answer: D

Correct answer: it accounts for the time value of money

The simple payback treats a pound received in year five as equal to one received today, which is exactly the defect the discounted form was devised to remedy. The other three are all true, including the second - measuring exposure is the legitimate use of the method, provided it is not asked to measure profitability as well.