# Uncertainty in Investment Planning Valuing Uncertainty – Keith Gregory, United Utilities.

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Uncertainty in Investment Planning Valuing Uncertainty – Keith Gregory, United Utilities

Structure The problem A single measure and statistical bias Lessons from various industries –Debt markets –Real options (finance and petroleum industries) –Capital Asset Pricing Model (CAPM) – regulated utilities –Insurance OK – So What?

The Problem

Should a project with significant uncertainties be prioritised the same as one with no uncertainties. Project costing £1m that will definitely deliver the benefits. A project costing £0.5m that with a probably 0.5 will deliver the benefits. But if it doesn’t we will still need the £1m project. Project costing £1mA project expected to cost £900k - but the costs are uncertain and could be anywhere between £500k and £2m. Carry out a project at £1m that we think will solve the problem. Build a pilot plant at £100k that will provide certainty in the design and the costs. Build a detention tank that will definitely solve the foul flooding problem. Build a Sustainable Urban Drainage Solution (SUDS) that will probably solve the flooding problem with less environmental costs.

Objective and Assumptions Objective: How can we score a project to prioritise the more certain projects and solutions over the less certain ones? Assumption 1: The current Investment Prioritisation system monitorises benefits Assumption 2: A measure of uncertainty can be applied to the costs and benefits of each project

What makes a good solution? Intellectually defensible. The method has to be acceptable to finance and regulatory teams. Understandable – project managers need to know why their projects have not been approved and what further work may be necessary to improve the project’s score. Modest additional data requirements. Modest amounts of additional management time. Consistent with expectations.

Statistical Bias

How do we measure the value of a project Does Statistical Bias Matter? Suppose we have the expected value of the costs and an expression of the uncertainty in these costs. Suppose we have the expected value of the benefits and an expression of the uncertainty of these benefits. Should we use –NPV(Benefits) - NPV(Costs) –NPV(Benefits) / NPV(Costs) (Benefits per £) –NPV(Costs) / NPV(Benefits) (£s per benefit) –Log (NPV(Benefits) / NPV(Costs)) –Something else Any non-linear transformation under uncertainty will generate a statistical bias. This makes it even more important to get the expression right. If we bias-correct Benefits/Cost the prioritisation will be different to if we bias-correct Cost/Benefit.

Statistical Bias No Solution here. Just questions. What is an appropriate measure? Does the measure need bias correcting? Does the bias correction lead to illogical consequences. Do not underestimate the importance of these questions! If your investment prioritisation system is to take into account uncertainty – this may be the biggest issue. If your investment prioritisation system does not take into account uncertainty – this may still be your biggest issue – but who will recognise the issue?

Using the Debt Market

Motivation by example Total company debt = £2bn. (Not a real company) Cost of debt at £2.5bn = 2% p.a. rising linearly to 2.1% at £3bn. Project 1 costs £750m. Cost of borrowing rises to 2.05% or £56.365m per annum. Project 2 may cost £500m or £1bn (each with probability 0.5). If £500m cost of borrowing is 2% or £50m per annum. If £1bn cost of borrowing rises to 2.1% or £63m per annum. Or on average £56.5m per annum. Therefore the expected premium of project 2 over project 1 is £135k per annum. Project 2 is equivalent (in terms of average repayments) to a project costing about £755m – so perhaps it should be penalised by £5m compared to project 1.

So, why don’t I like it? In principle this is very elegant as we have used a measure of how much an external company is prepared to invest. However… 1.The cost of debt is lower than the cost of equity (see the section on CAPM below). Therefore we could argue that there is an advantage to borrowing more so long as it can be added to the RCV so that an equity return can be generated. When the capital incentive scheme, willingness to pay and the affordability of customer bills are considered this gets very complicated. Does this argument still hold under the Future Price Limits proposal from Ofwat? 2.Logically, this can only be applied to costs – not to benefits. Banks lend money - not pipe bursts or foul flooding incidents. 3.In practice, the risk penalties will be very small.

Real Options

Financial Options – Monday 19 October 1987 In Economics the movements of stocks, options and shares are normally modelled using a Geometric Brownian Motion Processes. In 1987 many Banks and other Financial Institutions were using Geometric Brownian Motion Processes in their investment models. However, stocks, options and shares DO NOT follow Geometric Brownian Motion Processes – this may have contributed to Black Monday. Two of the three developers of the econometric models won the Nobel Prize in Economics in 1997. Myron Scholes and Robert Merton. Fischer Black died in 1995 – Nobel Prizes are not awarded posthumously.

Real Options 1 Real Options are not quite the same as financial options – but are related. Geometric Brownian motion is defined by the following stochastic differential equation: dX t = X t (  dt +  dW t ) Where X t is the stock price,  is the drift and  is the volatility. This is combined with exercise prices, interest rates, expiration dates, hedging policies,… (beyond the scope of this presentation)

Real Options 2 Expected Benefits less Opex less capitalised maintenance. Capex cost. Real options assumes it is known - +/- 15%? Uncertainty in expected cash flows – is it really Geometric Brownian Motion? In Water Industry there are risks and opportunities to be included here.

Real Options 3 One of the biggest advantages of Real Options is that it can be used to value flexibility. How much additional capacity should be built for future supply/demand? Is it worth building a ground water treatment works that could, in the future, also treat surface waters? The amount work involved in doing this correctly is enormous. This works great when the primary uncertainty varies “like a stock price”. Ideal for the petroleum industry where the oil price varies appropriately. Not ideal for the Water Industry. Personally, I think Real Options has a place in the Water Industry but only for certain key projects - not for all projects.

CAPM Capital Asset Pricing Model

What is the CAPM Used by Ofwat to determine cost of capital. Used by almost (?) all utility regulators worldwide. Used as a measure of the riskiness of stock market investments. E(R i ) = R f +  i (E(R m ) – R f ) R i is the return on the investment R f is the risk-free rate of return R m is the return of the market (typically based on the FTSE All Share Index).  i is the CAPM beta that measures the riskiness of the investment.

CAPM – Ofwat Final Determination at PR09  =0. This give the risk free rate and should represent an investment with no uncertainty. 0<  <1. This range is for an investment that has some risk but has less risk than the market as a whole.  =1. This investment is typical of the market.  >1. This is a risky investment – greater risk than the market as a whole.

Investment planning Suppose each investment is assigned a beta – depending on: Risks & CBA accuracy (both for costs and benefits) Two potential approaches. The required rate of return could be increased for more uncertain projects, or Discount rates could be varied from project to project. Note: a water company discount rate is normally WACC+”risk free interest rate”. So different discount rates do make sense. I have intentionally been vague on exact details of calibration of beta as it is largely dependent on the risk appetite of individual companies.

CAPM notes I don’t like the idea of differential discount rates. This devalues longer term benefits whilst not devaluing short term expenditure (even if the uncertainty is in short term costs not long term benefits). However, if the methodology is used to determine a target rate of return that is based on the project beta – this sound sensible. The linkage to the regulatory system is a strong positive.

Insurance

Insurance methods E(X) is the expected (or average) cost or benefit in project X. Var(X) is the variance of the cost or benefit in project X. F(t;X) is the distribution function of the cost or benefit. Pure risk Premium P = E(X). This is similar to a standard investment prioritisation method where there is no formal penalty applied for risk. Premium with Safety/Security Loading. P = (1+k) E(X). This method is very common– for example in car insurance. If a sufficient number of independent items are insured the variance becomes irrelevant – the loading is applied to cover operating costs and generate profits. The Variance Principle. P = E(X) + a Var(X) where a is a positive constant. The Standard Deviation Principle P = E(X) + b  Var(X) where b is a positive constant. The Quantile Premium. P = F -1 (1-e ; X). Thus if e=5% the premium will make a profit with probability 95% and a loss with probability 5%. Note that, in many cases, this is equivalent to the Standard Deviation Principle.

Insurance methods – candidate methods Pure risk Premium P = E(X). No uncertainty. Premium with Safety/Security Loading. P = (1+k) E(X). No uncertainty – all projects equally penalised. The Variance Principle. P = E(X) + a Var(X) where a is a positive constant. Possibility The Standard Deviation Principle P = E(X) + b  Var(X) where b is a positive constant. Possibility The Quantile Premium. P = F -1 (1-e ; X). Often, this is equivalent to the Standard Deviation Principle. If there are low probability/high cost risks it doesn’t work.

Insurance methods – Variance or Standard Deviation If a project is actually the combination of two identical but independent sub-projects then it would make sense for the combined project to be ranked equally to the sub-projects. If a project is actually the combination of two projects with the same uncertainties (i.e. if one works then both will). Once again one might expect the combined project to be ranked equally to the sub-projects. One might expect the penalty for a whole programme to be equal to the sum of the penalties for the individual projects. Neither is the clear winner.

Thank You

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