A few years ago I was embarrassed by getting this wrong. Asset Management can be confusing because some values are in current dollars and others in future dollars.

1. NPV for Asset Management Engineers WA Integrated Asset Management, 1 December 2016
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Net Present Value for Asset Management
Engineers
Hein Aucamp
WA Integrated Asset Management
WA Integrated Asset Management is an
Infrastructure Asset Management company
serving Local Government and the mining
sector based in Perth, Western Australia.
www.waiam.com.au
A confession
I have a confession to make. About 3 or 4 years ago I was embarrassed because I got this wrong. My
background is engineering. If my background had been accounting, I would probably have been safer.
Different dollar values in Asset Management
Somehow I had drifted into thinking that a Net Present Value calculation does nothing more than
remove inflation from future dollar values. But it does more than that: it compares those future dollars
to a proper use of money.
And to those of us in Asset Management, it is not always obvious that a comparison is involved.
When we wear our Asset Management hats, we are usually not consciously making comparisons
about how well the money is being used. We are usually focused on how to manage the assets we
have got and which are aging, and about which we have no choice.
One difficulty with Asset Management is that we are dealing with different dollar values depending
on the documents we are using:
 Asset Management Plans, with their 20 year projections, are in current dollar values. Every
single figure, now and in the future, represents the purchasing power of a dollar in this
financial year.
 Financial budgets, on the other hand, are in nominal real dollar values. Future estimates in
income are the actual dollars that will be collected. Inflation is included. The dollar amounts
will be higher, but their purchasing power will be eroded by inflation.
So we need to be careful. For example, the Long Term Financial Plan contains information from both
Asset Management Plans and budgets, with their different dollar value figures. In the LTFP you have
a choice whether to use current dollar values or nominal real dollar values. So the LFTP has to have
an adjustment of either the Asset Management Plan figures or of the expected budgets to be able to
relate them to each other.
My specific difficulty was in calculating an Asset Renewal Funding Ratio (ARFR) from 10 years of
current dollar values in an Asset Management Plan. I got confused because inflation was already
stripped out, so I thought an NPV adjustment was not required, and that a simple sum would do.1
1
The ARFR is defined in the IPWEA AIFMG and also required of Councils in Western Australia by the DLG
Asset Management Framework and Guidelines.

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The Present Value and Net Present Value formulas
So let’s have a look at these formulas and understand precisely how to use them depending on what
we are trying to achieve.
As you know, the Present Value formula gives us the value in today’s dollars of a future amount. But
even when we use these exact words, we can mean slightly different things by value in today’s
dollars.
This is the formula: 𝑃𝑉 =
𝑉
(1+𝑖) 𝑛:
 V is the nominal (face) value n years from today.
 i is the discounting rate.
And as you also know, the Net Present Value formula is the sum2
of more than one future value to
allow us to relate a future income or expense stream to a figure in today’s dollars.
When we use these formulas, we need to get i right, because it differs depending on what we are
doing. There are 3 different parts making up i, and we need to choose between them.
Here are the three parts:
 The total discounting rate: let’s call it it.
 The inflationary part of the discounting rate: let’s call it ii.
 The real part of the discounting rate: let’s call it ir.
It will be easier for us to start with ii.
The inflationary part of the discounting rate ii
This represents the erosion of value because of inflation. In 2012 (around the time I made my mistake
with NPV), the AIFMG gave an example of 3.5%.
If you are adding or removing inflation to relate Asset Management Plan figures to budgetary figures,
use only ii, and use it in the Present Value (not the Net Present Value) formula.
For example, if you were in 2012, you would have taken a 2016 budget figure of $1,000 and
calculated it to be
$1,000
(1+0.035)4 = $871.44 in 2012 dollars.
When you apply adjustments to individual items, such as columns of yearly figures in a spreadsheet,
you will almost always be either multiplying or dividing by the Present Value formula using ii as the
discounting rate.
The total discounting rate it and the real discounting rate ir
The total discounting rate it is the interest rate achievable in a safe investment. In 2012 an example of
8.0% was given in the AIFMG. The 10 year bond rate is often used. It is larger than inflation.
The real part ir is the portion of it which is net over inflation. You calculate this by division, not by
subtraction: (1 + 𝑖 𝑟) =
(1+ 𝑖 𝑡)
(1+𝑖𝑖)
. In 2012, it would have been
(1+ 0.080)
(1+ 0.035)
= 1.0435, which means ir was
4.35%.
2
Technically it could also be a single figure, but this doesn’t often occur in Asset Management calculations.

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The reason that these terms (it and ir) are important is the implicit comparison I mentioned earlier.
The NPV formula does not simply relate a future stream of incomes or expenditures to present day
values. It takes something additional into account. If I keep my money this year, and if I follow good
investment practices which beat inflation, it will be worth more next year in real terms.
E.g. if I had $1,000 in 2012, and invested it at the bond rate, in 2013 it would have been worth:
 $1,000 * (1 + 0.08) = $1,080 in nominal real dollars.
 $1,000 * (1 + 0.0435) = $1,043.50 in 2012 current dollars.
On the other hand, if I had kept the $1,000 without investing it, in 2013 it would have been worth:
 $1,000 in nominal real dollars.
 $1,000 / (1 + 0.035) = $966.18 in 2012 dollars.
When the Net Present Value formula is prescribed (as it is for the Asset Renewal Funding Ratio), it
includes this implied comparison. It includes as a reference whether proper use is being made of the
money, and whether the money is beating inflation by as much as it should be.
So if you are adding values together to evaluate future income or expense streams, you will almost
always use ir or it (and not ii) in a Net Present Value formula:
 Use ir if you are adding current dollar values (e.g. projections in the Asset Management Plan).
 Use it if you are adding nominal future dollar values (e.g. future budgets which include
inflation).
 Use either ir or it when adding figures from your Long Term Financial Plan, depending on
whether it is written in current dollars or nominal future dollars.
Summary
In general, the summary below will apply. But make sure that you aren’t dealing with an exceptional
case.
Activity Formula to Use Discount Rate to Use
Adjusting individual figures to add or remove inflation Present Value ii
Summing real nominal dollar figures in future years Net Present Value it
Summing current dollar figures in future years Net Present Value ir
Note about Excel Present Value formula
Be careful of the Excel PV() formula. It works differently from the one I have presented above. It
sums the specified value over n years, instead of calculating one value n years in the future.