*NPV is a great tool. But used blindly it might not give the outcome you need for your project. This blog, written by Global Manager, Tarrant Elkington, talks about the power of incremental analysis.*

In project announcements Internal Rate of Return (IRR) tends to take equal, if not greater, importance than Net Present Value (NPV) (perhaps depending on which tells the best story to the market). Typically, we optimise for NPV with the IRR as a by-product. From experience, often lower capital projects tend to attract higher IRRs for the same NPV, leading it to be an attractive metric for investors and financiers.

I have seen a number of cases where junior mining companies have completed their “definitive” or “bankable” feasibility study based on a larger project that maximises NPV, only to resort to having to update such studies considering a much smaller project that minimises CAPEX and increases IRR at the expense of NPV, after realising that these larger projects are difficult to finance.

IRR is very closely linked to NPV. The IRR is essentially the discount rate that makes the NPV zero. It is the rate of return that we expect to receive from investing in the project. The higher the better. If your NPV is positive, it means that your IRR is higher than the discount rate. If your NPV is negative, it means that your IRR is less than the discount rate.

However, IRR tends to be a trial and error sort of metric. There is no direct calculation, and no block additivity property that can be exploited like NPV.

Please correct me if I am wrong, but I don’t think there is an optimiser out there that directly maximises IRR. But that doesn’t make it an impossible task, albeit a challenge I hadn’t thought about until writing my last post.

Given we have optimisers that can help us to optimise projects for NPV, why can’t we augment them to maximise IRR? The short answer is, “we can”, with a little “outside the box” thinking. The solution I arrived at is quite simple and can be easily achieved with commercial NPV optimisers.

#### How to Maximise IRR

So, our objective here is to find the highest possible IRR for our project, using available tools, in the shortest period of time.

To relate IRR back to known mine planning concepts, your discount rate effectively sets a “cut-off” to your IRR: those aspects of the project that combine to give you a rate of return greater than the discount rate will be retained, those that do not will be discarded. As my colleague Allan Earl, suggested to me “Perhaps we should be considering a cut-off return, rather than a cut-off grade”. A fascinating thought. We want to use this property to converge on the highest IRR solution possible for our given project configuration.

The process is straightforward, and we can walk through it together. Let’s consider a copper project with a four-stage pit. We incorporate capital optimisation, allowing the optimiser to select the amount of processing and mining capacity, against their respective capital costs.

In this case I use Snowden’s Evaluator software, but you could do the same, or similar, with another commercially available tool. One caveat is that the project needs to incorporate all of your capital in the solution. Without capital most projects will have very high IRRs. If your tool doesn’t support it, you can work around this by including a “heavy bench” at the start of mining, at the cost of the project capital, similar to the “heavy block” exclusion zone workaround for pit optimisation.

You could do a “brute force” method, where you optimise NPV at a full range of discount rates. Export the results and compare the NPV and IRR of each solution. For fun (or punishment, I am not sure) I tested this out. I took the project and completed NPV-optimised schedules for discount rates ranging from 1% to 40% in 1% increments. For each case I measured NPV (both at the discount rate NPVDR used, and at the standard 10% NPV10), CAPEX, IRR, as well as the peak processing and mining capacity.

This produced some interesting results (Figure 1). At a 1% discount rate, we get a low production rate, low CAPEX option, because the optimiser does not apply much penalty to later cash flows. We get an IRR of about 27.5%. The IRR (and mining and processing capacity as seen in Figure 2) raise quickly up to a discount rate of 5% before hitting an inflection point with an IRR of 37%. Beyond a 5% discount rate the IRR increases at a slower rate until hitting a maximum of 41.8% with a discount rate of 40%. Trials of discount rates above 40% returned no answer. The NPV10 remains steady from 5% discount rate to 30% with the IRR rising slowly. In this range the capacity increases slowly, plateaus and then decreases.

It begs the logical question of which option we should choose? As we often see in a range of strategic options, the top of the “hill of value” (credit to Brian Hall) is quite flat, leaving us with a range of viable alternatives. In my view as long as you are on, or near, the top of the hill you can make any choice you like.

Below the NPV10 versus the IRR is plotted (Figure 3). Aside from discount rates 1-3%, all other scenarios lay on the “NPV-IRR frontier” where increases in NPV10 are traded-off for reductions in IRR. I would argue that any point on this frontier could be a rational choice. Which option would you choose?

To repeat this brute force method (with 40 scenarios) in reality, with tight budgets and timelines, would be infeasible. So, we need a more efficient way to work our way through these scenarios.

One option would be to simply look at greater intervals. You would lose resolution, but we see that IRR rises with NPV until it can no longer produce a solution. The local optima will be the global optima. So, you will not miss your top solution by much. When you find the discount rate at which there is no longer a solution, then backtrack at smaller increments until you find a solution again.

Another option would be to start at a high discount rate and work backwards until you find a solution.

Either way you could probably find a good range of solutions with 4 or 5 well selected scenarios.

**So What?**

Given the importance placed on IRR as a metric in investment analysis and project financing, it must be given due consideration as a driver of mine planning strategy. Perhaps it could save project developers significant time and budget to focus on this metric from the outset. There is no point in optimising for NPV if that project configuration will never be financed!

As such, we need software tools and strategies to find the best possible solution. The process described in this blog is a start, a clunky workaround until one of the software vendors provide an automated path (which shouldn’t be too difficult to automate in my opinion). But at least it is a start.

I would encourage you to test it out with your project, and let us know what you learn.

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