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

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 tax rate. In addition, the case commented 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.

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 through the comment section below.

You can also download the case study on the impact of tax on IRR FREE!

I'm Dar'o P'rez Campuzano, and I would like to thank Naiyer for giving me this opportunity to write this guest post. I currently work with Siemens Gamesa in the marketing department doing mostly financial analysis. It's a pleasure to work with my colleagues at Competitive Intelligence and I must express my gratitude for their help and the things they have taught me. I am also working with the R&D team at LLM Aviation.

For any questions or suggestions you can get in touch with me through Linkedin**. **

Do you have some video courses?

hi, where can i get the sample in excel?