PROJECT IRR (INTERNAL RATE OF RETURN) AND EQUITY IRR

Recently, somebody raised a question to me bringing a project slide deck and asked me as to why there is a big spread between the figure for Project IRR (Internal Rate of Return) and Equity-holder IRR, both post-tax. Here, Equity-holder IRR is far above the Project IRR. Even though the Project IRR is moderate, but Equity-holder IRR brings sweet returns to the project owners.

I quickly replied that he needs to look into the slide deck to search for:

  • How much is the project has relied on debt financing, that is the debt : equity financing percentage (or using corporate finance terms, the capital or financial leverage of that project)?
  • How much is the spread between the interest rate of the debt financing versus the Project IRR?

As it is probably easier to explain this concept using Return on Assets (ROA, or ROI – Return on Investment), I briefly analogized the Project IRR to ROA and Equity-holder IRR to ROE (Return on Equity, or ROCE, Return on Common Equity). As a footnote, this analogy is not perfectly correct as ROA is mostly related to one period, for instance, year to year, and whenever, we are talking about Project IRR is measured using the lifetime of the project (which might extend for many years).

Part 1

Equity-holder IRR (or ROCE) will  exceed Project IRR whenever Project IRR (or ROA) exceeds the cost of capital coming from creditors (bank or bonds, for example) (and preferred shareholders, if the project has this as well). So long the equity-holder or project owner could find the debt financing (and/or preferred shareholders) with cost rate lower than the return to be generated from the utilization of that fund, then this means the project owners have been able to leveraged such debt financing for assets that could produce a return (this will be translated to cash flows) that high enough to service debt interest and principal, then the project will give us an excess return (the spread between the ROA and the debt cost rate). This “excess return” will all go or reaped by the common shareholders. This is what normally called “using OPM – Other People’s Money”.

Many books will explain such concept under financial leverage or capital structure leverage, the ability of the business to use lower cost debt financing to bring uplift to the return to the Equity-holders.

The higher the debt-equity percentage, this might push up (or even push down) the return to the shareholders (or in this case Equity-holder IRR). As an example, I use the following assumptions as the simplified illustration purposes:

  • Project IRR (or ROA) = 12% (scenario 1) or 7% (scenario 2)
  • Annual interest rate on debt financing = 9%
  • Debt – equity financing weigh = 70% : 30%
  • No corporate tax (and personal tax)

From the above illustration, we could see that whenever ROA is higher than the after-tax debt financing, then the use of the debt financing into the project will have positive impact to the return to the equity-holder, as reflected to higher ROE from 12% (all equity) to 19%. This increase of 7%, which is the spread between ROA and after-tax interest, magnified by the Debt to Equity (D/E) ratio, could be calculated using the following formula:

ROE = ROA + Debt/Equity * (ROA – after-tax interest) => 12% + 7/3 * (12% – 9%) = 12% + 7% = 19%.

So under Scenario 1, although the net income available for equity-holder ( = 5,7) is much lower compared to that one under all-equity scenario ( = 12), yet, the use of equity base is much lower as well, from 100 to only 30 that is needed to be provided by the equity-holder, so the ROE here of 19% reflects the financial strategic use of leverage by the project owner.

However, the use of financial leverage is not coming without risk. From the above formula, we see that Debt-Equity ratio is like a magnifying lenses or magnifier factor, it will magnify (making something bigger and worse) whatever numbers it received, for example, under Scenario 1, we have good case, but it will come a rainy day, where the business could not yield higher or equal to the the after-tax cost of debt financing, in this case the ROA, let’s say drop to 7%, instead. Then our magnifier will make boost down the return to the equity-holder even deeper.

Under Scenario 2, the return to equity-holder will only be 2% (ouch!, better to keep that 30 equity into the time deposit with much lower risk, than into the business). So be careful, the dose may make the poison to the business.

Part 2

From this formula that ROE = ROA + Debt/Equity * (ROA – after-tax interest), assuming we have good hope that that ROA and after-tax interest rate is constant along the project lifetime (note: even this is not constant for ROA, this relationship still works), we will see that the ROE (or return to the equity-holders) will have a linear function to the Debt-Equity ratio. This should not come as a big surprise, that we know have the positive relationship between ROE, and D/E ratio (but the relationship between ROE and Debt amount is not linear). If we are wearing the equity-holder’s hat, then knowing that the debtholder, or creditor, who has a prior or first claim on the [expected] cash flows to be generated by the project or business, then from the perspective of the equity-holders, they are holding both the business risk and the financial risk of the project. This will translate into higher risk on the part of equity-holders, and as many financial concept of pairing return-risk element, then higher risk will necessitate the Equity-holders to demand higher return as a compensation. Whenever the debt amount being used is higher, then the higher is the risk to the equity-holder, who is the residual claimant.

Here we see that presence of Debt into the project will bring with it the financial risk, and from the creditors’ perspective, they don’t want to assume this financial risk, and we will see the creditors will take necessary steps to either reduce or both reduce and transfer this financial risk to the equity-holders. It is very common we see that the creditors in order to ensure that they have first-class priority in terms of both debt repayment of principal and payment of interest, they will demand the hard and soft assets as collaterals, and imposing negative and positive (=restrictive) covenants into the credit agreement, which ultimately have one aim, that is to entitle the creditor to have first demand and priority on early-and-immediate repayment if the financial condition of the business appears to falter down. In other words, no commercial banks will accept a debt-type return while taking equity-type risk!

Part 3

With the positive relationship between ROE and ROA with the presence of Debt, will that mean the  business will use 100% debt financing?

Financial theorists have said “no” (mostly falling under capital structure researches, which will focus on [static vs dynamic] trade-off, or pecking order, o signaling theory, or market timing propositions, or called Corporate Debt Policy).

As the creditors will really be concerned over the repayment of its principal and interest, they will make sure that they could accept the business risk before they jump into funding that business. Any [very] high business risk, then the creditors will strive to steer away, and let such high risky business be funded all with equity (for example, seed-start-ups business, which mostly the funding will come from 3Fs (Founders-Friends-Fools), Angel Capital, or Venture Capital). Even if the creditors decide to finance the business, the heavier use of debt financing will make it likely for the creditors to increase as well, the borrowing costs, both in terms of nominal borrowing costs (interest rate) and also the marginally higher borrowing rates (this is the % of interest increase). The latter is similar to the tax that the car owner have the pay, if he/she owns more than one car under the same name or address, the second car will pay marginally higher tax rate. This will narrow down the “spread” (from the above formula è (ROA – after-tax interest), which means that magnifying effect of the debt use is reduced, lowering the incremental benefit of increasing financial leverage.

From the equity-holders, they have reason as well, for example, maintaining the healthy financial flexibility, that is their ability to use debt financing to pursue any investment opportunities that could give them higher yield, or to respond to unforeseen expense and expenditures that might surface in the normal course of the business. The external aspects of the business will come into calculation, for instance, whether the market of their products have saturated, and any externalities of the projects. The higher the level of the debt funding being used, the lower the financial flexibility that the business will have. This will also be the concern of the creditors, which might impose the Debt-to-Equity ratio of maximum certain amount, for example, 2x.

Part 4

As the closing of this article, I would like to demonstrate from where this formula ROE = ROA + Debt/Equity * (ROA – after-tax interest) is derived.

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