Discounted cash flow: accounting for uncertainty

Valuation is the process of estimating price. The methods used to determine value attempt to model the thought processes of the market and thus estimate price by reference to observed historic data. This can be done using either an explicit model, that models the worth calculation of the most likely bidder, or an implicit model, that that uses historic data suitably adjusted as a short cut to determine value by reference to previous similar sales. The former is generally referred to as the Discounted Cash Flow (DCF) model and the latter as the capitalisation (or All Risk Yield) model. However, regardless of the technique used, the valuation will be affected by uncertainties. Uncertainty in the comparable data available; uncertainty in the current and future market conditions and uncertainty in the specific inputs for the subject property. These input uncertainties will translate into an uncertainty with the output figure, the estimate of price. In a previous paper, we have considered the way in which uncertainty is allowed for in the capitalisation model in the UK. In this paper, we extend the analysis to look at the way in which uncertainty can be incorporated into the explicit DCF model. This is done by recognising that the input variables are uncertain and will have a probability distribution pertaining to each of them. Thus buy utilising a probability-based valuation model (using Crystal Ball) it is possible to incorporate uncertainty into the analysis and address the shortcomings of the current model. Although the capitalisation model is discussed, the paper concentrates upon the application of Crystal Ball to the Discounted Cash Flow approach.

Cash flow management in construction firms

The level of insolvencies in the construction industry is high, when compared to other industry sectors. Given the management expertise and experience that is available to the construction industry, it seems strange that, according to the literature, the major causes of failure are lack of financial control and poor management. This indicates that with a good cash flow management, companies could be kept operating and financially healthy. It is possible to prevent failure. Although there are financial models that can be used to predict failure, they are based on company accounts, which have been shown to be an unreliable source of data. There are models available for cash flow management and forecasting and these could be used as a starting point for managers in rethinking their cash flow management practices. The research reported here has reached the stage of formulating researchable questions for an in-depth study including issues such as how contractors manage their cash flow, how payment practices can be managed without damaging others in the supply chain and the relationships between companies’ financial structures and the payment regimes to which they are subjected.

A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

The appraisal of data centres: deconstructing the cash flow

This paper analyses the appraisal of a specialized form of real estate - data centres - that has a unique blend of locational, physical and technological characteristics that differentiate it from conventional real estate assets. Market immaturity, limited trading and a lack of pricing signals enhance levels of appraisal uncertainty and disagreement relative to conventional real estate assets. Given the problems of applying standard discounted cash flow, an approach to appraisal is proposed that uses pricing signals from traded cash flows that are similar to the cash flows generated from data centres. Based upon ‘the law of one price’, it is assumed that two assets that are expected to generate identical cash flows in the future must have the same value now. It is suggested that the expected cash flow of assets should be analysed over the life cycle of the building. Corporate bond yields are used to provide a proxy for the appropriate discount rates for lease income. Since liabilities are quite diverse, a number of proxies are suggested as discount and capitalisation rates including indexed-linked, fixed interest and zero-coupon bonds.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Entropy application to improve construction finance decisions

In financial decision-making processes, the adopted weights of the objective functions have significant impacts on the final decision outcome. However, conventional rating and weighting methods exhibit difficulty in deriving appropriate weights for complex decision-making problems with imprecise information. Entropy is a quantitative measure of uncertainty and has been useful in exploring weights of attributes in decision making. A fuzzy and entropy-based mathematical approach is employed to solve the weighting problem of the objective functions in an overall cash-flow model. The multiproject being undertaken by a medium-size construction firm in Hong Kong was used as a real case study to demonstrate the application of entropy. Its application in multiproject cash flow situations is demonstrated. The results indicate that the overall before-tax profit was HK$ 0.11 millions lower after the introduction of appropriate weights. In addition, the best time to invest in new projects arising from positive cash flow was identified to be two working months earlier than the nonweight system.

Dissipation of shear-free turbulence near boundaries

The rapid-distortion model of Hunt & Graham (1978) for the initial distortion of turbulence by a flat boundary is extended to account fully for viscous processes. Two types of boundary are considered: a solid wall and a free surface. The model is shown to be formally valid provided two conditions are satisfied. The first condition is that time is short compared with the decorrelation time of the energy-containing eddies, so that nonlinear processes can be neglected. The second condition is that the viscous layer near the boundary, where tangential motions adjust to the boundary condition, is thin compared with the scales of the smallest eddies. The viscous layer can then be treated using thin-boundary-layer methods. Given these conditions, the distorted turbulence near the boundary is related to the undistorted turbulence, and thence profiles of turbulence dissipation rate near the two types of boundary are calculated and shown to agree extremely well with profiles obtained by Perot & Moin (1993) by direct numerical simulation. The dissipation rates are higher near a solid wall than in the bulk of the flow because the no-slip boundary condition leads to large velocity gradients across the viscous layer. In contrast, the weaker constraint of no stress at a free surface leads to the dissipation rate close to a free surface actually being smaller than in the bulk of the flow. This explains why tangential velocity fluctuations parallel to a free surface are so large. In addition we show that it is the adjustment of the large energy-containing eddies across the viscous layer that controls the dissipation rate, which explains why rapid-distortion theory can give quantitatively accurate values for the dissipation rate. We also find that the dissipation rate obtained from the model evaluated at the time when the model is expected to fail actually yields useful estimates of the dissipation obtained from the direct numerical simulation at times when the nonlinear processes are significant. We conclude that the main role of nonlinear processes is to arrest growth by linear processes of the viscous layer after about one large-eddy turnover time.

Policy making without legislating: the self-regulation of commercial property leasing

The terms of a commercial property lease covers aspects such as rent, alterations to premises and the ability to leave; consequently they have a significant impact on cash flow and the ability of a business to develop. In contrast to the heavily-legislated residential sector, commercial landlords and tenants in the UK are largely free to negotiate the terms of their contract. Yet, since the property crash of 1989/90, successive governments have taken an interest in commercial leasing; in particular there is a desire to see landlords being more flexible. UK Government policy in this area has been pursued through industry self-regulation rather than legislation; since 1995 there have been three industry codes of practice on leasing. These codes are sanctioned by government and monitored by them. Yet, 15 years after the first code was launched, many in the industry see the whole code concept as ineffective and unlikely to ever achieve changes to certain aspects of landlord behaviour. This paper is the first step in considering the lease codes in the wider context of industry self-regulation. The aim of the paper is twofold: First a framework is created using the literature on industry self-regulation from various countries and industries which suggests key criteria to explain the effectiveness (or ineffectiveness) of self-regulation. This is then applied to the UK lease codes based on research carried out by the authors for the UK Government to monitor the success of all three codes. The outcome is a clearer understanding of the possibilities and limitations of using a voluntary solution to achieve policy aims within the property industry.