Tax impact on IRR

As Naiyer posted a while ago the relationship between project IRR and equity IRR, constitute a curious trio along with the Cost of Debt (CD) in project finance. Below graph indicates how the relationship between EIRR/PIRR inverses when the cost of debt equals project IRR.

Later, Naiyer asked himself, can equity IRR be lower than project IRR? Using one of his analyses, he proved how that could be true (even when the cost of debt is lower than project IRR) due to a long construction period for example. This is depicted in the following figure.

But? what about tax liabilities?

Adding taxes to the equation

Taxes are one of the most common headaches for corporates but some useful tools have been developed in financial engineering in order to minimize their handicaps. In this business case, (the same used by Naiyer in his previous posts) tax liabilities are added to the project in order to check their influence on both IRRs. As the following cash flow shows, for a given condition, the imposed Tax Rate (TR) decreases both IRRs. This is due to the fact that taxes are applied to the total cash flow as well as to the one from equity resulting in tax impact on IRR

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Using the previous cash flow and sweeping along the cost of debt value [5% to 17.5%] the following graphs can be obtained (Debt ratio = 80% and Tax rate = 0%, 20% & 40%). It is obvious that increasing the corporate tax rate pushes both IRRs downwards due to an overall loss of efficiency. In addition, the equity IRR-cost of debt intersection is displaced above the project IRR line, thus giving rise to some areas where equity IRR is greater than project IRR and cost of debt is greater than project IRR.

If the previous cost of debt sweeping is also carried out along the tax rate dimension, it is possible to better understand this behavior. The following figure shows this for 2 different debt ratios (0% and 80%). In both cases, it can be observed how equity IRR and project IRR (which are equivalent in the debt ratio=0% case; red surface) decrease while increasing the tax rate. In addition, the case commented on in the previous paragraph (equity IRR > project IRR and cost of debt > project IRR) is also observed in the debt ratio = 80% plot and its probability increases directly with tax rate (blue plane and green surface over red surface simultaneously).

So, what are the findings?

The effect of adding taxes to the cash flow has a direct impact on the IRRs, lowering them due to the loss of revenue caused. Sometimes they will affect more equity IRR or project IRR depending on other particularities such as loan amortization period or sale value. therefore, resulting in tax impact on IRR.

In addition, as explained by Naiyer, equity IRR, project IRR and cost of debt values cross at the same point for simple projects. Nevertheless, some financing particularities (e.g. non-zero taxes or long construction periods) can change this behavior and displace the equity IRR-cost of debt cross above or below the project IRR value. In these singular regions, equity IRR and cost of debt can be both either higher or lower than project IRR simultaneously.

Hope you enjoyed this post on tax impact on IRR. If you have any questions, let me know in the comment section below.

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