## 2.1    No Minimum Tax

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### Permanent investment model (no taxes)
- Period 0: investment of I units of capital; profit π0 = −I.
- Period 1: accounting profit π1 = [(1+θ)(p+δ)] I, where θ is inflation, p is real economic return net of economic depreciation δ.
- Period 2: π2 = (1+θ)^2 (p+δ)(1−δ) I; continues until asset obsolescence.
- Net present value (NPV) of the investment:
  - ∑_{t=0}^{∞} π_t = −I + ∑_{t=1}^{∞} (1+θ)^t (p+δ) (1−δ)^{t−1} I / (1+i)^t = (p−r) I / (r+δ),
  - where i is the nominal interest rate and r is the real interest rate.
- Interpretation:
  - If p = r, economic rent is zero (marginal investment).
  - If p > r, the investment yields economic rent.
  - (p+δ) equals real return before depreciation, interest expense, and tax (EBIDTA).
- Note: (1+i) = (1+θ)(1+r).

### Standard corporate income tax (CIT) with tax depreciation φ
- Tax depreciation function φ; e.g., straight-line 5-year: φ = 20 percent annually.
- Taxable profit in period 0: π^T_0 = −φ(I).
- Taxable profit in period t (>0), before loss carryforward adjustment:
  - π_t = (1+θ)^t (p+δ) (1−δ)^{t−1} I − φ(K_t),
  - with K_0 = I, K_1 = I − φ(I), K_2 = I − φ(I) − φ(I − φ(I)), ...
- Assumption for comparability: tax value of losses is refundable or equivalently carried forward with interest (unless mentioned otherwise).
- Statutory CIT rate τ; investment fully equity-financed.
- Tax amounts each period:
  - T_0 = −τ φ(I).
  - T_t = τ (1+θ)^t (p+δ) (1−δ)^{t−1} I − τ φ(K_t) for t>0.
- NPV of total tax T (without time subscript):
  - T = −τ A + τ (p+δ) / (r+δ) I,
  - where A ≡ ∑_{t=0}^{∞} φ(K_t) / (1+i)^t and for convenience A/I ≡ ˜A.

### Average effective tax rate (AETR) under CIT (equity-financed)
- AETR = T / [ p/(r+δ) I ] = τ (1 + δ/p) − τ ˜A / [ p/(r+δ) ].
- Limits and comparative statics:
  - As δ/p → 0 and p/(r+δ) becomes very large, AETR → τ.
  - AETR increases as τ increases (given profitability) or as profitability declines (given τ).
  - Higher depreciation allowances lower AETR by raising A.
  - High inflation or less generous tax depreciation increases AETR by lowering A.
- Policy relevance:
  - AETR matters for discrete location choices for new investments by multinationals generating high profitability from proprietary assets.

### Investment distortion — marginal effective tax rate (METR)
- METR corresponds to marginal investment with no economic rent.
- METR = (p̃ − r) / p̃,
  - where p̃ = 1/(1−τ) ( r+δ − τ ˜A (r+δ) ) − δ.
- Without tax, marginal investment yields p = r.
- If METR = 0, marginal investment unaffected by tax; METR > 0 implies tax wedge making marginal investment unprofitable; METR < 0 implies marginal subsidy.
- Under CIT, equity-financed investment faces positive METR increasing in τ.

### Debt bias under standard CIT
- Debt-financed investments benefit from interest deductions → lower AETRs than fully equity-financed investments.
- For degree of debt financing 0 ≤ α ≤ 1, AETR becomes:
  - AETR = τ (1 + δ/p) − τ ˜A / [ p/(r+δ) ] − τ α ψ i,
  - where ψ > 0 is a composite parameter (ψ = (r+δ)/[ p [ i − θ + δ(1+θ) ]] ; see Appendix).
- Two elements of debt bias:
  - Interest deductions (term −τ α ψ i).
  - Interest deductions need not be tied to the normal return and can exceed it.
- Consequences:
  - METR for fully debt-financed investment can be negative due to excessive interest deductions.
  - Extent of negative METR depends on inflation, depreciation, and tax rate; higher inflation, higher depreciation, higher τ increase debt bias.
  - Example: at τ = 20 percent, AETR can decline from 23.1 percent (full equity-financing) to as low as 3.5 percent (full debt-financing, α = 1).
- Policy implication: literature calls for eliminating tax-favored debt treatment.

### Neutral alternatives and remaining distortion
- Comprehensive Business Income Tax (CBIT) treats debt as equity by denying interest deductions and exempting interest income → neutralizes debt bias; AETR on debt-funded investment under CBIT follows Equation 5.
- CBIT does not address investment distortion (METR remains > 0).
- Two efficient rent tax systems that address both investment distortion and debt bias: cash-flow taxation and the Allowance for Corporate Equity (ACE).
- Before analyzing those systems, importance of refunding losses for efficiency is highlighted.

### Role of refunding the value of tax losses
- Many CITs allow carrying losses forward but without interest; relaxing full-refundability increases NPV of the tax on investment.
- Modeling indefinite loss carryforward without interest (e.g., loss from period 0) increases T in Equation 4 by i/(1+i) φ(I).
- No closed-form expression for METR or AETR if losses generated in multiple periods; Appendix provides a routine for quantifying AETRs and METRs allowing multi-period loss carryforward.
- Key insight: given an investment profile and parameterization, AETRs and METRs are always higher (and NPV of tax depreciation lower) without full loss offset.
- Quantitative illustration:
  - For τ = 20 percent and fully debt-financed, AETR increases from 3.5 percent to 6.5 percent when full loss offset is relaxed (an increase in AETR of almost 45 percent).
  - In absence of full loss offset, interest deductions (with common depreciation schemes) can make METR zero — CIT non-distorting for investment but still distorting financial structure in favor of leverage. METR cannot be negative in this system (unless refundable tax credits exist).
- High inflation exacerbates impact of incomplete loss offset because CIT is imposed on nominal profit while inflation reduces real value of carried-forward amounts without interest.

*Source: 2.1 No Minimum Tax (original content unit).*

### 2.1    No Minimum Tax

### 2.1    No Minimum Tax

### Permanent investment model (no taxes)
- Period 0: investment of I units of capital; profit π0 = −I.
- Period 1: accounting profit π1 = [(1+θ)(p+δ)] I, where θ is inflation, p is real economic return net of economic depreciation δ.
- Period 2: π2 = (1+θ)^2 (p+δ)(1−δ) I; continues until asset obsolescence.
- Net present value (NPV) of the investment:
  - ∑_{t=0}^{∞} π_t = −I + ∑_{t=1}^{∞} (1+θ)^t (p+δ) (1−δ)^{t−1} I / (1+i)^t = (p−r) I / (r+δ),
  - where i is the nominal interest rate and r is the real interest rate.
- Interpretation:
  - If p = r, economic rent is zero (marginal investment).
  - If p > r, the investment yields economic rent.
  - (p+δ) equals real return before depreciation, interest expense, and tax (EBIDTA).
- Note: (1+i) = (1+θ)(1+r).

### Standard corporate income tax (CIT) with tax depreciation φ
- Tax depreciation function φ; e.g., straight-line 5-year: φ = 20 percent annually.
- Taxable profit in period 0: π^T_0 = −φ(I).
- Taxable profit in period t (>0), before loss carryforward adjustment:
  - π_t = (1+θ)^t (p+δ) (1−δ)^{t−1} I − φ(K_t),
  - with K_0 = I, K_1 = I − φ(I), K_2 = I − φ(I) − φ(I − φ(I)), ...
- Assumption for comparability: tax value of losses is refundable or equivalently carried forward with interest (unless mentioned otherwise).
- Statutory CIT rate τ; investment fully equity-financed.
- Tax amounts each period:
  - T_0 = −τ φ(I).
  - T_t = τ (1+θ)^t (p+δ) (1−δ)^{t−1} I − τ φ(K_t) for t>0.
- NPV of total tax T (without time subscript):
  - T = −τ A + τ (p+δ) / (r+δ) I,
  - where A ≡ ∑_{t=0}^{∞} φ(K_t) / (1+i)^t and for convenience A/I ≡ ˜A.

### Average effective tax rate (AETR) under CIT (equity-financed)
- AETR = T / [ p/(r+δ) I ] = τ (1 + δ/p) − τ ˜A / [ p/(r+δ) ].
- Limits and comparative statics:
  - As δ/p → 0 and p/(r+δ) becomes very large, AETR → τ.
  - AETR increases as τ increases (given profitability) or as profitability declines (given τ).
  - Higher depreciation allowances lower AETR by raising A.
  - High inflation or less generous tax depreciation increases AETR by lowering A.
- Policy relevance:
  - AETR matters for discrete location choices for new investments by multinationals generating high profitability from proprietary assets.

### Investment distortion — marginal effective tax rate (METR)
- METR corresponds to marginal investment with no economic rent.
- Solve for post-tax p̃ that makes post-tax economic rent zero by setting difference between Equations 4 and 1 to zero and solving for p̃ (user cost of capital).
- METR = (p̃ − r) / p̃,
  - where p̃ = 1/(1−τ) ( r+δ − τ ˜A (r+δ) ) − δ.
- Without tax, marginal investment yields p = r.
- If METR = 0, marginal investment unaffected by tax; METR > 0 implies tax wedge making marginal investment unprofitable; METR < 0 implies marginal subsidy.
- Under CIT, equity-financed investment faces positive METR increasing in τ.

### Debt bias under standard CIT
- Debt-financed investments benefit from interest deductions → lower AETRs than fully equity-financed investments.
- For degree of debt financing 0 ≤ α ≤ 1, AETR becomes:
  - AETR = τ (1 + δ/p) − τ ˜A / [ p/(r+δ) ] − τ α ψ i,
  - where ψ > 0 is a composite parameter (ψ = (r+δ)/[ p [ i − θ + δ(1+θ) ]] ; see Appendix).
- Two elements of debt bias:
  - Interest deductions (term −τ α ψ i).
  - Interest deductions need not be tied to the normal return and can exceed it.
- Consequences:
  - METR for fully debt-financed investment can be negative due to excessive interest deductions.
  - Extent of negative METR depends on inflation, depreciation, and tax rate; higher inflation, higher depreciation, higher τ increase debt bias.
  - Example: at τ = 20 percent, AETR can decline from 23.1 percent (full equity-financing) to as low as 3.5 percent (full debt-financing, α = 1).
- Policy implication: literature calls for eliminating tax-favored debt treatment.

### Neutral alternatives and remaining distortion
- Comprehensive Business Income Tax (CBIT) treats debt as equity by denying interest deductions and exempting interest income → neutralizes debt bias; AETR on debt-funded investment under CBIT follows Equation 5.
- CBIT does not address investment distortion (METR remains > 0).
- Two efficient rent tax systems that address both investment distortion and debt bias: cash-flow taxation and the Allowance for Corporate Equity (ACE).
- Before analyzing those systems, importance of refunding losses for efficiency is highlighted.

### Role of refunding the value of tax losses
- Many CITs allow carrying losses forward but without interest; relaxing full-refundability increases NPV of the tax on investment.
- Modeling indefinite loss carryforward without interest (e.g., loss from period 0) increases T in Equation 4 by i/(1+i) φ(I).
- No closed-form expression for METR or AETR if losses generated in multiple periods; Appendix provides a routine for quantifying AETRs and METRs allowing multi-period loss carryforward.
- Key insight: given an investment profile and parameterization, AETRs and METRs are always higher (and NPV of tax depreciation lower) without full loss offset.
- Quantitative illustration:
  - For τ = 20 percent and fully debt-financed, AETR increases from 3.5 percent to 6.5 percent when full loss offset is relaxed (an increase in AETR of almost 45 percent).
  - In absence of full loss offset, interest deductions (with common depreciation schemes) can make METR zero — CIT non-distorting for investment but still distorting financial structure in favor of leverage. METR cannot be negative in this system (unless refundable tax credits exist).
- High inflation exacerbates impact of incomplete loss offset because CIT is imposed on nominal profit while inflation reduces real value of carried-forward amounts without interest.

*Source: 2.1 No Minimum Tax (original content unit).*

### 2.3    Tax Incentives under a Standard CIT and a Minimum Tax

### 2.3    Tax Incentives under a Standard CIT and a Minimum Tax

### Types of domestic tax credits and their mechanical effects
- Pillar Two distinguishes two domestic tax credit types:
  - Qualified refundable tax credits (QRTCs): refundable as cash (or equivalents) within four years. QRTCs increase the covered income (denominator) by the full amount of the credit, causing the Pillar Two effective rate to decline.
  - Non-qualified refundable tax credits (NQRTCs): any other tax credits are deemed NQRTCs and reduce the covered tax (numerator).
- Comparative effect on Pillar Two effective rate:
  - A NQRTC lowers the Pillar Two effective rate by more than a QRTC of the same amount, and hence gives a higher τ topu p (Table 1).
- Notation and mechanics:
  - Let X denote the amount of the tax credit so that the domestic tax is (τπc t) − X t.
  - Average tax payments (ATR) in period t for QRTCs and NQRTCs are given as ATR_Q_t and ATR_NQ_t in Equations 12 and 13 (see source).
- Key formal result (Proposition 3, under full loss offset):
  - (a) Both QRTCs and NQRTCs increase the top-up tax by less than they reduce the amount of the total tax. Hence, the total tax is lower with either QRTCs or NQRTCs than under a CIT without tax credits.
  - (b) The QRTC implies a lower AETR than the NQRTC if the SBIE is low, and vice versa. The NQRTC leads to a lower AETR than the QRTC in the limit as SBIE → πc.
- Numerical illustration:
  - Fully equity-funded investment with pre-tax profitability of 20 percent and τ = 10 percent (minimum tax binding):
    - AETR without incentives: 15.3 percent.
    - AETR with QRTC: 12.3 percent.
    - AETR with NQRTC: 14.7 percent.
  - Marginal investment at τ = 10 percent:
    - METR with no incentives: 17.7 percent.
    - METR with QRTC: 6.9 percent.
    - METR with NQRTC: 16.5 percent.

### Implication summary for tax incentives under Pillar Two
- Tax credits reduce total tax compared to CIT without credits, but their impact on AETR and METR depends on credit type and SBIE.
- QRTCs are relatively more effective at lowering AETRs when SBIE is low; NQRTCs can be more effective as SBIE approaches πc.
- Pillar Two classification (QRTC versus NQRTC) alters whether credits affect numerator or denominator of the effective rate, producing different behavioral and distributional outcomes.

---

### 3    Cash-Flow Tax

### 3.1    No Minimum Tax — R-based cash-flow tax: definition and properties
- Tax base: net real transactions (R-based) — includes only real (non-financial) cash flows.
  - Gross inflows: sales, including sales of capital goods.
  - Gross outflows: all expenses including labor costs, and purchases of intermediate and capital goods.
  - Excludes: financial transactions like interest payments, variations in net debt, and dividend distributions.
- Loss treatment: immediate tax refunds or option to carry losses forward with an appropriate interest rate.
- Relation to CIT and immediate expensing:
  - R-based cash-flow tax differs from a CIT with immediate expensing combined with interest deductions.
- NPV of total tax under R-based cash-flow tax (Equation 14):
  - TR−based = −τI + τ(p−r)/(r+δ) I = τ(p−r)/(r+δ) I.
  - Decomposition:
    - First component: net present value of standard CIT payment overtime: −τA + τ(p+δ)/(r+δ) I.
    - Second component: reduction due to immediate expensing: −τI + τA = τ(A − I).
  - Comparative statics: higher τ (↑τ), higher discount rate (↓A), or lower standard depreciation rate (↓A) increases benefit of immediate expensing.
- AETR under R-based cash-flow tax (Equation 15):
  - AETR_R−based = τ(1 − r/p).
  - As economic rent increases (↑p), AETR converges to statutory τ because r/p → 0.
- Efficiency (Eliminating investment distortions):
  - Pre-tax economic rent = (p − r)/(r+δ).
  - Post-tax economic rent under cash-flow tax = (1 − τ)(p − r)/(r+δ).
  - Solving for user cost that sets post-tax economic rent to zero gives p̃ = r. If p = r, Equation 15 collapses to zero for any τ.
  - Therefore, METR = 0 for all τ: cash-flow tax is efficient — it does not affect the decision to undertake the marginal investment.
- Eliminating debt bias:
  - R-based cash-flow tax disallows interest deductions; Equation 15 lacks a −ταψi term. System is independent of financing mode and eliminates debt bias.
- R-based cash-flow tax vs. immediate expensing without refunds:
  - When losses are not refunded, N periods are needed to absorb losses; N decreases as p increases and for sufficiently high p, N = 1.
  - AETR in non-refundability scenario (Equation 16):
    - AETR_R−based, no refund = τ [1 − r/p] + [1 − Σ_{t=1}^N (1+θ)^t (p+δ) (1−δ)^{t−1} / (1+i)^t] / [p/(r+δ)] (see source).
  - METR formula: METR = (p̃ − r)/p̃ with p̃ defined implicitly (Equation 18).

### 3.2    A Minimum Tax with an R-based Cash-Flow System
- Pillar Two mechanics unchanged: Pillar Two effective rate unaffected by immediate expensing.
- Now πc t = πt − net interest deduction − loss refunds, reintroducing debt bias because top-up rate and base depend on financing.
- Effects by financing type:
  - Equity-financed investment:
    - Top-up tax can arise only if τ is below 15 percent; top-up rate τtopup t = 15% − τπc t / πc t = 15% − τ.
  - Debt-financed investment:
    - Top-up rate becomes smaller: τtopup t = 15% − τ(πc t + net interest deduction)/πc t.
    - Top-up base is same irrespective of financing.
- NPV of tax on equity-financed investment under Pillar Two (Equation 19):
  - TR−based,Pillar2 = τ(p−r)/(r+δ) I + max(0, 15% − τ) Σ_{t=1}^∞ max(0, (πc t − SBIE t))/(1+i)^t.
- AETR under Pillar Two (Equation 20):
  - AETR_R−based,Pillar2 = τ(1 − r/p) + max(0, 15% − τ) Σ_{t=1}^∞ max(0, (πc t − SBIE t))/(1+i)^t / [p/(r+δ)].
- Implications:
  - If τ > 15%, METR remains zero because no top-up applies.
  - If τ < 15% and πc t − SBIE t > 0 for at least one t:
    - Equity-funded investment: R-based cash-flow tax no longer efficient and METR > 0; resulting AETR higher than in absence of minimum tax.
    - Debt-funded investment: R-based cash-flow tax remains efficient with METR = 0 even in top-up region; resulting AETR same as absent minimum tax.
  - If πc t − SBIE t ≤ 0 ∀ t, no top-up tax applies and R-based cash-flow tax retains efficiency (METR = 0).
  - If τ ≥ 15%, R-based cash-flow tax retains efficiency for any investment and AETRs identical with or without minimum tax.
- Kink and counterintuitive comparative:
  - Minimum tax generates a kink in the AETR.
  - AETR can increase as statutory τ decreases when a top-up applies (upper right panel of Figure 4): raising τ up to 15 percent can be beneficial for the marginal investment because the top-up tax falls on normal return that would be untaxed if τ > 15 percent.
- Role of SBIE and intangibles:
  - When minimum tax binds, AETR increases as share of intangibles in total assets increases because SBIE declines.
  - For highly profitable investments, even if 50 percent of assets are intangibles, difference in AETRs is moderate, but extreme cases where SBIE eliminates top-up tax can produce large differences.
- Effect of non-refundability:
  - Without refund of tax losses, the zero METR result (without minimum tax) is abolished; METR and AETR increase in τ, with a kink at 15 percent.

---

### 4    ACE (Allowance for Corporate Equity)

### 4.1    Without a Minimum Tax — definition and evaluation
- ACE provides an allowance for normal returns to equity, maintaining neutrality with respect to financing mode.
  - Implemented either as allowance of corporate capital or as notional deductions for equity at the normal return rate (i).
- Neutrality properties:
  - ACE is neutral with respect to tax depreciation method under full refundability (Keen and King, 2002).
  - ACE is neutral with respect to inflation when allowance is specified correctly.
- Correct specification of ACE base:
  - Allowance must be calculated on the tax-depreciated value of capital Kt, not the non-depreciated initial investment I.
  - Formula in source (Equations 21 and 22) specify πT0 and πTt with ACE adjustments based on φ(Kt).
  - Allowance in period 0 is zero; in period 1 allowance applies to remaining non-depreciated value.
  - Mis-specifying ACE on the entire investment (non-depreciated value) leads to inflation-related and τ-related errors.
- Quantitative implications of mis-specification (Figure 5):
  - For marginal investment and τ = 15 percent, failing to account for depreciated value underestimates METR by 8 percentage points.
  - Correct model predicts zero METR irrespective of τ.
  - Underestimation of AETR declines as profitability increases; underestimation of METR is more severe than AETR at high profitability.
- Formal result (Proposition 5, under full loss offset and absence of minimum tax):
  - ACE implies the same AETR as the R-based cash-flow tax (Equations 14 and 15) and a zero METR.

### ACE: effects on investment distortion and debt bias
- Eliminating investment distortions:
  - METR under ACE is zero, so tax does not affect marginal investment decisions.
  - AETRs on economic rent under ACE match those under R-based cash-flow tax (with or without minimum tax).
- Eliminating debt bias:
  - ACE neutralizes tax-motivated financial structures because equity returns receive allowances similar to interest deductions.
  - Interest deduction under ACE is lower than under standard CIT:
    - Under standard CIT, deduction for debt in each period: i ((1+θ)(1−δ))^t ∀ t ≥ 0.
    - Under ACE, interest deduction accounts for normal return and is i(1−φ)^t ∀ t ≥ 1.
  - Neutrality under ACE depends on discount rate and requires allowance rate equals normal rate of return (at which interest is deducted).

_Italic: wpiea2024057-print-pdf — https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024057-print-pdf.pdf_

### 4.2    Introducing a Minimum Tax under an ACE

### 4.2    Introducing a Minimum Tax under an ACE

### Overview
- Under Pillar Two rules, the ACE can be classified either as QRTCs or NQRTCs (see Section 2.3). Full loss offset is needed for the efficiency of the ACE. Designing the ACE as a QRTC maintains full loss offset; relaxing refundability classifies the ACE as a NQRTC, which is inefficient even in the absence of a binding minimum tax. The NQRTC case reflects practice in some ACE countries that allow carrying the ACE forward without interest.

### The ACE as a QRTC and a Minimum Tax
- As a QRTC, the ACE raises covered profit, which lowers the Pillar Two effective rate (by raising the denominator), and thus the top-up tax rate increases as given by: max(0,15%− τπc t / (πc t + (τik t) ) ). The top-up tax base is πc t + (τik t) − SBIE t.
- Two immediate observations:
  - (i) the ACE top-up base is larger than that for the R-based cash-flow tax since (πc t + τik t − SBIE t) > (πc t − SBIE t);
  - (ii) the ACE top-up rate is always higher than the R-based top-up rate (Table 2).
- Combining modifications with Equation 14 (ACE yields identical expression for the AETR without a minimum tax), the NPV of the tax and corresponding AETR under a fully refundable ACE (as a QRTC) and a minimum tax are:
  - TACE+Pillar2 = [ τ(p−r) / (1+r) I ] + Σ_{t=1}^∞ max(0, 15% − [ τπ_t / π_t + τiK_t ]) max(0, (π_t + τiK_t − SBIE_t)) / (1+i)^t. (Equation 23)
  - AETRACE+Pillar2 = τ[1 − r/p] + Σ_{t=1}^∞ max(0, 15% − (τπ_t / π_t + τiK_t )) max(0, (π_t + τiK_t − SBIE_t)) / (1+i)^t p / (r+δ_I). (Equation 24)
- Example, in t=1:
  - τπ1 / π1 + τi(K1) = τ((1+θ)(p+δ)I − φ(I−φ)) / ((1+θ)(p+δ)I − φ(I−φ) + τi(I−φ(I))). (Equation 25)
  - Note that φ(I) is deducted from profit in period 1 because it is carried forward from period 0.
- Key insights:
  - TACE+Pillar2 > TR−based+Pillar2 (given τ) as long as π_t + τiK_t > SBIE_t in at least one t. Therefore, the AETR is higher under the ACE with a top-up tax than under the cash-flow tax with the top-up.
  - The lower the depreciation, the higher the effective rate of the ACE, widening the difference between systems.
  - The ACE is no longer neutral with respect to inflation: as inflation increases, TACE+Pillar2 goes up and the ACE moves further away from the R-based tax.
  - The AETR increases with τ and profitability and has a kink as previously shown (panel b of Figure 6).
  - Without any top-up tax, the AETRs for both systems coincide and the METR remains zero.

- Proposition 6. Under a minimum tax, an ACE that is regarded as a QRTC, and a full loss offset that is regarded as a timing measure for the top-up tax:
  - (a) The threshold τACE QRTC below which the top-up tax rate becomes strictly positive is given by:
    - τACE QRTC_t = 15% πc t / (πc t − 15%(iK_t)).
  - (b) If [ πc t + (τiK_t) − SBIE_t ] ≤ 0 ∀t, no top-up tax applies ∀τ, and the METR under the ACE is zero.
  - (c) If [ πc t + (τiK_t) − SBIE_t ] > 0 and τ < τACE QRTC_t for any t, then there is a top-up tax and the METR > 0.
  - (d) Under (c) above, the top-up tax amount and hence the METR are larger than under the R-based cash-flow tax, ceteris paribus.
- Proof: See Appendix.

- Figure 6 (calibration notes):
  - The figure assumes an inflation rate of 5%, a real interest rate of 5%, an economic depreciation rate of 25%, and a depreciation rate for tax purposes of 15%.
  - ‘Pure R or ACE’ depicts METR and AETR before introducing a minimum tax.
  - The ACE leads to a higher METR and AETR than the R-based cash-flow tax under a top-up tax.

### The ACE as a NQRTC and a Minimum Tax
- If tax loss refund is unavailable and the ACE is deemed a NQRTC:
  - Pillar Two effective rate declines because of a decrease in covered taxes by the amount of the ACE: 15% − τπc t − τiK_t / πc t, but the top-up base is not affected by this ACE: πc t − SBIE_t.
  - The ACE in this case has a METR > 0 even without a minimum tax.
- NPV of total tax and AETR for NQRTC ACE:
  - TACE,NQRTC = [ τ(p−r) / (r+δ) I ] + Σ_{t=1}^∞ max(0, 15% − τ(1 − iK_t / πc t )) max(0, (πc t − SBIE_t)) / (1+i). (Equation 26)
  - AETRACE,NQRTC = τ[1 − r/p] + Σ_{t=1}^∞ max(0, 15% − τ(1 − iK_t / πc t )) max(0, (πc t − SBIE_t)) / (1+i)^t p / (r+δ_I). (Equation 27)
- Example, in t=1:
  - 1 − iK1 / πc1 = 1 − i(I−φ(I)) / ((1+θ)(p+δ)I − φ(I−φ(I))). (Equation 28)

- Proposition 7. Under a minimum tax and an ACE that is regarded as a NQRTC:
  - (a) The threshold τACE NQRTC below which the top-up tax rate becomes strictly positive is given by:
    - τACE NQRTC = 15% πc t / (πc t − ik_t), and hence τACE NQRTC_t ≥ τACE QRTC_t ∀t.
  - (b) If [ πc t − SBIE_t ] ≤ 0 ∀t, no top-up tax applies ∀τ, but the ACE remains inefficient, with METR > 0, due to non-refundability.
  - (c) If [ πc t − SBIE_t ] > 0 and τ < τACE NQRTC_t for any t, then there is a top-up tax and the METR > 0.
  - (d) The top-up tax amount if the ACE is QRTC cannot exceed that if it is NQRTC.
- Proof: See Appendix.

- Comparative insights:
  - The threshold τ needed to prevent the top-up tax is lower when the ACE is classified as a QRTC than as a NQRTC, but remains higher than 15%.
  - Part (b) in both propositions indicates a situation of a very large SBIE sustained throughout the investment life; even then ACE is not efficient for all investments.
  - The higher top-up rate on the smaller base under the NQRTC can overcompensate, resulting in a higher top-up tax amount than under the QRTC ACE (unless SBIE_t = π_t ∀t).
  - Empirical illustration: METR for both the NQRTC ACE or cash-flow without refunds is about 15% at τ = 5%, whereas it is around 9%–10% in the QRTC case (panel (a) of Figure 6).

### The Tax Treatment of Losses Under Pillar Two
- Pillar Two provides for indefinite carryforward of losses, but treatment of tax-loss refunds or interest on loss carryforwards is unclear.
- The analysis so far assumes such policies do not affect the Pillar Two effective rate (treated like a temporary timing measure), or that the investment does not generate loss periods.
- This assumption gives lower bounds for METRs and AETRs since the Pillar Two effective rate is unaffected.
- If tax loss refunds are treated as QRTCs then:
  - (i) equivalence between loss carryforward with interest and refunding tax losses breaks (the former would then be NQRTCs);
  - (ii) the Pillar Two effective rate declines and thus METRs and AETRs become higher under a top-up tax than the baseline;
  - (iii) the ACE generally yields lower METRs and AETRs than the R-based cash-flow tax (Figure 7), because the ACE spreads credits over multiple years generating lower overall top-up taxes than the R-based cash-flow tax which gives large initial credits and hence top-ups.
- Policy implication: Pillar Two warrants rules regarding treatment of tax losses, ideally conducive to efficiency.

- Figure 7 (calibration notes):
  - Assumes inflation rate 5%, real interest rate 5%, economic depreciation rate 25%, tax depreciation rate 25%, assets entirely tangibles, payrolls comprise 50% of tangibles, SBIE is 150% of tangibles.
  - Both panels assume refunding the value of tax losses is considered a qualified refundable tax credit (QRTC) under Pillar Two.

### Putting It Together: Comparing the Effects of Different Tax Designs on Investment under a Minimum Tax
- Equity-funded investment (panel (a) of Figure 8) summary:
  - For any τ, METR is highest for commonly existing CIT systems that do not refund tax losses.
  - Switching to immediate expensing (without refunding losses) reduces METRs by multiple percentage points.
  - Under the R-based cash-flow tax, METR is zero as long as the minimum tax does not result in a top-up tax. With a top-up tax (e.g., τ = 10%), the R-based METR becomes positive but remains the lowest among designs.
  - The ACE outperforms the cash-flow tax if both systems do not allow refunding tax losses, especially absent a top-up tax.
- Debt-financed investment (panel (b) of Figure 8) summary:
  - Despite the minimum tax, METR can be negative under a CIT with full loss offset, driven by excessive interest deductions.
  - Interest deductions can compensate for denying refunding tax losses in the CIT, eliminating investment distortion (METR = 0) but encouraging corporate leverage.
  - Under ACE or cash-flow taxation, interest deductions are linked to the normal return; these systems do not generate negative METR even if tax losses are refunded.
- Two equivalent ways to make METR zero in the top-up region while being neutral with respect to financing decisions:
  - (i) define the top-up tax base as “EBIT_t − I_t” while allowing carryover with interest (apply τ × (EBIT_t − I_t) if EBIT_t − I_t < 0);
  - (ii) permit deductions for the normal return by modifying the top-up tax base to: “π_t − (ik_{t−1})”, also allowing carryover with interest.
  - Both options require allowing carry-forward of the value of tax losses with interest.
- Notable outcomes:
  - Under minimum taxation and common CITs that do not refund the value of tax losses, METR can be negative (a subsidy) despite a top-up tax (panel (c) of Figure 8). This is attainable for any τ with a large QRTS.
  - For debt-financed investment, credit amounts can be lowered by combining with debt deductions; for equity-funded investment, combination would be immediate expensing and a QRTC.
  - Engineering identical negative METRs irrespective of financing mode is challenging because credit size must depend on financing structure.
- Personal taxation interactions:
  - Under standard CIT, high personal taxes on interest income compared to dividends and capital gains reduce corporate debt bias given τ (King, 1974).
  - If equity and debt are taxed similarly at the individual level, ACE or cash-flow tax neutralizes corporate debt bias and retains zero-METR even after personal taxes. The minimum tax does not change this interlink between neutrality and personal taxation.

### Policy Conclusions and Implications
- The analysis establishes equivalence (in NPV terms) between ACE and cash-flow tax before introducing a minimum tax and highlights conditions required for that equivalence.
- Relaxing refunding of tax losses makes ACE and cash-flow tax inefficient and breaks their equivalence; without refunding losses, ACE results in a lower METR than the R-based cash-flow tax because the NPV of foregone refunds is lower.
- Under Pillar Two, the minimum tax can fall on the normal return and changes the balance between ACE and R-based cash-flow tax: both top-up rate and top-up base are higher under the ACE than under the R-based cash-flow tax for moderate to low statutory CIT rates.
- Pillar Two entails debt bias as it tolerates interest deductions but not notional deductions to equity.
- From a policy standpoint:
  - Avoiding the top-up tax with appropriate domestic economic rent tax design eliminates distortions to investment and financing structure.
  - Example: METR for new investments is zero under an R-based cash-flow tax with statutory CIT rate at least 15%. In this system, METR is zero for all investments, making a two-tier system redundant.
  - A global minimum tax design should not interfere with domestic efficient rent tax designs. Equivalence between efficient rent designs under minimum taxation can be achieved by defining the top-up tax base to reflect the normal return (e.g., EBIT after deducting investment and allowing carryforward).
  - Refunding tax losses (or carryover with interest) in domestic systems should not trigger a minimum tax.
- Research gaps and future directions:
  - Effective tax rates are defined in NPV terms, but Pillar Two is applied yearly; AETRs and METRs under a top-up tax depend on realization of accounting profits in specific years (timing profile).
  - Further research is needed on how different investment characteristics imply different timing and how investors can influence accounting profit timing and magnitude.
  - Under Pillar Two, AETRs and METRs depend on assets and payrolls of other projects in the country through SBIE; exploring the link between payoffs of new and existing investments merits further work.

*Source: 4.2 Introducing a Minimum Tax under an ACE, wpiea2024057-print-pdf*

### Chapter 10.

### Chapter 10.

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### Major thematic areas reflected in the references
- Dividend taxation and corporate investment (e.g., Alstadsæter et al. (2017); Yagan (2015); Moon (2022)).
- Cash-flow taxes, ACE systems, and comprehensive business income taxation (e.g., Auerbach and Devereux (2018); Hebous and Ruf (2017); Sandmo (1979); Sørensen (2017)).
- International tax policy, global minimum tax design, and profit allocation (e.g., OECD (2021); Beer et al. (2023); Johannesen (2022); Janeba and Schjelderup (2023); Haufler and Kato (2024)).
- Taxation and investment location, effective tax rates, and incentives (e.g., Devereux and Griffith (1998, 2003); Klemm (2008); Maffini et al. (2019); Oxford CBT (2017)).
- Debt–equity bias, leverage, and the deductibility of interest (e.g., Europen Commission (2022); IMF (2016); Boadway and Keen (2010)).
- Methodological and theoretical foundations for corporate tax analysis (e.g., King (1974); Hall and Jorgenson (1967); Meade Committee (1978); Mirrlees Review (2011); Keen and Konrad (2013)).

*Efficient Economic Rent Taxation under a Global Minimum Corporate Tax Working Paper No. WP/2024/057*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024057-print-pdf.pdf_