Sometimes calculating project IRR and equity IRR can be tricky, and in this post we will discuss the reasons for the same.

The internal rate of return (IRR) can be defined as the rate of return that makes the net present value (NPV) of all cash flows equal to zero. In a previous post I have discussed the basic concepts and calculation of IRR and NPV. If you want to refer back, click here for the IRR-NPV post.

Calculation of the internal rate of return considering only the project cash flows (excluding the financing cash flows) gives us the project IRR.

Consider a project with construction cost of $ 1,000,000 and annual rental income of $ 120,000. Assume the property will be sold in the 10^{th} year for $ 1,607,023. You can construct the project cash flows and calculate the project IRR by using the Excel IRR formula. You can also download the excel spreadsheet for this calculation. The download link is at the end of this post.

**Calculating Equity IRR**

Calculation of the internal rate of return considering the cash flows net of financing gives us the equity IRR. It means the project is funded by a mix of debt and equity. If the project is fully funded by equity, the project IRR and Equity IRR will the same. If the project is fully funded by the debt, equity IRR simply doesn’t exist.

Now consider the same example again. Assume 30% of the project cost is funded by the equity and remaining 70% by the debt. Assume the cost of equity to be 14% and the cost of debt 8%. The weighted average cost of capital (WACC) will be 9.8%. Note that the weighted average cost of capital will not affect equity IRR. It is only the cost of debt which matters. Assume the term of debt is 10 years.

You can project the cash flows for equity holders and calculate the equity IRR using the same Excel formula as above. This is demonstrated below:

Wasn’t it simple? It is.

**Can equity IRR be lower than project IRR?**

Some readers often ask me if the equity IRR can be lower than the project IRR. And I always say the same thing – yes, it can be.

So, in what circumstances the equity IRR will be lower than project IRR?

The equity IRR will be lower than the project IRR whenever the cost of debt exceeds the project IRR. Note it is the cost of debt and not the weighted average cost of capital. See below the relationship between the cost of debt and equity IRR.

In the above chart, did you notice that when the cost of debt is equal to the project IRR, the equity IRR is equal to the project IRR?

Note that the cost of equity doesn’t impact either the project IRR or the equity IRR. Cost of equity affects the weighted average cost of capital (WACC) and hence the NPV calculation. It affects both project NPV and NPV for the equity holders.

If you are looking for the relation between project NPV and equity NPV, refer this post Net Present Value and Returns to the Equity Holders.

You can download the project IRR and equity IRR calculation spreadsheet for FREE. It also has this interactive graph and the loan amortization schedule.

Hope you enjoyed this post on project IRR and equity IRR. What do you think, use the comment section below.

## 39 Response Comments

Excellent presentation. I got clear information what I was looking for

Thanks Raghav; I’m glad you liked it.

Thanks

you really explained the difference really well. saved me time from reading the book

Fantastic !!!!

Great article. Thank you for making internet a better place.

Oke this is quite clear.

But consider a partially debt financed project, where you have interest during construction (IDC). This IDC must be capitalized in accounting, and thus is part of a project’s costs. Do you take this into account when calculating a project’s IRR?

For example, Total Installed Costs of a project is 2.5 M$. Total capital expenditure (thus adding the IDC) is 2.9 M$. When calculating Project IRR, use 2.5 M$ of 2.9 M$?

Thanks Paul for stoping by.

Interest incurred during construction should not be taken into account for the purpose of calculating project IRR. However, the same will be taken into account while calculating equity IRR.

Hope this helps.

Naiyar, thank you for you quick answer,

Is it common practice to take Shareholders Dividends into account when calculating Project IRR, i.e. subtracting Shareholders Dividends from Net Income to calculate a Project’s Total Cash Flow?

Paul, in fact shareholder dividends should not be taken into account while calculating project IRR. Thanks

Thank you allot Naiyar, I’m performing audits on cash flow models. Apparently my company did not understand the concept of Project IRR completely.

You are welcome Paul.

In private equity deals, when you have different set of equity holders, with different preferences, shareholder dividends will be taken into account for calculating equity IRR. But again it depends on, for which set of equity holders you are calculating the IRR!

Dear Sir,

I did not understand the explanation, can equity IRR be lower than project IRR?

Yes Gargi, the equity IRR be lower than the project IRR. Download the Excel file from the link provided at the bottom of the post. Play with the cost of debt, you will be able to understand the connection between project and equity IRRs.

Very nice!

Crystal clear concepts and presentation.

Thank you for sharing your knowledge

Excellent. Very well explained. Do you have other such pieces and where do I find them?

Thanks.. Very helpful

Thanks Isha; I’m glad you found it helpful.

Naiyer – thanks this was really useful for me. I do have a question though. If the debt repayments were structured differently I get very different results. If the debt was via interest each year and full initial value payback in year 10 (still sees same IRR over debt length) then teh equity cashflow no longer makes sense (negative). I’m sure I’m looking at it wrong but can you help?

I’m glad Rob that you found this post useful. Yes equity IRR will be different if the debt is structured differently. If the loan is with bullet repayment (balloon loan), the equity IRR will be much higher. In the case study attached in this post, I don’t see any negative equity cash flow if I consider a balloon loan.

Naiyer – I’m currently working for a developer and we’ve been running multiple investment scenarios for a specific project. In one scenario I’m deducting the initial equity contribution from gross sales proceeds at exit for my IRR calculation. Is this correct? or should I omit the equity payback at exit?

Rick, equity payback should not be taken into account while calculating the project IRR. However, while calculating the equity IRR, it should be considered if you are calculating the equity IRR for a different set of equity holders – it will be a cash outflow. If there is only one equity holder, it will have no impact as you are adding it back to the equity cash flow.

Hope this helps.

Dear Naiyer,

Thanks for all your explanations above.

I would like to clarify whether there could be any other circumstances under which the equity IRR for a project is less than the project IRR? I am reviewing a model for a ship financing deal in which the project IRR seems to be higher than the cost of debt (though less than the WACC), and yet the equity IRR seems to be lower than the project IRR.

Could a high cost of equity cause the equity IRR to be less than the project IRR (and consequently the equity NPV would also be much less than the project NPV)?

Thanks a lot,

Manob Gupta

Thanks Manob for stopping by.

There are many other circumstances, where the equity IRR for a project will be lower than the project IRR.

However, both project IRR and equity IRR are independent of cost of equity.

Higher cost of equity will result in higher WACC, and lower project NPV. Higher cost of equity will also result in equity NPV being lower than the project NPV, because equity cash flow is always discounted at cost of equity and not WACC. You should refer to http://naiyerjawaid.com/discounted-cash-flow-analysis-discount-rate/ for this.

Hope this helps.

fantastic article ….concise to the point great

Hi Naiyer,

I’m facing a similar situation with Manob. Project IRR is above cost of debt, yet my equity IRR is below that of Project IRR. Could the timing of payouts to equity holders be the cause of this? In my scenario of 20 years cashflows with fixed debt repayments, equity holders only start receiving dividends in year 12. In a different scenario with sculpted debt repayments, when equity holders start receiving dividends in year 10, equity IRR is higher than project IRR. Can I have your view on this.

I don’t think this should be happening. If you can email me your model, I will be in a position to offer better view.

Hi Naiyar,

Thanks a lot

Really it is an excellent article and made things quite clear. I was able to solve some dummy exercises successfully. However while working on actual model facing the same situation, where equity IRR is lower than Project IRR despite the cost of debt is less than project irr.

The difference in scenario is as follows:

It is a big project, and needs execution (construction) time extending to three- four years. The capital requirement is also phased thus the funding or the release of equity component. In this case Interest during construction period is being considered as the part of project cost while calculating the equity IRR and NOT while calculating the project IRR. I feel this is causing the reduced equity IRR as the reference project cost is being increased. So I want to know, whether in this case equity IRR can be less as compared to project IRR or we need to have same project cost in both cases. Does that mean we need to consider Interest During Construction (IDC) as part of project cost even while calculating Project IRR. In my kind of project the costs are also spread after completion of project (operation and maintenance costs) but it is not making difference, what i have checked with dummy exercise.

Thanks Sanjay for your comment.

This should not be happening. The equity IRR will always be greater than the project IRR as long as the cost of debt is lower than the project IRR.

If you feel comfortable, you can email me your model, of course after removing sensitive information, so that I can provide useful comment.

How to calculate cost of equity and cost of debt?

Cost of debt will be what the bank or any other source of debt charges you.

Calculation for the cost equity is complicated and can’t be covered in this comment.

I will write a separate post on this.

What about taxes on the income? Why don’t you tax-effect the interest rate on the debt since interest is tax-deductible?

Thanks Warren;

Yes, interest is tax deductible. But this example was to illustrate a finance concept.

And if the project fully funded by the debt, how to compute the IRR?

Since there is no equity participation, equity IRR doesn’t exist.

How would you calculate Project + Equity NPV and Project + Equity IRR in a situation where the the new investor comes in as a 50% partner, but pays a premium for the 50% (i.e. original 50% equity was 5 million, but new partner pays 7 million)? Please keep in mind that the 2 million premium does not enter the capital of the company, but is paid to the shareholders (share transaction). I see it not affecting the FCFF line, however, once at FCFE I would basically split it into two lines (50%/50%) and effect a capex of 5 million for one line (original investor), and capex of 7 million for the other line (new investor). Your feedback and comment is very much appreciated.

IRR and NPV for two sets of equity holders will be different.

The premium paid by the second set of equity holders will be taken into account while calculating the equity IRR for the first set of equity holders.

Dear SIr,

I want to know that, if the debt/equity ratio is 99:1, then how does it reflect to the equity IRR , and whether this is considerable or not?

Dear Naiyer,

In a joint development project of 2 equity partners, assuming the debt proportion is fixed, the equity portion is to be shared between the partners,

My question:

1. will the Equity IRR for the respective partner be dependent on the proportion of their equity participation?

2. If one partner is managing the project and earns a fee for taking that responsibility, will the equity IRR of the passive partner be dependent on the proportion of equity it takes up? I have run the model, it appears that the equity IRR for the passive partner is not dependent on the proportion of its equity participation. We will then have to ask what is the incentive for the passive partner to take up more equity?

Appreciate your comments.

Gillian,

Generally the project free cash flow to the equity holders, is shared between the equity holders in the ratio of their equity participation.

If this is the case in your model, then the equity IRR for the each partner will directly depend on the proportion of their equity participation (other parameters being constant).

It looks like there is some error in your model. If you want, you can share your model with me and I can provide feedback.