Effective tax rates

EFFECTIVE TAX RATES

General definition

Nominal or real effective tax rates

Nominal effective tax rates

Real effective tax rates

Alternative effective tax rate measure

GENERAL DEFINITION

Effective tax rates are a way of getting a feel for how ‘heavily’ or ‘lightly’ income tax is being imposed on an investment asset or project relative to a neutral tax treatment:

Effective tax rate = (pre-tax return – post-tax return) x 100%

-------------------------------- (1)

pre-tax return

The degree to which an income tax system under study taxes a particular asset/project 'heavily' or 'lightly' is measured against a neutral tax system that taxes either nominal or real economic income. The asset/project's pre- and post-tax returns in equation (1) are expressed in nominal or in real terms depending on whether the severity of the tax imposed on the asset/project is being compared to a neutral nominal or real system, respectively. However,

a project's real return = the project's nominal return - inflation.

Therefore,

pre-tax real return - post-tax real return = pre-tax nominal return - post-tax nominal return.

Thus, the pre- and post-tax returns in the numerator of equation (1) are determined from the (nominal) cash flows of the asset/project regardless of whether the severity of the tax imposed is being compared to a neutral nominal or real system. The pre-tax return of the project/asset under study in the denominator of equation (1) is, however, expressed in nominal or real terms depending on whether the neutral benchmark being used is nominal or real, respectively.

Regardless of the neutral benchmark used, the further the effective tax rate is above the statutory rate of tax being imposed on the asset/project, the more heavily income tax is impacting on the asset/project relative to neutral taxation and the further the effective tax rate is below the statutory rate the more lightly income tax is impacting on the asset/project.

A central question is when to use the project/asset's nominal pre-tax return and when to use its real pre-tax return in the denominator of equation (1). The answer is to use nominal pre-tax return when the tax base of the income tax system under study includes nominal interest and to use real pre-tax return when real interest is included in the tax base under study. To mix up nominal and real returns is like 'comparing apples and oranges'- as is often done with pre-tax return in the denominator set on a real basis (perhaps because taxing real economic income is seen as the ideal to be aimed at) even though income, including interest income, is generally assessed on a nominal basis in the actual tax system under study. With an essentially nominal income tax system under study, effective tax rates obtained using the project/asset's real pre-tax return in the denominator of equation (1) will invariably be much higher than the statutory rate, reflecting the taxation of inflationary income, but will say little about how 'heavily' or 'lightly' tax is imposed relative to a neutral tax on nominal economic income.

NOMINAL OR REAL EFFECTIVE TAX RATES

Neutrality of income taxation requires income tax arrangements to impose a specific but generally-applicable wedge between the pre-tax discount rate and the post-tax discount rate used by an investor to assess investment viability. This wedge is a necessary, but not sufficient, condition for neutral impact on investment decision-making: the overall structuring of tax provisions so as to tax economic income does the rest. The shape of the required discount rate wedge depends on whether the tax provisions are structured to tax nominal economic income or real economic income:

neutral nominal income tax arrangements require the pre-tax discount rate (r) to be reduced by the tax in proportion to the investor's tax rate (t) - achieved through symmetrical assessment of nominal interest payments) - that is,

post-tax discount rate = r(1 - t)
neutral real income tax arrangements require the discount rate to be reduced by the tax in proportion to the investor's tax rate times the ratio of the difference between the pre-tax discount rate and the inflation rate (i) to the pre-tax discount rate - achieved through symmetrical assessment of real interest payments - that is,

post-tax discount rate = r(1 - t) + i.t = r(1 - t(r -i)/r).

Risk aside, an investment marginal before tax has a pre-tax net present value (NPV) of zero. That is, the investment's positive cash flows discounted at the investor's pre-tax discount rate match the investment's discounted negative cash flows (including capital expenditures). The investment's pre-tax return then matches the pre-tax discount rate. After tax on either the nominal or real economic income of the investment, the NPV of the investment remains zero - so the investment remains marginal after tax with either its:

post-tax nominal return matching the investor's post-tax discount rate - r(1 - t) - if nominal economic income is being taxed; or
post-tax real return matching the investor's post-tax discount rate - r(1 - t(r -i)/r) - if real economic income is being taxed.

It would make no sense to seek to confirm that the investment remained marginal after being taxed on its nominal economic income by comparing its post-tax return to a return that might have been achieved had the investment's real economic income been taxed.

Thus, expressing effective tax rates expressed in nominal or real terms depends on the structure of the income tax system under study. If nominal interest is included in the income tax base, the effective tax rate should be expressed in nominal terms – that is, with pre-tax returns of projects/assets under study in the denominator of equation (1) specified in nominal terms. With nominal interest included in the income tax base, year-by-year nominal tax values of all relevant assets and liabilities would usually be reflected in taxable income (as with most income tax systems) – although inflation indexing of some selected transactions might sometimes be included.

Alternatively, if the income tax system being studied incorporates real interest in its base, effective tax rates should be expressed in real terms. Effective tax rates would be calculated with pre-tax returns in the denominator of equation (1) expressed in real terms (ie nominal returns less the general rate of inflation). With real interest included in the income tax base, changes in the real tax value of assets and liabilities would likely be reflected in taxable income. For example, included in taxable income would be the losses in real tax value of assets over a year measured by the tax values of the assets at the start of the year times the general rate of inflation. In fact, this same adjustment for losses (and gains) in real values of financial assets (and liabilities) – that is, value of asset/liability at start of year times the general inflation rate – is the adjustment that turns symmetrical treatment of nominal interest into symmetrical treatment of real interest.

NOMINAL EFFECTIVE TAX RATES

With nominal interest in the income tax base:

Nominal effective tax rate = (pre-tax nominal return – post-tax nominal return) x 100%

------------------------------------------------- (2)

pre-tax nominal return

If all nominal economic income from a marginal project - that is, ignoring risk, a project with a zero before-tax NPV - were being taxed in the year it is earned,

post-tax nominal return = pre-tax nominal return – pre-tax nominal return x statutory tax rate.

That is (the relevant discount rate wedge),

post-tax nominal return = pre-tax nominal return x (1 – statutory tax rate).

And, thus, substituting in equation (2),

effective tax rate = statutory tax rate.

To illustrate with a numerical example, take the situation where inflation is at 3% and the going inflation-affected nominal interest rate is 10%. With no risk, a marginal project (comprising a single depreciating tangible asset) has a before-tax internal rate of return (IRR) of 10% – and a NPV of zero with discounting at 10%.

With all economic income (incorporating annual reduction in value of the depreciating asset) from the marginal project taxed in the year it is earned, the after-tax IRR of the project for an investor with a 47% tax rate is 5.3% (10% x (1 – 0.47)). With discounting at 5.3%, the after-tax NPV is again zero.

In these circumstances, the (nominal) effective tax rate is the same as the 47% statutory rate – that is, (10 – 5.3) x 100 / 10 %. The project is not being taxed too heavily or too lightly, but neutrally.

If, instead of economic depreciation, declining balance depreciation were allowed at 15%, the nominal effective tax rate would decline below the 47% statutory rate to 45.9% to reflect the slight lessening of the tax impost on the project relative to a neutral situation. Reflecting this situation also is the positive after-tax NPV and the 5.4% after-tax return, somewhat above the 5.3% available from financial markets. If other projects were taxed more neutrally, there might be expected to be some upward pressure on prices and/or costs relevant to the project under study and some downward pressure on the project's pre-tax return, pushing the after-tax return towards 5.3%.

REAL EFFECTIVE TAX RATES

With real interest in the income tax base:

Real effective tax rate = (pre-tax nominal return – post-tax nominal return) x 100%

---------------------------------------------- (3)

pre-tax real return

If all real economic income from a marginal project (again, ignoring risk, a project with a zero before-tax NPV) were being taxed in the year it is earned,

post-tax real return = pre-tax nominal return – (pre-tax nominal return - inflation rate) x statutory tax rate.

That is, (the relevant discount rate wedge),

post-tax real return = pre-tax nominal return x (1 – statutory tax rate) + inflation rate x statutory tax rate.

And, again, substituting into equation (3),

effective tax rate = statutory tax rate

as in the nominal interest case.

To illustrate again with a numerical example, take the same situation as in the nominal interest illustration where inflation is at 3% and the going inflation-affected nominal interest rate is 10%. With no risk, the marginal project (a single depreciating tangible asset) again has a before-tax IRR of 10% – and a NPV of zero with discounting at 10%.

With all real income from the marginal project - including economic depreciation plus allowance for annual loss in real value - taxed in the year it is earned, the after tax IRR of the project for an investor with a 47% tax rate is 6.71 - that is, 10% reduced by the proportion 0.329 or 10% x [1 – 0.47x(0.1 - 0.03)/0.1]. In other words, with 3% inflation, only the real 7% income is taxed, reducing the 10% return by 3.29 percentage points (ie 7%x0.47) to 6.71%. With discounting at 6.71%, the after-tax NPV is again zero.

In these circumstances, the (real) effective tax rate would be the same as the 47% statutory rate – that is, (10 – 6.71) x 100 / 7 %. The project is not being taxed too heavily or too lightly, but neutrally.

Take the situation now where the tax arrangements are changed so that only 15% declining balance depreciation is allowed, with no additional allowances for year-by-year losses in real value due to general inflation, despite the fact that symmetrical treatment of real interest is part of the tax arrangements under study. With this change, the real effective tax rate increases significantly above the 47% statutory rate to 65.6%. This indicates how much more heavily the changed tax arrangements impact on the project relative to neutral taxing of real economic income. Reflecting this situation also is the negative after-tax NPV and the after-tax return of 5.4%, well below the 6.71% available from financial markets. If other projects were taxed more neutrally, resources would be expected to flow out of projects like the one under study with consequent downward pressure on prices and/or costs and upward pressure on the such projects' pre-tax returns, pushing their after-tax returns towards 6.71%.

ALTERNATIVE EFFECTIVE TAX RATE MEASURE

The effective tax rate measure in equation (1) may be viewed as blunt measure of the tax impact of a project or asset. A project's rates of return that feed into the measure are summary statistics of the overall year-by-year cash flows of the project. These overall statistics, and associated effective tax rate measure, may mask a great deal of variability in cash flows across the years of the project's life.

An alternative way of computing effective tax rates is to compare the present value of the income tax payable by the project year-by-year under the tax system being studied with the present value of the corresponding year-by-year economic income of the project. Annual economic income includes annual change in value of the project’s assets and liabilities - with nominal or real value changes used depending on whether symmetrical treatment of interest in the system under study is in nominal or real terms, respectively. Taxing all of a project’s annual economic income each year would again result in an effective tax rate equal to the statutory rate. But because this measure incorporates specific year-by-year variations in income and tax paid, it would be expected to invariably produce different effective tax rates than would the measures in equations (2) and (3).