Present Worth and Annual Worth Analysis Questions and Answers

Answer: C

Correct answer: differ only in their costs

Where the alternatives provide the same service, revenues are identical and cancel out of the comparison, leaving only costs. It is then clearer to work with equivalent uniform annual cost, in which the better alternative is the smaller figure, than with an annual worth that would be negative for both.

Answer: D

The revenues must be identical for them to cancel, which is what service equivalence means. Where one alternative gives better output or longer availability, that difference has to be valued and brought into the comparison.

Answer: A

The invested capital must be recovered and interest paid on it throughout, and the salvage receipt reduces what has to be recovered. The usual form multiplies the first cost less salvage by the capital recovery factor and adds interest on the salvage.

Answer: B

Part of the capital is recovered at disposal instead of having to be earned from operations, so less must be recovered annually. Being at the far end of the life, however, it is discounted heavily and often matters less than expected.

Answer: C

Correct answer: effectively perpetual

\[ CC = \frac{A}{i}. \] Capitalised cost is the sum which, invested at \( i \), would fund the annual cost for ever. It is the natural treatment for bridges, dams, roads and endowments - assets with no meaningful terminal date - and it is simply the present worth of a perpetuity.

Answer: D

It is the limiting case of the series present worth factor as the number of periods tends to infinity, the factor tending to one over i. The interest on that principal exactly meets the annual cost for ever, leaving the capital intact.

Answer: A

Selecting one rules all the others out, as with competing designs for the same bridge or competing machines for the same duty. Independent projects, by contrast, may be chosen in any combination subject only to the budget.

Answer: B

Correct answer: select the combination with the greatest total present worth within the budget

Independent projects can be taken in any combination, so the problem is to choose the set that maximises total present worth subject to the budget. This is not the same as taking them in order of present worth: a large project may crowd out two smaller ones worth more between them.

Answer: C

If no action is a real possibility, it is the baseline against which the others must justify themselves. Where a service must be provided somehow, do-nothing is infeasible and the comparison is between the active alternatives only.

Answer: D

Correct answer: cannot be changed by any choice now available

A cost already incurred is identical whichever course is now taken, so it cannot distinguish between the alternatives and must be excluded from both sides. It is not that the money did not matter - only that no decision available now can affect it.