Present Worth and Annual Worth Analysis Questions and Answers

Answer: A

Discounting at the minimum attractive rate of return means a non-negative present worth shows the project earns at least that rate. A negative figure means the money would do better in the alternative the rate represents.

Answer: B

Correct answer: earns exactly that rate and no more

A present worth of zero means the discounted receipts exactly cover the discounted outlays at the rate used, so the project returns precisely the minimum attractive rate. It is the break-even case: acceptable but with no margin, and the rate at which it occurs is the project’s internal rate of return.

Answer: C

Correct answer: the same study period

Present worth is an absolute quantity, so an alternative evaluated over ten years accumulates more of everything than one evaluated over five, whatever their relative merits. Comparing them on their own lives compares two different questions, which is why either the least common multiple or an explicit study period must be used.

Answer: D

Correct answer: repeated until the horizons coincide

If one alternative lasts four years and another six, both are assumed to be replaced by themselves until they reach twelve, and the whole twelve years is discounted. The assumption is that identical replacement will be available at the same cost - which is what makes the method sound or unsound depending on the case.

Answer: A

Correct answer: technology or costs will have changed before the repetition

The method rests on identical replacement, so it fails wherever that is implausible: fast-moving equipment, a changing cost base, or a service that will not be needed at the end. In such cases a defined study period with estimated market values is the honest treatment.

Answer: B

Correct answer: an estimated market value at the end of the period

Cutting the analysis short at the study period does not destroy the value remaining in the asset, so that value is brought in as a terminal cash inflow - the price it could actually be sold for at that date. Book value is an accounting figure and the original salvage value applies to a different date, so neither serves.

Answer: C

Correct answer: the end of the study period

Present worth, future worth and annual worth are three positions for the same equivalence and always agree in their ranking. Future worth places the equivalent sum at the horizon, which suits questions naturally asked in those terms - what a fund will be worth at the end, or what a project accumulates by a target date.

Answer: D

Correct answer: multiplying the present worth by the capital recovery factor

\[ AW = PW \times (A/P, i, n) = PW \times \frac{i(1+i)^n}{(1+i)^n - 1}. \] Dividing by the number of periods would ignore interest entirely, which is the arithmetic mistake this option is placed to catch.

Answer: A

Correct answer: needs no common study period for unequal lives

Because annual worth is already expressed per period, an alternative living four years and one living six can be compared directly - provided each is assumed to repeat at its own life, which is precisely the assumption the least common multiple makes explicit. It is the same assumption, arrived at with less arithmetic.

Answer: B

Correct answer: always give the same accept-or-reject decision

\( AW = PW \times (A/P, i, n) \), and the capital recovery factor is always positive, so multiplying by it cannot change a sign. A positive present worth therefore means a positive annual worth and the same decision. The two are the same measure expressed at different points in time.