Benefit Cost Analysis Questions and Answers

Answer: A

Where the outcome is lives saved or examinations passed, the analysis compares cost per unit of outcome rather than forcing a monetary value onto it. It can rank alternatives delivering the same kind of outcome but cannot say whether any is worth doing.

Answer: B

Correct answer: the project is worth undertaking at all

Cost effectiveness compares alternatives on cost per unit of outcome and can say which is the cheapest way to achieve something, which is valuable where the benefit resists monetary valuation. What it cannot say is whether the outcome is worth its cost, because that comparison requires both sides in the same units.

Answer: C

Benefits less disbenefits gives 450 000, and dividing by the 300 000 of agency cost gives 1.50. The project is acceptable, the ratio comfortably exceeding unity, which is the same conclusion a positive present worth would give.

Answer: D

Correct answer: 1.43

The modified convention puts the disbenefit into the denominator: \[ \frac{500{,}000}{300{,}000 + 50{,}000} = \frac{500}{350} = 1.43. \] The conventional form gave 1.50 on the same figures, and both exceed one - which illustrates the point that the two agree on the decision while differing on the number.

Answer: A

The capital recovery factor at 8 per cent for twenty years is 0.10185, and multiplying by 2 million gives 203 700. Comparison must be on the same basis, so the first cost is annualised rather than the benefits capitalised.

Answer: B

Dividing 250 000 of annual benefit by 203 700 of annualised cost gives 1.227. The project is acceptable at 8 per cent, though not by a wide margin, so the discount rate assumed will matter a great deal to the conclusion.

Answer: C

Correct answer: 0.93

\[ \mathrm{annual\ cost} = 2{,}000{,}000 \times 0.13388 = 267{,}760, \qquad \frac{250{,}000}{267{,}760} = 0.93. \] At 8 per cent the same project gave 1.23 and was acceptable; at 12 per cent it fails. Nothing about the project has changed - only the rate - which is why the discount rate is so often the decisive assumption.

Answer: D

Correct answer: 1.00

\[ \frac{\Delta B}{\Delta C} = \frac{1.9 - 1.4}{1.5 - 1.0} = \frac{0.5}{0.5} = 1.00. \] The extra half million buys exactly half a million of benefit, so the increment is on the margin: it neither adds nor destroys value, and the choice between P and Q must rest on considerations outside the arithmetic.

Answer: A

Individual ratios cannot decide between mutually exclusive alternatives because they ignore scale. Here the increment's ratio is exactly unity, so the extra half million is neither worth spending nor worth withholding.

Answer: B

The product of the hours saved and the value per hour gives 12 million a year of benefit. That value per hour is a shadow price rather than a market price, and it is usually the most contested figure in the whole study.