Rate of Return Analysis Questions and Answers

Answer: C

Correct answer: use the present worth method instead

Present worth at the minimum attractive rate is unambiguous, requires no root-finding, and gives the right accept-or-reject decision whatever the shape of the cash flow. Choosing among several roots is arbitrary, since none of them is the project’s return in any meaningful sense.

Answer: D

Correct answer: is not necessarily the best choice

The rate of return is a ratio and takes no account of scale. Earning 40 per cent on 10,000 adds less value than earning 18 per cent on 100,000 when the alternative use of money returns 10 per cent. Choosing between mutually exclusive alternatives therefore requires incremental analysis or a straight comparison of present worths.

Answer: A

The question is whether the additional capital required by the dearer alternative earns the minimum attractive rate, since that increment is what is actually being decided. If it does, the dearer alternative is preferred.

Answer: B

Correct answer: increasing first cost

The analysis proceeds by asking, of each additional increment of investment, whether that increment itself earns the required rate. That question only makes sense working upward from the cheapest alternative, so the ordering is by increasing first cost and the do-nothing option is the starting defender.

Answer: C

Correct answer: the dearer alternative is preferred

The extra money spent is itself earning more than the minimum attractive rate, so spending it is worthwhile even though the dearer alternative may show a lower overall rate of return. The dearer alternative then becomes the defender and is tested against the next one up.

Answer: D

Correct answer: currently held to be best

The defender is the incumbent - the alternative that has survived the comparisons made so far. Each further alternative challenges it, and the challenger replaces it only if the increment between them earns the required rate. The terminology comes from replacement analysis, where the defender is the asset already in service.

Answer: A

Where investment is genuinely optional, the cheapest active alternative must first justify itself against doing nothing at all. Where the service must be provided, do-nothing is infeasible and the cheapest alternative becomes the opening defender.

Answer: B

Correct answer: their present worths are equal

The crossover or Fisher rate is the discount rate at which two alternatives are equally attractive, and it is the internal rate of return of the incremental cash flow between them. On either side of it the preference reverses, which is exactly why comparing internal rates alone can mislead.

Answer: C

Correct answer: the higher first cost

At low discount rates, distant receipts retain most of their value, so the larger project - which typically has bigger cash flows further out - wins. As the rate rises those distant flows are penalised more heavily, and above the crossover rate the smaller, quicker-returning project takes the lead.

Answer: D

Correct answer: cumulative receipts to recover the first cost

Payback answers a single question: how long before the money is back. It is a measure of exposure rather than of profitability, which is why it is used alongside present worth or rate of return rather than instead of them.