NPV and IRR Explained: Reading the Two Numbers in Every Mining Study

Introduction

A mining study can run to hundreds of pages, but the news release usually leads with two numbers: the net present value (NPV) and the internal rate of return (IRR). Both are standard tools of corporate finance. Both are easy to quote and easy to misread.

In Canada, Form 43-101F1, the required format for technical reports, asks the economic analysis to include annual cash flow forecasts, a discussion of NPV, IRR and payback, a summary of taxes and royalties, and a sensitivity analysis. This guide explains each of those pieces. All numbers below are invented for illustration and do not describe any real project.

NPV measures how much. IRR measures how fast. Neither measures how certain.

Why Future Dollars Are Worth Less

A dollar received in five years is worth less than a dollar today. Money in hand can earn a return, and money promised in the future carries risk. Discounting is the arithmetic that adjusts for this.

The present value of a future amount is that amount divided by (1 + r) for each year of waiting, where r is the discount rate. Suppose a project expects $100 million of cash flow in year five:

• At a 5% discount rate, its present value is about $78 million.
• At an 8% discount rate, it is about $68 million.

The further away the cash flow and the higher the rate, the smaller its value today.

Net Present Value

NPV takes every year's projected cash flow, discounts each one back to today, adds them up, and subtracts the upfront capital cost.

Suppose a hypothetical project costs $200 million to build and is then expected to generate $60 million of cash flow a year for six years.

The project is the same in every row. Only the discount rate changes, and the NPV falls by more than half between 0% and 10%. This is why the first thing to check is which rate the headline uses. Studies state it, often as "NPV5%" or "NPV at 8%".

A positive NPV means that, on the study's assumptions, the project returns more than the discount rate. It does not mean the project will be built or that the assumptions will hold.

Internal Rate of Return

IRR answers a different question: what discount rate would make the NPV exactly zero? For the hypothetical project above, that rate is about 20%. In plain terms, the project's projected cash flows repay the $200 million and earn roughly 20% a year on it over the life of the mine.

IRR is popular because it is a single percentage that can be compared with a company's cost of capital or with other projects. It has real limits:

• It ignores size. A small project costing $20 million and earning $10 million a year for six years has an IRR of about 45%, more than double the larger project, but its NPV at 5% is only about $31 million against $105 million.
• It favours early cash. Projects that pay back quickly score well even if they are short-lived.
• It can mislead when cash flows change sign. A large closure or expansion cost later in the life can produce more than one mathematical IRR, or none.
• It implies reinvestment at the same rate, which may not be realistic.

Pre-Tax vs After-Tax

Depending on where it is, a mine can owe federal and provincial income taxes, a provincial mining tax or royalty, and royalties to private holders. Form 43-101F1 asks the economic analysis to summarize the taxes, royalties and other government levies that apply.

Pre-tax NPV and IRR are usually higher than after-tax figures. Some releases lead with the pre-tax numbers. Both are legitimate, but the after-tax figures are closer to what would actually reach the company. Royalties and streams are covered in a separate guide.

Reading the Sensitivity Table

Form 43-101F1 asks for sensitivity analysis using changes in commodity price, grade, capital and operating costs, or other significant inputs. The result is usually a table or a spider chart.

Continuing the example, suppose the $60 million a year comes from $150 million of revenue less $90 million of costs. At a 5% discount rate:

A 20% swing in revenue, which could come from metal price or grade, moves this hypothetical NPV from positive to negative. That is typical of projects with thin margins: small changes in price or grade have large effects. The sensitivity table shows how much room the base case has.

What the Numbers Leave Out

• The study stage. Under NI 43-101, a preliminary economic assessment that includes inferred resources must say with equal prominence that it is preliminary, that inferred resources are too speculative geologically to be categorized as reserves, and that there is no certainty it will be realized. A separate guide covers PEAs, pre-feasibility and feasibility studies.
• Financing. Many studies show project economics before any debt or new equity. Funding the capital cost may mean issuing shares, which spreads the value across more owners. See reading a junior's capital structure.
• Corporate costs and time. Head office costs, permitting delays and construction overruns are often outside the model or simplified.
• The price deck. The metal price assumed drives revenue. Compare it with the study date and with the sensitivity table.

What to Check

• The discount rate behind the headline NPV.
• Pre-tax or after-tax, and which figure the release leads with.
• The metal price assumed and the date of the study.
• The capital cost and payback period, which Form 43-101F1 also asks the study to discuss.
• The sensitivity table, and how close the project comes to a negative NPV.
• The resource categories behind the mine plan and the study stage.

The full economic analysis is in the technical report filed on SEDAR+, generally within 45 days of the study results first being disclosed. Read it before relying on a headline, and speak to your own adviser before making any investment decision.