What it means
Most investment appraisal assumes a simple story: you spend money now and receive money later. The cash flow signs are negative once and then positive.
An unconventional pattern breaks this, for example when a project needs large clean-up costs at the end of its life. Mining, oil and gas, nuclear power and landfill are typical examples because they involve large decommissioning or restoration costs after the income has been earned.
Some leasing arrangements and projects with major mid-life refurbishments also show several sign changes. The pattern is also common in deals where a customer pays a large deposit up front and the supplier incurs most costs later.
The main technical problem is that the internal rate of return (the discount rate at which the net present value is zero) may have more than one answer. A project with two sign changes can have two different rates that both make the net present value equal to zero.
A manager comparing either one with the cost of capital can reach the wrong conclusion. The safer measure is net present value, which discounts every cash flow at the required rate and adds them.
Net present value stays well defined regardless of how many times the signs change, and it can be plotted against a range of discount rates to see how the project behaves. A modified internal rate of return is another option, because it reinvests inflows and finances outflows at stated rates and gives a single answer.
Analysts should therefore check the sign pattern of every project before quoting an internal rate of return. It takes only a minute, and it avoids presenting a number that a sceptical board member can easily challenge.
Spreadsheet functions add to the risk, because they typically return only one answer and give no warning that others exist. A simple habit is to plot net present value against a range of discount rates and note where the line crosses zero.
If it crosses more than once, the internal rate of return should not be used on its own.
In practice
Real-world examples.
Example
A mining company spends $50,000,000 to build a mine, earns $120,000,000 over ten years, and must then pay $30,000,000 to restore the land. Because the final cash flow is negative, the project has an unconventional pattern, and the finance team relies on NPV. It discounts the final restoration cost at the same rate as every other cash flow.
Example
A wind farm developer plans a $10,000,000 turbine overhaul in year 12 of a 20-year project. The cash flows change sign twice, so the team runs NPV at several discount rates before approving the plan. The results show the project adds value across the whole range of sensible rates.
Example
A software supplier receives a $2,000,000 deposit at contract signing, spends $1,500,000 on development in later years and receives the balance on delivery. The signs go positive, negative and then positive, and the finance team tests the project with a modified internal rate of return.
Formula
Calculation
NPV = CF0 + CF1 / (1 + r) + CF2 / (1 + r)^2
A project has cash flows of -$1,000,000 now, +$5,000,000 in year 1 and -$6,000,000 in year 2. At a discount rate of 100%, NPV = -1,000,000 + 5,000,000 / 2 - 6,000,000 / 4 = -1,000,000 + 2,500,000 - 1,500,000 = $0. At a discount rate of 200%, NPV = -1,000,000 + 5,000,000 / 3 - 6,000,000 / 9 = -1,000,000 + 1,666,667 - 666,667 = $0. Both 100% and 200% are valid internal rates of return, so the measure gives two answers and cannot be used on its own.Case study
Seen in the real world.
Northfield Quarrying is an illustrative, fictional company that proposed a new site with heavy up-front equipment costs, ten years of profitable output and a land restoration bill at the end. The analyst's spreadsheet reported an internal rate of return of 14%, well above the 10% hurdle.
A senior reviewer noticed that the final year showed a $9,000,000 outflow and asked for the net present value at different discount rates. The profile crossed zero twice, so the spreadsheet had simply returned the first solution it found.
The illustrative conclusion was that the headline 14% was not a safe basis for the decision. The board used NPV at its 10% cost of capital, saw that the project still added value, and approved it with a restoration fund set aside from early profits.
Watch out
Common mistakes.
- Quoting the internal rate of return without checking how many times the cash flow signs change.
- Picking whichever of several internal rates looks best, instead of switching to net present value.
- Forgetting end-of-life costs such as restoration or decommissioning when building the cash flow forecast.
Questions
People also ask.
Why can there be more than one internal rate of return?
The equation behind the rate is a polynomial, and each change in sign can add another solution.
What should I use instead?
Net present value is the safest measure, and the modified internal rate of return can be used when a single percentage is needed.
Are unconventional cash flows rare?
No, they are common in resource, infrastructure and leasing projects with large closing or refurbishment costs.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%Related