# Appendix A Ranking by benefit-cost ratio

Chapter 3 suggested a broad initial prioritisation of initiatives (e.g. priorities A, B and C) for program development. It also pointed to several possible approaches that could assist jurisdictions if they choose to undertake more detailed prioritisation. Ranking by benefit–cost ratio (BCR) was one of those techniques. BCR is the ratio of economic benefit to economic cost of a proposed initiative.

If the BCR accounts for all benefits and costs, economic efficiency (i.e. net economic benefit to society, where net benefit is benefits less costs) is maximised by undertaking initiatives in descending order of BCR until the budget is exhausted. This approach identifies the package of initiatives that yields the maximum combined net benefit out of all the possible packages of initiatives that fit within the budget constraint. Objectives other than economic efficiency will be advanced if they are consistent with economic efficiency.

This appendix discusses some issues related to ranking initiatives by BCR.

## A. 1 Combinations of initiatives

Ranking by BCR is not guaranteed to give the best economic efficiency outcome if initiatives are large relative to the budget constraint and, after funding the last initiative that can be afforded, there are still some funds left over. To demonstrate this: consider an example where after funding higher-BCR initiatives, there is $100 million left in the budget. The next three proposals in the BCR order of merit are A (cost$50 million, BCR 4.0), B (cost $100 million, BCR 3.5) and C (cost$50 million, BCR 2.0).

After funding initiative A, the remaining $50 million is insufficient to pay for initiative B. Initiative C, however, could be included. The total benefits from implementing initiatives A and C together would be [$50m × 4.0] + [$50 million × 2.0] =$300 million. However, if the $100 million were used instead to fund initiative B, the total benefits would be$100 × 3.5 = $350 million. Different combinations may have to be tested to find the best (maximum net present value) combination out of all possible combinations that fit within the budget constraint. ## A. 2 Borrowed funds and marginal BCR Under a budget-constrained approach, government agencies should seek to shift funds through time by borrowing or lending at the discount rate to fund projects where the BCR for the marginal initiative (or the cut-off point) is consistent over time. To demonstrate this, say that the marginal BCR is 2.0 this year and will be 3.0 next year. If$1 of capital spending was shifted from this year’s budget to next year’s budget, society would forgo $2 in benefits. The$1 could be invested elsewhere for the year so it would be worth $1 × (1 + r) next year, where r is the discount rate. The benefit from investing this amount in next year’s initiatives would be$3 × (1 + r), which is worth $3 when discounted back to this year. The net gain to society is$1 in benefit in present value terms. As more funds are shifted from this year to next year, the marginal BCR this year will rise and the marginal BCR next year will fall. When the point is reached at which the marginal BCRs are equal, no further gains can be made by shifting funds through time.

The implication for governments is that investment budgets should be expanded in times when there is a strong demand for funds (expressed in greater numbers of initiatives with high BCRs) and contracted in times when demand is weak, with a view to maintaining a fairly constant cut-off BCR over the long term.

## A. 3 Incremental BCR and staged initiatives

A further source of complexity is staged initiatives. There may be a choice to delay a stage or stages of an initiative until a later period. For ranking in the present period, subsequent stages of the initiative may be treated as separate initiatives with the incremental BCR used for ranking.

## A. 4 Combining BCR and SMT results

A government might give a more (or less) strategically meritorious initiative a higher (or lower) score (or ranking) than the initiative would receive from consideration of the BCR alone. Such decisions might be facilitated by having multiple levels of pass for the SMT. For example, there could be a ‘high pass’ and a ‘low pass’. An initiative with a ‘high pass’ on the SMT could be accorded preference over an initiative with a higher BCR but a ‘low pass’ on the SMT. For proposals where non-monetised factors are likely to play a greater role in decision-making, having multiple levels of pass for the SMT is a useful method.

The advantage of multiple levels of pass for the SMT is that this approach can be used to highlight initiatives that score particularly well on achieving government objectives. Examples include small initiatives or initiatives in less-populous areas that cannot be accepted on the basis of the CBA alone. Multiple levels of pass for the SMT can also increase the transparency and consistency of the assessment process.

An enhancement is to link SMT pass levels with BCR hurdle levels. However, if the number of levels of SMT pass is set far above 2, the assessment process may become overly complicated, with considerable subjectivity introduced in determining ratings of initiatives.

## A. 5 BCR hurdles

The use of hurdles for BCRs is optional. A decision has to be made about whether to employ a hurdle ratio and, if so, whether initiatives with a BCR below the hurdle ratio should be rejected.

When BCR hurdles are used, a ratio of 1.0 implies that uneconomic initiatives (i.e. initiatives with negative net present value) should be rejected. When funds are scarce relative to the supply of initiatives with BCRs above 1.0, the hurdle ratio should be set well above 1.0 if it is to be an economically efficient rationing mechanism.

It is important to decide whether the assessment process should include the flexibility to accept initiatives that are assessed to be poor on economic efficiency grounds, whether in absolute terms (that is, BCR<1.0) or relative to other initiatives. Presumably, those initiatives would be attractive on other grounds if they were to be accepted. The trade-off of greater flexibility to accept less efficient initiatives is that the program will be tilted in a way that gives less weight to the economic efficiency objective. BCR hurdles provide a safeguard against this.

There are several ways to use a BCR hurdle, with at least five options being available:

• Hurdle BCR: A hurdle BCR is specified and any proposal that falls below the hurdle is rejected outright. It might be decided to set a higher hurdle ratio for the rapid CBA than for the detailed CBA, because of the greater likelihood of optimism bias in projections of costs and benefits for the rapid CBA. A lower hurdle ratio might be set for off-network initiatives in low-demand regional areas.
• Hurdle BCR = 1.0: No uneconomic initiatives will be accepted.
• Multiple hurdle ratios: This option is linked with the idea of having multiple levels of pass for the SMT. For example, under a two-tier system, there would be a lower hurdle ratio for initiatives that achieve a high pass on the SMT and a higher ratio for initiatives with a low pass. Table A.1 illustrates the concept.
• No hurdle ratio: Governments may accept low-BCR initiatives, including uneconomic initiatives, in preference to high-BCR initiatives where they are considered to have high strategic merit or perform well on the adjusted CBA or are particularly effective in meeting certain objectives favoured by the decision-maker.
• Quota system: An upper limit could be imposed on the percentage of funds applied to initiatives with BCRs below the hurdle ratio (1.0 if the quota is to prevent economically inefficient initiatives). Some jurisdictions impose a percentage target (e.g. 95 per cent) for funds spent on economically justified initiatives (BCR above 1.0).

Some of these options allow equity considerations to be injected into the decision-making process.

Table 1: Two-tier Strategic Merit Test pass - BCR hurdle system
SMT
BCR Fail Low pass High pass
Below lower BCR hurdle Reject Reject Reject
Between lower and upper BCR hurdle Reject Reject Accept
Above upper BCR hurdle Reject Accept Accept