Present Worth and Annual Worth Analysis Questions and Answers

Answer: A

Correct answer: what the asset would actually fetch

Market value is an economic quantity established by what a buyer would pay; book value is an accounting one, being cost less accumulated depreciation under whatever method was chosen. The two are related only by coincidence, and it is the market value that enters a replacement decision because only it represents money forgone.

Answer: B

A high rate penalises distant cash flows, so the alternative whose burden lies in the future is treated more leniently and the capital-intensive one loses its advantage. The ranking can reverse at some rate, which is the crossover point.

Answer: C

Correct answer: crossover or incremental rate of return

At the crossover rate the two alternatives have identical present worths and the preference between them reverses. It is the internal rate of return of the incremental cash flow, and knowing where it lies relative to the minimum attractive rate is what makes an incremental comparison decisive.

Answer: D

First costs and operating costs can often be estimated closely, whereas the appropriate rate is a matter of judgement. Showing that the ranking holds over a plausible range of rates is what makes a recommendation robust.

Answer: A

Correct answer: 13 730

\[ PW = -100{,}000 + 30{,}000 \times (P/A, 10\%, 5) = -100{,}000 + 30{,}000 \times 3.7908 = 13{,}724. \] The undiscounted receipts total 150,000, so discounting removes some 36,000 of apparent value - which is the whole point of the calculation.

Answer: B

Multiplying the present worth of 13 730 by the capital recovery factor of 0.2638 gives 3622 a year. The positive sign agrees with the present worth, as it always must, since the two differ only by a positive multiplier.

Answer: C

Correct answer: 15 820

\[ EUAC = 50{,}000(A/P, 10\%, 10) + 8{,}000 - 5{,}000(A/F, 10\%, 10) \] \[ = 50{,}000 \times 0.16275 + 8{,}000 - 5{,}000 \times 0.06275 = 8{,}138 + 8{,}000 - 314 = 15{,}824. \] Note the salvage enters through the sinking fund factor and reduces the annual cost, since it is a receipt at the end rather than a payment.

Answer: D

Dividing 12 000 by 0.06 gives 200 000, which is the principal whose interest alone would meet the cost for ever without touching the capital. Halving the interest rate would double the capitalised cost, so the figure is highly rate-sensitive.

Answer: A

Correct answer: 9255

\[ EUAC_A = 20{,}000 \times (A/P, 10\%, 10) + 6{,}000 = 20{,}000 \times 0.16275 + 6{,}000 = 3{,}255 + 6{,}000 = 9{,}255. \] The two components pull in opposite directions between the alternatives: A is cheap to buy and dear to run, and B the reverse.

Answer: B

Correct answer: 9196

\[ EUAC_B = 35{,}000 \times 0.16275 + 3{,}500 = 5{,}696 + 3{,}500 = 9{,}196. \] B is cheaper by 59 a year, which on figures of this size is well inside the accuracy of the estimates. The honest conclusion is that the two are effectively equal and that other considerations should decide.