The results are still useful in suggesting that in Africa the returns to MA may be up to 50% lower than in the US following Donaldson & Hornbeck (2016). A reason for this may be the prevalence of other market inefficiencies, often of a regulatory nature (Herrera Dappe et al., 2024). A prudent assumption is that in Africa MA gains translates into economic activity at a ratio of 4:1.

In the following, instead of computing exact returns, I determine the returns needed in order to break even. This will take the form of a reverse macroeconomic present discounted value (PDV) calculation. African GDP in 2022 was 2.81 trillion 2015 USD. The median growth rate in 2000-2022 was 4.1%. If we are pessimistic, let it be 3% going forward. I discount the future by 10%. This is a reasonable rate given that stock market returns are generally below this—the MSCI World has a long-term return rate of 8-9%. Emerging market bonds yield even lower returns, around 6%, according to the EMBI index by JP Morgan. So at the macroeconomic scale, it is very difficult to invest with more than 10% returns. I also assume that the horizon of policymakers is 30 years and disregard benefits accruing after 30 years. With these assumptions, I calculate the change in the macroeconomic growth rate of Africa needed to break even in PDV terms for each of the three scenarios proposed above as well as the full/consensus construction and upgrade scenarios considered in Sections 5.4 and 5.7. Table 8 reports these calculations.

Table 8: Break Even Changes in the Macroeconomic Growth Rate for Different Investments

|**Work Package**|**Cost**|**%**∆**MA**|**BEG** (4.1%)|**BEG** (3%)|
|---|---|---|---|---|
|Full Extension (_↑_RE)|$56.1B|3_._9_−_5_._5|0.31% _→_4.113|0.50% _→_3.015|
|Consensus Extension (_↑_RE)|$12.1B|2_._4_−_4_._0|0.07% _→_4.103|0.11% _→_3.003|
|Full Upgrade (_↑_TE)|$105.7B|27_._0_−_42_._1|0.58% _→_4.124|0.94% _→_3.028|
|Consensus Upgrade (_↑_TE)|$45.0B|21_._2_−_33_._1|0.25% _→_4.110|0.40% _→_3.012|
|All Links _>_$1/min/$|$60.9B|26_._8_−_38_._1|0.33% _→_4.114|0.54% _→_3.016|
|All Links _>_$2/min/$|$36.6B|24_._0_−_30_._6|0.20% _→_4.108|0.32% _→_3.010|
|All Links _>_$4/min/$|$17.0B|19_._5_−_20_._4|0.09% _→_4.104|0.15% _→_3.005|

_Notes:_ Table shows the cost in 2015 USD PPP of different investment packages, their MA %-gain under the worst frictions and frictionless scenarios, and the change in Africa’s macroeconomic growth rate needed to break even after 30 years under realistic (4.1%) and pessimistic (3%) baseline growth.

I illustrate their interpretation using the largest consensus package containing all links with _>_ $ 1/min/ $ marginal returns. It costs $ 60.9B and yields a MA gain between 26.8% (worst frictions scenario) and 38.1% (no frictions). Under the 4.1% baseline growth scenario, the growth rate needs to change by 0.33% to 4.114% to yield a return of $ 60.9B in PDV terms after 30 years. Comparing the 26.8% lower bound to 0.33% yields a ratio of 81:1. Thus, if changes in MA translate to changes in the growth rate at 81:1 or higher, the package is macroeconomically feasible.

This appears very plausible given the 0.5 elasticity of Donaldson & Hornbeck (2016) and the _∼_ 0.33 elasticity of Table 7 suggesting a ratio of 3:1 (prudent estimate is 4:1). However, many things can go wrong. First, growth could be slower at 3%, requiring a 0.54% increase in the growth rate or a return ratio above 50:1. Then, the package could end up being more expensive for various reasons related to terrain, weather, corruption or delays. Assuming it turns out twice as expensive, this would require a ratio above 25:1. Finally, if the investment is financed through debt, it could adversely affect both the total costs and the macroeconomic growth rate by limiting fiscal space and worsening credit ratings. Such forces could lower the required return ratio to as low as 10:1. Nevertheless, this is still above 4:1. Thus, overall, these back-of-the-envelope calculations suggest that large-scale _optimal_ investments in Africa’s road network are macroeconomically feasible.

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