The Bridge That Was Not Built
A development bank is appraising two competing uses of a 9 billion taka allocation in a riverine district. Option A is a bridge that would cut travel time to the district town from 3 hours to 40 minutes for an estimated 22,000 daily users. Option B is a package of rural feeder roads, small irrigation, and a cold-storage facility serving 60,000 farm households. The bridge's traffic forecast assumes 6 percent annual growth in vehicles, based on the last decade, but the district's main crop has recently faced a disease outbreak and out-migration is rising. The appraisal manual requires an economic rate of return above 12 percent and a benefit-cost ratio above 1.2. The bridge's preliminary economic IRR is 13.4 percent; the rural package's is 11.1 percent but it has a benefit-cost ratio of 1.35 against the bridge's 1.22. The bank's board meets in a month.
1. The two options appear to give contradictory rankings under IRR and benefit-cost ratio. Explain why this can happen and which criterion should govern here.
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Why rankings can conflict. The IRR and the benefit-cost ratio can rank projects differently when the projects differ in scale and in the time profile of costs and benefits.
- The bridge is large and front-loaded in cost, with benefits that accrue over a long life. Its IRR of 13.4 percent is just above the 12 percent hurdle, and its BCR of 1.22 is just above 1.2.
- The rural package is smaller and more granular, with benefits that begin earlier (irrigation and cold storage yield returns within a season or two). Its IRR of 11.1 percent is below the 12 percent hurdle, yet its BCR of 1.35 is higher.
The apparent contradiction is resolved by remembering that the IRR is a rate and the BCR is a ratio of discounted totals. A project can have a high BCR and a lower IRR if its benefits are spread over a long horizon and discounted heavily, or if its costs are small relative to benefits but the net return per taka invested is high. Conversely, the bridge's IRR clears the hurdle but its BCR is thin - it is a large, marginal project.
Which should govern. Two rules matter:
- The hurdle is a constraint, not a ranking device. The manual says IRR must exceed 12 percent. The rural package at 11.1 percent fails the hurdle as stated. That is a real problem for the appraisal, not a technicality.
- When projects differ in scale, BCR is the better ranking device if the budget is fixed at 9 billion and cannot be split. But if the rural package can be scaled or phased, the correct comparison is the marginal BCR of each taka.
Judgement. The bank cannot simply pick the higher BCR while ignoring the failed hurdle. It should first re-examine the rural package's IRR - if its benefits are understated (e.g., cold storage reduces post-harvest loss that is not monetised), the IRR may clear 12 percent, in which case it dominates on both criteria. If not, the honest conclusion is that the manual's dual criteria are inconsistent and the board must decide which binds.
2. Assess the robustness of the bridge's 13.4 percent IRR to the stated risks. What sensitivity analysis would you demand before the board vote?
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The IRR is fragile. It clears the 12 percent hurdle by only 1.4 percentage points. That is a thin margin against a traffic forecast that is the single largest driver of benefits.
Why the forecast is suspect.
- The 6 percent vehicle growth is extrapolated from the last decade. But the district's main crop has a disease outbreak and out-migration is rising. Both are negative shocks to the demand for crossings. Extrapolating past growth through a structural break is the classic forecasting error in transport appraisal.
- The 22,000 daily users is a point estimate with no stated range. If actual traffic is 15 percent below forecast, the IRR likely falls below 12 percent, because benefits scale roughly with traffic while costs are fixed.
Sensitivity analysis to demand.
- Switching values. Find the traffic level at which IRR = 12 percent. If that is, say, 18,500 users, the project fails on a 16 percent shortfall - well within forecast error. This single number should decide the vote.
- Scenario analysis with a disease-and-out-migration scenario, not just a symmetric ±10 percent band. The downside is skewed; symmetric sensitivity hides it.
- Growth-rate sensitivity: rerun with 2 percent and 0 percent vehicle growth, not just 6 percent.
Other sensitivities to demand.
- Travel-time valuation. Time savings are the main benefit; the value of time assumed for a largely agricultural population should be checked against local wages, not national averages.
- Construction cost overrun. Bridges routinely overrun; test +20 percent and +40 percent.
- Optimism bias correction. Apply the standard uplift to both costs and demand.
Recommendation. The board should not vote on a point-estimate IRR of 13.4 percent. It should require the switching value on traffic and a downside scenario. If the project fails at plausible traffic shortfalls, the thin BCR margin (1.22 vs 1.2) confirms it is marginal, and the board should either defer the bridge pending crop recovery evidence or reallocate toward the rural package after re-appraising its IRR.