Introduction

Government agencies evaluating AI investments typically use deterministic ROI calculations that assume on-time, on-budget delivery with full adoption. These calculations ignore well-documented risk factors specific to both public sector procurement and AI technology deployment. This paper presents a Monte Carlo simulation framework that incorporates two categories of empirically-grounded failure modes: (1) general government project risks documented in public administration literature, and (2) AI-specific technical risks absent from standard ROI tools.

We apply the framework to two illustrative case studies — tax administration in Brazil and municipal services in Saudi Arabia — to demonstrate how failure-adjusted projections differ from deterministic estimates. We present these as illustrative applications of the methodology, not as generalizable findings.

Risk Taxonomy

Category 1: Government Project Risks

These risks apply to any large-scale government technology project:

Category 2: AI-Specific Technical Risks

These risks are unique to AI/ML deployments and absent from standard government IT risk frameworks:

These AI-specific factors compound with standard government risks, increasing the gap between deterministic and failure-adjusted projections.

Methodology

Monte Carlo Simulation

We run 5,000 simulations per case study. Each simulation samples from all risk distributions simultaneously and computes NPV at government-appropriate discount rates:

$$\text{NPV}$$i = \sum{t=0}^{T} \frac{B_t \cdot \alpha_i(t) \cdot m_i \cdot d_i^t - C_t \cdot o_i}{(1+r)^t}

where:

• $\alpha_i(t)$ is the adoption S-curve with sampled ceiling and procurement delay
• $m_i$ is the sampled benefit multiplier
• $d_i$ is the annual model degradation factor
• $o_i$ is the cost overrun multiplier
• Benefits and costs are zeroed after any sampled defunding year

The adoption S-curve follows a logistic function: $\alpha(t) = \frac{\alpha_{ceil}}{1 + e^{-0.8(t - t_{delay} - 3.5)}}$

Input Parameter Estimation

Investment and benefit estimates are derived from comparable government technology procurements:

Brazil — Tax Administration AI:

• Investment: BRL 450M. Derived from Brazil's Receita Federal technology modernization budget allocations (BRL 300-500M range for major system overhauls, per Receita Federal Annual Report 2023) and comparable international tax AI procurement scales (HMRC Connect: GBP 100M+, ATO analytics: AUD 200M+).
• Annual benefit estimate: BRL 1,700M at full adoption. Composed of: (a) revenue uplift of BRL 1,100M based on 0.05% of BRL 2.2T tax collection — the benchmark reference is HMRC Connect which achieved approximately 1.5% uplift (reported in UK NAO, HMRC's Approach to Tackling Tax Evasion and Avoidance, HC 978, Session 2022-23, p. 24); we apply a deep discount to account for Brazil's more complex tax environment; (b) BRL 600M in operational efficiency from audit targeting, error reduction, and compliance deterrence effects.
• Benefit multiplier: Uniform(0.5, 1.5). This represents uncertainty around the already-discounted base estimate, not around the original benchmark. Since our base estimate (0.05%) is already at 1/30th of the HMRC benchmark (1.5%), the multiplier captures whether actual performance is even lower than our conservative base (0.5x) or somewhat better (1.5x) — noting that even at 1.5x, the estimate remains at only 1/20th of the HMRC benchmark. The range is consistent with the general parameter uncertainty ranges specified in UK HM Treasury, The Green Book 2022, Supplementary Guidance, for early-stage appraisals where empirical calibration data is unavailable.

Saudi Arabia — Municipal Services AI:

• Investment: SAR 280M. Estimated based on comparable international municipal AI procurement scales (Singapore BCA CORENET: SGD 150M+; Dubai Smart Dubai operations investments of similar magnitude reported in municipal annual reports) and Saudi government technology spending patterns documented in OECD Government at a Glance 2023.
• Annual benefit estimate: SAR 470M at full adoption. Composed of: (a) SAR 250M labor cost savings from 20% reduction in expatriate municipal operations workforce — conservative relative to Singapore's reported 35% operational efficiency gains (Singapore BCA, Annual Report 2022/2023); (b) SAR 220M in processing efficiency, fee acceleration, and error reduction.
• Benefit multiplier: Uniform(0.5, 1.5), same basis as Brazil — uncertainty around the already-conservative base estimate.

Discount Rates

• Brazil: 8%. Reflects Brazilian sovereign risk premium. The Brazilian Central Bank SELIC rate was 10.5% in Q3 2024; 8% represents a real discount rate appropriate for long-term government investment appraisal.
• Saudi Arabia: 6%. Reflects lower sovereign risk and sovereign wealth fund benchmark returns. Saudi Arabia's credit rating (Fitch: A+) supports a lower risk premium.

Results

Case Study 1: Brazil Tax Administration

Sensitivity ranking: Adoption ceiling (highest impact), benefit multiplier, procurement delay, model degradation rate, cost overrun. The dominance of adoption and benefit parameters over cost parameters indicates that the primary risk is whether the system achieves operational integration, not whether it can be built.

Case Study 2: Saudi Arabia Municipal Services

Saudi Arabia shows slightly higher P(NPV>0) than Brazil despite lower BCR, driven by lower political defunding risk (3% vs 5%) attributable to the centralized Vision 2030 mandate.

Context: Historical Government IT Outcomes

We compare our failure-adjusted BCRs against published outcomes from comparable (not identical) government technology programs:

Our estimates fall within the range of historical outcomes. This suggests plausibility but does not constitute validation — the comparison is between different project types, scales, and institutional contexts.

Discussion

Contribution and Scope

This paper contributes a simulation framework, not a generalizable finding. The deterministic-vs-adjusted gaps observed in our two case studies (ratios of 2.5x and 2.6x) are illustrative of the methodology's output, not a universal correction factor. Establishing a reliable correction factor would require application to a large sample of completed government AI projects with known outcomes — a dataset that does not yet exist.

AI-Specific vs General IT Risks

The inclusion of AI-specific risk factors (data drift, algorithmic bias, talent scarcity, model degradation, vendor concentration) distinguishes this framework from standard government IT risk assessment. To quantify their marginal impact, we ran the Monte Carlo twice for each case study: once with only government project risks (Category 1) and once with both categories. The difference in median NPV was 12% for Brazil and 9% for Saudi Arabia — an 8-12% additional reduction driven primarily by model degradation (cumulative accuracy loss reducing benefits by 15-45% over 10 years) and talent cost premiums (20-80% higher personnel costs).

Limitations

1. Two case studies provide illustration, not evidence of generalizability. The framework must be applied to additional sectors, countries, and — critically — retrospectively to completed projects before any generalizable conclusions can be drawn.
2. Input parameters are estimates. While we derive them from published benchmarks with documented reasoning, they are not verified against actual project data from Brazil or Saudi Arabia.
3. The benefit multiplier range is based on HM Treasury guidance for general IT projects. AI-specific benefit uncertainty may follow a different distribution. Empirical calibration from completed government AI deployments would improve this parameter.
4. AI risk factor distributions are estimated from general ML deployment literature, not government-specific studies. Government AI deployment failure modes may differ systematically from private sector patterns documented in the ML literature.
5. No ex-post validation. The framework has not been tested against actual government AI project outcomes.

Conclusion

We present a Monte Carlo simulation framework for government AI investment appraisal that incorporates both standard public sector project risks and AI-specific technical risks. Application to two case studies demonstrates substantial gaps between deterministic and failure-adjusted projections, driven primarily by adoption uncertainty and benefit estimation rather than cost factors. The framework is intended as a practical tool for government analysts preparing investment cases, not as a source of generalizable correction factors. Validation against actual completed government AI project outcomes is the necessary next step.

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