## The Economics of Electrification Part Two – Cost-Benefit Analysis and Calculating a Net Present Value

Here’s the second part of my discussion of the economics of electrification. You can find part one here.

In order to assess whether electrification of a given line should go ahead, the costs need to be weighed against the benefits through a formal cost-benefit analysis. On top of this, we need to account for the cost of capital and opportunity cost (or what else we could spend the money on). A broadly accepted way of doing this is by calculating the Net present Value (NPV) – the Wikipedia article explains this far better than I can, and is worth reading. Also worth reading is the article on the time value of money – don’t get too worried about it though.

Here’s what the NPV equation looks like, taken from Wikipedia:

$\mbox{NPV} = C_0 + \sum_{t=1}^{N} \frac{C_t}{(1+r)^{t}}$

If you find the maths intimidating, don’t worry about it – I’m generally terrible at maths so I just use excel to work everything out for me. There’s a link later in this post which allows you to plug in your own numbers and see how changes impact on the viability of a project.

The discount rate and opportunity cost

The discount rate puts money in the future into present value terms. Economists tend to believe that a dollar is worth more to you now than it will be next week – the discount rate measures how much less it will be worth next week. The higher the discount rate, the greater the value placed on the present. In practice though, the discount rate used in these calculations is the cost of capital. The discount rate is also really handy for measuring opportunity cost, so if you can earn 8% by putting that money in the bank, or another project (like using the money to buy more trains) brings in 8% – these figures can be used very effectively as the discount rate and deliver some interesting insights.

Setting the right discount rate is really important – set it too high and worthwhile projects look non-viable; set it too low and non-viable projects look worthwhile. I think a discount rate of somewhere around 7-8% is reasonable for these sort of projects. This article explains very well why setting an appropriate discount rate is necessary.

Most intriguingly, it has been suggested that in reality, politicians face very high effective discount rates – around the 20% mark. With a short electoral cycle, politicians often view the present as much more important than the future. A project with benefits in 20 years (well beyond the current political cycle) is less likely to occur than a pork-barrel which yields political benefits almost immediately. This theory is, in my view, a pretty good explanation of why politicians in Australia are so unlikely to properly support rail.

Some results

So now I’m going to set up a very basic NPV calculation in excel, looking at the potential electrification of the Geelong line. The main assumptions I’m making are below. All of these assumptions have problems, but if anything they favour electrification (with perhaps the exception of the 50 year life of the project).

– The capital works for the project would be in the order of $276 million. This is based on the very optimistic assumption of the project costing half of what Craigieburn cost per km. See part one for details. – No new expenditure for rollingstock would be required. V/Line are going to have to buy lots more anyway and it makes little difference whether they buy more diesel trains or new electrics and cascade the Vlocitys off the Geelong line. – Service levels would be held constant – The life of the project would be 50 years – The discount rate is 8% Quantifying costs is not so hard – quantifying benefits is difficult. Now to be clear, I don’t believe that there are any economic benefits to electrifying Geelong while service levels are so low. This diagram from part one explains why. But I’m going to make up some absolute best case benefits for the sake of the exercise. Let’s pretend that that electrification will reduce net maintenance levels such that it cuts 5% out of V/Line’s$342.3 million annual expenditure. That’s $17.1 million. Furthermore, let’s pretend that the ‘spark effect’ exists, and that each of the Geelong line’s 2.57 million annual passengers gets an extra$2 utility per trip. That’s $5.1 million per year. These are the results when the numbers are put into excel (thanks to this website for showing me how to do it properly). Electrification still doesn’t stack up for Geelong even when the costs are underestimated and the benefits overestimated – the NPV is negative to the tune of$4.4 million!

So that’s that – I don’t think the numbers support Geelong electrification unless there are going to be a lot more services running. I’d highly recommend playing around with the NPV in excel by changing around the discount rate, initial investment, benefits and life of the project. Just for fun, behave like a politician and crank up the discount rate to 20%. You’ll understand why we don’t have more infrastructure with long term benefits!

### 24 Responses

1. […] part two I’ll set up a basic cost-benefit analysis which will provide a more formal way of weighing up […]

2. The economics of the Ballarat line would be slightly different because of the Ingliston Bank (the steepest rail grade in Victoria).

3. Excellent work Phin – we can tackle the dribblers together.

I will use that site to help put my Pakenham/Stony Point timetables up

Your result is somewhat sensitive to discount rate but you don’t get any real change in NPV until discount rate 4% which is unrealistic for Australia

4. Thanks Riccardo – I appreciate the complement! You’re right about the discount rate – it can be very handy for making the result come out how you want! It amazes me that the World Bank get away with running discount rates of over 10% for a lot of their stuff. It basically makes third world infrastructure investment look bad when it isn’t.

5. Fully agree Tom – electrification is viable earlier on the hilly lines.

6. If we know certain other demand elasticities it might make a difference:

-time reduction (possibly cross-elasticity with drive time) assuming you develop an electric train faster than the current diesels

-quality of service and comfort (hard to see how you would improve on current Velo without major shift)

and supply elasticities

-fuel cost as a total of all costs (Phin correctly suggests, it is a total maintenance spend, and while you are not paying for fuel, you may be paying for overhead line crews)

-conductor versus fare evasion (these are more expensive fares in many cases than the ordinary suburban ones, but still, once the conductor has checked them (say from Lara to Little River) no longer needed if the driver can prevent people getting on at Werribee, you could have the conductor get off and check in the other direction.

7. Just so we can be clear for anyone who isn’t.

1920s electrification was justified for high frequency services that were previously steam

1950s electrification was justified for freight alone (which never really materialised)

1980s electrification in NSW and Qld was justified for freight and much higher interurban passenger frequencies than were contemplated in Victoria (and were all approved during 1979-80 fuel crisis)

In all cases it was about reducing costs, for high frequency freight or passenger routes.

Not done for fun.

8. Riccardo, I think that “quality of service and comfort” can be discarded because any improvements are not specific to electrification. Unless you can find me a model of train that could only possibly be built for an electrified network. Similarly, the ticketing system has little to do with electrification.

So really, you are only looking at time reduction and fuel costs.

9. Further to my previous post. If you grouped improvements that are not specific to electrification (lets call them “non-core benefits”) that would be bundled together as part of an electrification programme then you could adjust the NPV.

For example, if there is a saving in maintenance costs that is insufficient to justify the capital cost of conversion, then grouping it with other non-core improvements that have positive NPVs as a package would result in a NPV for electrification, if balanced correctly.

10. That should read “non-core improvements” I think :-s

I agree, hard to find an electric train that improves on comfort of Velo (and is inherently so because it is electric) – maybe the noise of the motor?

As I posted before, I think a lot of the patronage increase since RFR is the ‘spark effect’ without the spark. Major improvement in service frequency (rather than journey time) and comfort from new cars, as well as a price drop.

12. My part three on the Pak line is in – covers the Oakleigh to Springvale section and how urban planning can support my model

13. On an unrelated note, Yarra trams has released a ‘wind tram’ for the 96 line – a tram powered by wind energy and decorated ‘with an eye-catching wind farm design’ http://www.yarratrams.com.au/desktopdefault.aspx/tabid-39/44_read-1331/

14. I’ve posted on Adelaide and cow dung on my blog – a challenge for you Phin to do the benefit:cost ratio vs electrification

15. I like the idea of politicians facing a high discount rate, makes a lot of sense really that they seem so incapable of facing long-term issues

16. Interesting ideas here. I’m not so sure about your ‘Fisherman’s bend’ proposal. Melbourne needs a port and industrial area served by transport links so it seems to make little sense to develop there.
Moreover, we need to decentralise our urban structure. Ie. Make Dandenong an active competitor to the CBD.

Tarneit link? Who on earth wants to go from a paddock (Green Wedge) to Werribee or Caroline springs? Seems totally ludicrous.

17. I don’t see any point electrifying to Geelong or anywhere else unless you are going to run a minimum half hourly frequency with even more trains than that in peak.

The QR interurbans are a special case because we already had a 25KV mainline electrification up the NCL (now no longer used by freight), and there was a desire to run an uniform electric fleet. QR did not have a tradition of fast interurban loco hauled trains the way Victoria has.

On this basis I am inclined to think that the only interurban electrifications in Australia that actually need to be electric based on current service patterns are Robina (QLD), Mandurah (WA), Gosford/Wyong (NSW), Wollongong (NSW) and Katoomba (NSW). Rosewood is just a suburban service, not interurban at all, and Nambour is not justified at all but will be once the line is straightened & duplicated (project underway now).

In Victoria, I wouldn’t even consider taking the 1500V DC sparks any further with the possible exception of Melton. The existing V/Line services are fine. Even if a more frequent service is required, there are examples in the UK & Europe that show how to do it with DMUs – electrification is not a given.

18. […] to both Sunbury and Melton as part of the plan, but since I looked into it in these two posts, I’ve wavered somewhat. Electrification works well for high frequency metropolitan services, […]

19. Hi Phin! Wonderful site – I have only just stumbled across this gem after a bit of a break from railway enthusiasm.

I am somewhat of a centrist but lean towards the social-democratic (re left) side of things. I thought I would play a bit of the devils advocate for a while.

I don’t think NPV is valid for determining whether a project should go ahead for public infrastructure. If it were a private company, NPV is perfect, give you a straight gain/loss from an investment, you beaut! But a negative NPV from such a project may not represent a loss, rather it may represent an investment. It is crucial that such an investment be viewed in the context of the object being invested in, the community. For instance, the -4,4 million NPV has not factored in benefit to the community, say from better health from reduced diesel fumes.

Long drawn bow, ok I admit it, for Geelong, the numbers still don’t add up? Let’s take another (albeit still vague and still unproven) example.

Let’s look at the proposed Melbourne metro line, say it has a large negative NPV. According to what you have written above, then the investment should not proceed. But looking at reports from the Productivity Commission, congestion costs Australian cities billions annually. If a metro reduces this congestion and loss of productivity by more than the NPV for the life of the project, then the community has benefited overall.

Now, in an ideal world (the one Riccardo writes about) public transport fares reflect directly the efficiency of travelling collectively and correspondingly the use of a car is taxed and charged directly with respect to the social costs involved in terms of congestion, pollution etc. In the real world, this does not happen. Rather there are a myriad of subsidies and cross-subsidies for everything and it remains that private vehicles simply do not contribute to the social cost of their use. This is where the role of government is crucial to determining behaviour. There are some positive noises being made by both NSW and federal governments about congestion charging but there is still plenty of time before such initiatives take shape.

Until the time when the cost of congestion and lost productivity is factored into the cost of private vehicle use, then I would argue that it is the role of government to make such investments, as the community benefits as a whole. Here, an investment of 4,4 million is a rather small compared to other government projects.

Another aspect is that one should consider what the alternatives are. What is the cost of inaction? Does an investment of 4,4 million mean that a larger investment in roads can be deferred to a later date? The costs of inaction and resisting investment to increase productivity are large compared to the cost of action, PROVIDED the investment is sound.

Take the following link, which is a rather vague consultants report into a proposed high speed passenger tunnel in NSW.
http://www.planning.nsw.gov.au/whatsnew/pdf/tt_2.pdf
It’s a rather vague document but there is a bit which refers to the proposed projects all having NPV and cost-benefit ratio but a positive Internal Rate of Return, which is a measure of the efficiency of the investment. Not only that, I would argue that in the context of other investments, namely that the Stanwell Park viaduct is still subject of stresses that it was not designed for, and in the next 20 years substantial investment must be made to maintain the existing network, then it was a wise investment which went begging as the NPV and CBR nuts killed it.

In either case, with increasing fuel prices it will be interesting times.

/Dave

20. Hi DHT.

I think we can agree that public transport projects don’t have to be profitable to get the go-ahead, but you’ve hit the nail on the head without necessarily realising it. Road being subsidised does not necessarily make a case for rail being subsidised, it makes the case for reducing the subsidy for road.

The net result of subsidising road and rail is that transport overall is subsidised and too cheap. And I’m not exactly clear what objective that was meant to address.

If it was welfare, then it discriminates in favour of wealthy people who choose to buy big cars and big acreage blocks on the urban fringe, and it discriminates against poor people (and students) who live close in, who don’t need cars and maybe can or do use bikes. Very poor welfare targetting.

If it was environmental…then it is counter productive, it is anti-environmental. Transport produces carbon emissions and other pollution, either at the vehicle or at the power station.

If it was to promote urban planning, then it is also counter productive. Transport subsidies as currently delivered distort sensible urban planning.

I would also argue you have nothing to fear from my views on urban rail profitability. Rail subsidies, the ones Treasury fears, are recurrent (ie the operating subsidy) not capital. They would have no problems if you came to them for $500m for a new line to Rowville as long as you didn’t keep coming back year after year to ask for money to run it. Which places a special onus on transport planners and operators to get the investments right – right staffing, right technology, right operating practices, right fares. Hence my other hobbyhorses – don’t manufacture the stuff locally, don’t allow the unions and the discredited legacy rail managers near the system, have simple (idiot-proof) fares and run the services as “turn up and go” so they present a genuine alternative to road. This is Phin’s blog: so I’ll sign off here and certainly no intention to provoke animated discussion; I just wanted to clarify that I’m not trying talk about an ‘ideal’ but rather talk about how the actual system ended up in the pickle it’s in. 21. Many thanks Dave and Riccardo, and sorry for not replying sooner. Dave, I think you make some pretty valid criticisms regarding what is put into and left out of NPVs. My primary concern is not that the idea of running an NPV is bad (I think it’s a good thing to weigh up costs and benefits of a project in a formalised way), but what is actually included and how on earth it’s valued is the issue. I mean – how do you accurately put a$ cost on amenity or congestion etc. It’s really hard to do properly and I certainly don’t have all the answers.

On the issue of looking at the alternatives – it’s absolutely important. The discount rate in the NPV can be used as a rough opportunity cost measure, but it tends to be standardised around the cost of capital.

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