So, You Have Optimised NPV. But Is It The Best Solution?

Sn0wdenadminLatest News, Technical Articles

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.

The focus on net present value (NPV) has increased in recent years and the software tools to achieve this are catching up. Some help to optimise many decisions simultaneously, an area generally referred to as “Global Optimisation” (more on this in a later post). But the ability to use software to optimise all these decisions subject to a single objective can be as dangerous as it is powerful.

In strategic mine planning, we typically look at the project in its entirety and provide investment metrics in totality. This is fine, but can mask some poor investment decisions on parts of the project. We know that the total NPV is optimised of the project (subject to the inputs of course!) but was there a better option? Did we squeeze ever last dollar out without consideration that the last portion may not be sensible in its own right?

Even if we have a magic “optimise everything” button, we still need to consider alternate scenarios. While these scenarios will not, by definition, find a higher NPV. But they will help you to understand the incremental cost of the last, or often least profitable, aspects of the mine plan. What happens if the last 1% of NPV cost an extra $200 M? Is that still worthwhile? Perhaps, at a qualitative level, the last 5% of NPV introduces additional risk that may derail the project (or may not). As I have come to learn, things are not always straight forward.

Below I give you a couple of examples of where incremental analysis, the financial analysis of two incremental options, could be useful. The first looks at quantifying the value of cutbacks (and in particular, the last cutback) and the second looks at a project portfolio capital allocation problem.

Incremental cutback analysis

Nested pit shell analysis, and a discounted cash flow key performance indicator, will push us to take the best material first from our pits. The areas that provide the highest grades and lowest strip ratios. On the flipside, we leave all the lowest value, highest strip ratio material to last.

Do you quantify each cutback as a separate investment? In the case of cutbacks of an open pit mine, the investment is typically ignored as it is subsidised by revenue from previous cutbacks. It took a consulting project where there was a period of break-even profitability in the middle of the mine life for me to investigate this. And the analyse drove some insights that I thought was worth sharing.

Analysing the investment potential of a cutback in isolation can be quite easy and can produce some interesting insights (and might terrify you!) Let me show you how through a realistic case study prepared for this post.

The first thing I did was to code the optimisation parameters onto the block model in a general mining package, along with the cutback number. I do this routinely as part of my optimisation validation process anyway (and recommend that you do the same) so it did not take any additional time.

As a first pass, we can look at the basic statistics (and cash flow) of each cutback (Table 1). I like to normalise cash flows on a $/t ore, $/t rock or $/t product basis.

Table 1                  Basic cutback metrics

Table 1                  Basic cutback metrics

Of note here, the first cutback (an operating cutback that had already removed much of its waste) produces over half of the profit with only 25% of the ore (and 10% of the total movement). It is pretty clear that things get much tougher in cutbacks 2 and 3.

We can go further than this and look at some more investment metrics behind each cutback by looking at the timing of the cash flows. Typically, cutbacks will have a cash burn as waste is stripped, prior to a period of positive cash flow when ore is reached. We do not often consider the maximum burn associated with a cutback; it just blends into the overall pit economics. However, with the use of nested pit shells, later cutbacks will often see higher and higher investments leading to lower and lower returns.

This can be seen for our example in Figure 1. In this plot I calculated the cumulative net cash flow (Revenue minus cost) with depth, in 10 m (or one bench) slices, easily reported from an aggregation of the block model.

Figure 1                Cumulative net cash flow for each cutback with depth

The first cutback is already in ore, thus positive cashflows are immediate. The second cutback requires an initial investment of approximately $130 M, before paying this back and returning an operating margin of approximately $285 M. The third cutback has double the investment, at almost $250 M, and returning $454 M. An investment of $250 M should not be taken lightly.

If we take it one step further, we can apply discounting to each stage to understand the indicative net present value of each stage. A simple way to do this is to utilise a maximum vertical rate of advance, and the pit depth, to apply discounting. Assuming a discount rate of 10%, a vertical rate of advance of 50 m/a, and normalising each cutback to a year 1 start, we can assign a discount rate to each bench (based on the earliest period in which it can be mined with the vertical advance constraints). In this example, we see that the discounted value of both cutback 2 and cutback 3 have dropped below $160 M, much lower than the undiscounted cash flow (as expected). In each case (cutback 2 and cutback 3) there are more than four years of negative cash flows before the cutbacks turn cash flow positive. The impact of timing of cash flows, with waste upfront and ore at the end of the cutback life has a significant impact.

Figure 2                Cumulative net discounted cash flow for each cutback with depth

Taking it one step further we can look at the Internal Rate of Return (IRR) for each cutback, the annualised rate of return we can expect from each cutback (Table 2). The IRR for cutback 1 is infinite because the investment has been sunk. Cutbacks 2 and 3 show IRRs of 35% and 25% respectively. In a mining context these are still healthy returns when compared to some whole of project investment metrics reported in the market.

Table 2                  Advanced cutback investment metrics

Given the timing issues, and the delay before we get revenue, we are greatly exposing the investment to a change in commodity prices. We are making a call on both cutback 2 and cutback 3 four years before we receive revenue; longer than it takes to build most process plants. A small negative swing in price can reduce the discounted value to zero or beyond.

What do we do with this information? We use it as part of a strategic analysis of options. A way of providing a common set of metrics. Would it be better to remove the last cutback and go underground? Should the company abandon (or sell) the operation after cutback 1 or 2 and invest its money in other, higher return projects if they are available? Should we reduce the size of the cutback 3 to improve its investment profile. The point is that we cannot make informed decisions without some analysis.

Are there other ways of looking at this information? Sure. There are probably many that I haven’t thought of, and which I would love to hear about. But hopefully this has been enough to get you thinking.

Project portfolio capital allocation

A few years ago, after a discussion with an executive in a large mining house, I came to understand that projects were more constrained by access to capital, than they were by the optimal configuration for a single project. For companies with a portfolio of projects, typically each year every project and operation would ask for capital to build or expand. Head office would then consider submissions, and often only fund a few of the requests. It wasn’t that the other requests were not value accretive, it was that there were other options that we better. Junior mine developers face a similar problem. They often have to sacrifice NPV in order to fund their projects, with financiers unwilling to take on the risk of large-scale projects. So what we are dealing with in mining, is a constraint on capital.

With that knowledge, we thought to build this as a constraint into Snowden's Evaluator optimiser and try and figure out the most optimal allocation of capital. When capital is shared between projects, we needed to optimise them together, even if they were completely independent projects. We tested it out with a three-mine example. And the results were fascinating!

To keep it as simple as possible, all three were projects awaiting development and were each seeking capital. Project 1 was a large low grade open pit. Project 2 was a high-grade underground mine, and Project 3 was a project starting with an open pit and progressing to underground. We modelled the capital and fixed costs considerations of each project, and let the optimiser decide on the amount of capital (mining and processing) to allocate to each project, simultaneously with the life of mine plan of each. A summary of these results is shown in Figure 3.

Figure 3                Scenario analysis of incremental capital allocation options

The first scenario had no limit on capital. Here, every project was effectively independent and received whatever capital it needed to maximise its own NPV. Each project had a similar NPV, but Mine 1 had 51% of the capital allocation.

The next step was to impose a capital constraint, at 80% of the capital from the first scenario. Incredibly, the NPV only dropped by 2%! Most of the reduction in capital came from Project 1, and the processing capacity. When we simultaneously optimise the mine plan and capital allocation, the mine plan can adapt to a reduction in capacity by increasing margin. I think that is pretty smart, and not something you would get in scaling a spreadsheet!

We then went further by taking 40% and 60% of capital away, with reductions in NPV of 11% and 27% respectively. Even at 40% of the capital all projects are funded, but in the most capital efficient manner possible.

What would you do in this situation? Personally, I wouldn’t be choosing the maximum capital option. Even though it maximises NPV, I would think that I could find better uses for the additional funds than to spend what equates to $200 M to get a 2% NPV uplift. Beyond that, I think it depends on preference.


You might think that I don’t like NPV as a metric. This couldn’t be further from the truth. I think that NPV is a fantastic metric (See my earlier post). It ties so many considerations together so neatly. But it is still only one metric, and one that has proven to bias answers towards projects that investors are unable or unwilling to fund.

Is there a better way? IRR is becoming more popular as a metric. It is similar to NPV as they are based on the same concept. It tends to push solutions towards less capital than an NPV objective, and more aligned with investors. However, there is no tool in the market (that I am aware of) to optimise this metric. But I have a simple workaround that I will share in my next post.

Whatever your selected metric, even if you think you can solve you mine planning problem with a magic button as software advances, there will always be the need to employ scenario analysis to understand the incremental value of your decisions. Otherwise poor incremental decisions will lay dormant until they come back to bite you later, either through undue risk exposure, project losses or the project not getting developed at all!

Have you thought about whether there is any unproductive capital in your NPV-optimised project plan?

Look out for future posts where I will delve into the world of strategic mine planning and optimisation, apply some of these topics, provide some tools and tricks and identify some of the big unsolved problems you might never have thought of. Please provide feedback, ask questions, and share your own experiences.

To keep up to date with Snowden please follow us on LinkedIn

Related Articles