Benefit Cost Analysis Questions and Answers

Answer: A

Correct answer: public sector projects

A private firm can measure its returns in its own receipts, but a public agency’s project produces benefits accruing to people who pay nothing directly - time saved, floods averted, lives spared. Benefit cost analysis exists to bring those into the same account as the money spent, which is why it belongs to the public sector.

Answer: B

Time saved by road users, floods averted and lives preserved are all benefits, and they are counted whoever in the community happens to receive them. Amounts the sponsoring agency itself spends are costs rather than benefits.

Answer: C

Noise from a new road, land taken from farmers and habitat destroyed are disbenefits, and they enter the analysis with a negative sign. Where they are put, in the numerator or the denominator, is what distinguishes the two ratio conventions.

Answer: D

Correct answer: the government or sponsoring agency

The costs in the denominator are the sponsor’s outlays: construction, land, operation and maintenance. What the public gives up appears elsewhere, as a disbenefit, and the contractor’s costs enter only through the price the agency pays. Keeping the perspective consistent is what prevents the same effect being counted twice.

Answer: A

Correct answer: costs

\[ B/C = \frac{B - D}{C}. \] Disbenefits are subtracted from benefits in the numerator, leaving the denominator as the agency’s costs alone. This is the conventional form, and it must be identified as such because the modified form gives a different number from the same figures.

Answer: B

Correct answer: denominator, added to costs

\[ B/C_{mod} = \frac{B}{C + D}. \] The modified convention treats a disbenefit as a cost borne by the public rather than as a benefit forgone. Since it moves a positive quantity from being subtracted above to being added below, it always gives a smaller ratio than the conventional form for an acceptable project.

Answer: C

Correct answer: accept-or-reject decision

Both conventions cross unity at exactly the point where net present worth crosses zero, since \( B - D > C \) and \( B > C + D \) are the same inequality rearranged. The numerical values differ and so may rankings, but whether a project passes does not depend on which form was used.

Answer: D

Correct answer: at least one

A ratio of one means the discounted benefits net of disbenefits exactly equal the discounted costs, so the project just earns the discount rate. Above one it is worth doing; below one it is not. The discount rate is already inside the calculation, which is why the criterion is unity rather than the rate itself.

Answer: A

Correct answer: zero

\[ \frac{B-D}{C} = 1 \quad\Longleftrightarrow\quad B - D - C = 0. \] The two criteria are the same statement written differently, which is why benefit cost analysis and present worth analysis never disagree about whether a single project should proceed.

Answer: B

The ratio is unchanged whether both are annualised or both discounted to the present, since the same capital recovery factor divides out of numerator and denominator alike. Mixing the two bases produces a meaningless number.