Let’s be courageous, part 9

(… continued from Let’s be courageous, part 8, posted on 9 Sep 2016).

Taxpayer’s Alliance Policy Analyst Harry Fairhead devotes one whole subsection of the section that deals with the business case (Section Two) of his briefing paper, Rich man’s toy: The case for scrapping HS2, to a complaint about the way that net present value has been determined in the HS2 benefit cost ratio (BCR) calculations: under the subheading Inappropriate discount rate he argues that the application of an “inappropriate discount rate may mean that the present value of the benefits and costs have been misrepresented and that the BCR analysis is flawed”.

I must confess that, in my reading about HS2, I have not encountered very much comment about this particular topic – perhaps this is because we are straying into the nuts and bolts of investment economic theory here, of little interest to the average reader – but I was stimulated sufficiently by Mr Fairhead’s charge of misrepresentation to investigate the subject.

The application of a discount rate in business case assessments takes account of “social time preference”, which is a principle that may be summarised by the old adage “a bird in the hand is worth two in the bush”. It takes account of the general preference of people to receive goods and services now rather than later, and is typified by the expectation that interest will be paid on money loaned. This means that £1 received, or spent, in the future will be worth less than £1 net present value and so needs to be “discounted” by a percentage to work out that net present value (see footnote 1). For the HS2 business case the discount rates that have been applied, stated to be in accord with the recommendations of WebTAG Unit 3.5.4 (August 2012) are 3.5 per cent up to 2043, 3.0 per cent between 2044 and 2088 and 2.5 per cent thereafter (see footnote 2).

So £100 to be received in a year’s time, with a discount rate of 3.5 per cent applying, has a net present value of £96.66 (100/103.5). If it is to be received in two years’ time the net present value is £93.35 (96.66×100/103.5), and so on (see footnote 3).

This leads to two important observations about the way that the discount rate affects net present value:

  • For any given vale of the discount rate, the net present value decreases as the time to the money being received or spent increases
  • For the same time period, the net present value is decreased as the discount rate is increased

For projects like HS2 the costs tend to be front heavy, as the costs of construction normally dominate, and the benefits accrue later, since the project must normally be operational before it can deliver benefits. This characteristic, together with the operation of the properties noted in the above two bullet points, leads to the BCR being better when the discount rate is lower. This effect is not insignificant. In its June 2011 report on HS2, commissioned by the Government, the consultancy company Oxera demonstrated that this was the case. It recalculated the BCR for the full network, as it was at the time, replacing the discount rate profile that had been used (3.5 per cent falling to 3 per cent after thirty years) by the same profile but with the rates reduced by 0.5 per cent (i.e. 3.0 per cent falling to 2.5 per cent after thirty years). The result was that the BCR increased by 1.0, without wider economic impacts (WEI), and by 1.2 if WEI were taken into account (see footnote 4).

Mr Fairhead bases his charge that an inappropriate value for the discount rate has been applied for the assessment of the HS2 business case upon the analysis in a March 2016 paper, Smoke and mirrors: how the cost of systematic risk has vanished from public sector appraisals and evaluations, published by consultancy company Europe Economics and authored by Stephen Topping, Managing Consultant for the firm.

In his paper, Mr Topping points out that the H M Treasury recommended discount rate was, prior to the 2003 revision of the Treasury Green Book, much higher than the currently recommended range of 3.5 per cent declining in steps to 1.0 per cent over longer terms; it was then 6 per cent. One of the drivers behind this reduction was, as Mr Topping expresses it, “the removal from the discount rate of the risk premium that was previously incorporated to reflect systematic risk”: Mr Topping deduces that this risk premium was 1.5 per cent, or one-quarter of the total discount rate.

Systematic risks are identified in the Treasury Green Book as “appraisal risks that are systematically related to the overall performance of the economy” resulting from “random factors unforeseen at the time of the appraisal”, and I guess that the stock market crash of 2008 would be a relatively recent example of such an event (see footnote 5).

The Treasury Green Book describes the revision made to the discount rate in the 2003 edition as one which “unbundles” it (see footnote 6). A memorandum submitted to the Commons Public Accounts Committee by H M Treasury clarifies the significance of this description: it explains that “it is now essential that other appraisal issues, which could otherwise be accounted for implicitly by using a higher rate, be dealt with separately and explicitly” and that the purpose of the unbundling is to “ensure that separate elements of an appraisal are now properly accounted for” (see footnote 7).

Despite this advice from H M Treasury, Mr Topping notes that a separate adjustment “to take account of the cost associated with systematic risk is not being made in practice” by those responsible for preparing the business cases for Government projects, “despite the fact that systematic risk is a key driver of the cost of capital in the private sector”. He adds that he “has never seen a cost-benefit analysis which included such a cost”: certainly, no account of it has made in the HS2 business case.

Mr Topping attributes this failure to a statement in the Treasury Green Book, that (see footnote 8):

“Given the size of national income relative to the scale of most individual projects, the cost of variability for projects that benefit the community as a whole is usually negligible.”

He deems this judgement to be “erroneous”, arguing that “the absolute cost of variability may still be significant” in the context of a project “given that the national income is very large compared to the scale of most individual projects”. Mr Topping concludes that the “implication is that public expenditure projects and policy proposals may appear to pass a cost-benefit test when they are not in fact worth doing”.

As I remarked above, I have not been able to find much in the way of commentary on this subject from other quarters, but I have identified one public figure who has picked it up. In an opinion piece in the Daily Telegraph, Archie Norman of ASDA and ITV fame and a former Conservative MP, ventures the opinion that the “Government’s case for HS2 assumes an absurdly low and declining discount rate” that “is not risk-adjusted”.

(To be continued …)


  1. A fuller explanation of the principle may be found in paragraphs 5.48 to 5.54 and Annex 6 of the publication The Green Book Appraisal and Evaluation in Central Government, H M Treasury, July 2011.
  2. See paragraph 3.4.15 in the publication The Economic Case for HS2 PFM v4.3: Assumptions report, HS2 Ltd/Department for Transport, October 2013.
  3. A table allowing net present values to be calculated for different delays in payment and various discount rates may be found on page 100 of The Green Book Appraisal and Evaluation in Central Government.
  4. See Table A2.2 in the report Review of the Government’s case for a High Speed Rail programme, Oxera for the House of Commons Transport Select Committee, June 2011.
  5. See paragraphs 34 and 35 in Annex 4 to The Green Book Appraisal and Evaluation in Central Government.
  6. See the Preface to The Green Book Appraisal and Evaluation in Central Government.
  7. See under the subheading Associated changes in the new edition of the Green Book in the document Further supplementary memorandum submitted by the HM Treasury Discount rate, H M Treasury written evidence to the House of Commons Public Accounts Committee, June 2003.
  8. See paragraph 38 in Annex 4 to The Green Book Appraisal and Evaluation in Central Government.

2 responses to this post.

  1. Posted by LesF on September 13, 2016 at 10:27 am

    Thanks for this enlightenment Peter. It’s always mystified me. A major factor of the cost of HS2 is that it will take at least 10 years of construction before any part of it is of any use. That’s because there will be no connections between London and the West Midlands. It’s a long time to wait for the benefits, while the disbenefits start from day one of construction. The alternative High Speed UK plan currently reviewed in Rail magazine has 7 times as many inter-town connections and would be built incrementally as were the motorways; build a bit and use it while you build the next. Consequently HSUK could be partly in use before HS2 despite the years lost going through the development process again. Incremental is better than excremental.


    • I’m sure Les that if the strategists at DfT had possessed the insight to think of an HSUK approach when they were evolving the plan to introduce high-speed technology into the UK main network, then HS2 wouldn’t have seen the light of day. As it is, a plainly superior approach has not even been given a fair appraisal because HS2 is “the policy”. It may not be best, but it is the policy and so must be right.


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