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. Nick French, Senior Lecturer in Real Estate and Jonathan Edwards Consulting, Fellow in Corporate Real Estate The Department of Real Estate & Planning, The University of Reading Business School Whiteknights, Reading, Berkshire, England, RG6 6AW Tel: +44(0) 118-931-6336 e-mail: [email protected] Laura Gabrielli, Contract Professor in Property Valuation IUAV Venice University of Architecture Urban Planning Department, Dorsoduro 2206 30123 Venice, Italy Tel: +39(0) 41-257-1387 e-mail: [email protected] Discounted Cash Flow: Accounting for Uncertainty Page 1 Discounted Cash Flow: Accounting for Uncertainty Nick French and Laura Gabrielli “Common professional standards and methods should be developed for measuring and expressing valuation uncertainty.” Recommendation 34, Mallinson Report, RICS 1994. Introduction The purpose of any Valuation is to determine the present value of a future cash flow. The value of an investment is the discounted value of all estimated future liabilities and benefits. Value is therefore based on future forecasts, which can be modelled either implicitly or explicitly. Only in cases where there is a predetermined fixed cash flow (rent) can a valuation be considered to be “correct”. Even, then the risk of non-payment of rent; the impact of the reversion or unforeseen expenses incurred limits this to a “best estimate”. In cases where the cash flow is subject to variation (growth), this “best estimate” becomes less certain. Thus, valuations are uncertain. The more accurate the future expectations the more robust the valuation. This highlights the importance of dealing with future expectations in the valuation process and suggests that the adoption of multiple scenarios will greatly facilitate the valuer in providing sound competent professional advice. For any valuation or appraisal method to have validity it must produce an accurate estimate of the market value or price of the property investment. Implicit valuation (or capitalisation) models can be valid models as they, in most markets, produce accurate estimates of price. The advantage of an explicit model is that it forces the valuer to question all inputs in the model. In the context of this paper, we are not proffering that one method is better than another. Indeed, French (1997) stresses that the important factor in the valuation process is using the method that is appropriate for the valuation problem in hand. Sometimes, an implicit model is the most appropriate; sometimes the explicit model. The premise of this paper is that, regardless of method chosen, all valuations are subject to uncertainty. The sources of uncertainty are rational and can be identified. Uncertainty can be described in a practical manner and it should be conveyed to clients in an understandable format. This will improve the content and the credibility of the valuer’s work. 1 Royal Institution of Chartered Surveyors Discounted Cash Flow: Accounting for Uncertainty Page 2 Uncertainty in Valuation Uncertainty impacts upon the valuation process in two ways; firstly the cash flows from investment are, to varying degrees, uncertain and secondly the resultant valuation figure is therefore open to uncertainty. This paper builds upon the analysis undertaken with the implicit model (see French and Gabrielli, 2004) by using a generic forecasting software package, Crystal Ball, which allows the valuer to work with familiar explicit pricing models set up in Excel. It looks at how uncertainty can be accounted for in the valuation and how it can be reported to the client in an effective and meaningful way. Uncertainty is a universal fact of property valuation. All valuations, by their nature, are uncertain. Yet they are generally reported to the client as a single point estimate without reference to the context or the uncertainty underpinning them. This paper argues that it is possible to inform the client of the reality of uncertainty without impugning the utility of the valuation. In the UK, there has been significant discussion and debate on this topic. The most recent report on valuation from the RICS, the Carsberg report (RICS, 2002) stressed that ways should be sought to establish an acceptable method by which uncertainty could be expressed in the valuation. The terms of reference of this report and other discussions are summarised in French and Gabrielli (2004). It should be stressed that this paper is concerned with value. That is the best estimate of the price of the building in the market on the date of the valuation. The valuation attempts to identify and estimate all the benefits and liabilities of ownership and, relative to the current market, assess the highest and best bid for the property. As with all markets, a property will be offered to the market and individuals will bid for its purchase. The property will trade at the highest bid, not at the level where there are most bids (see Peto, 1997). The valuation attempts to identify this figure; this is an estimate of price. Each possible bid for the property will be determined by the bidders particular circumstances. Each will carry out a ‘calculation of worth’, which is the individual bidder’s assessment of worth to them. It will be dependant upon the particular bidders assessment of the property and their own forecasts of the benefits of ownership. A calculation of worth is not a valuation and thus this is not considered in this paper. For a full explanation of the difference between Valuation Methods and Calculation of Worth see the RICS Information Papers of the same names (1997 a/b). 2 An alternative would be to use @risk which is a very similar software package Discounted Cash Flow: Accounting for Uncertainty Page 3 Implicit Valuation Models One of the paramount concerns of the profession is the need to ensure that valuations are presented to a client in a clear and unambiguous manner. Given that clients are becoming more sophisticated in the way they determine whether to buy or sell property, then the pricing model used to assess the most likely exchange price should reflect their thought process to the extent that this influences the market. In using the traditional implicit capitalisation model, the valuer is deriving the appropriate all risks yield (initial yield) from market evidence of other property transactions. The all risks yield is a convenient measure for the analysis and valuation of similar rack-rented investments. Effectively, the all risks yield states that such investments customarily sell for a certain multiplier (the YP) of the rental income. Adjustments to the all risks yield to reflect differences between comparables and the subject property are made subjectively. Although based on comparison, the all risks yield method does implicitly reflect rental growth, obsolescence and the resale price. As the all risks yield is adapted to reflect differences between comparables and the subject property, it has to reflect a multitude of factors from return on capital, security of income, ease and cost of selling, management costs, depreciation and rental growth. Where there are sufficient sales transactions on similar properties in the market, it is possible to build up a picture of market sentiment to be reflected in the choice of an appropriate all risks yield for the subject property. It is therefore possible to undertake a valuation without explicitly addressing the input variables discussed above. The valuation is simply a multiplication of the current rent and no explicit consideration is given to the impact of each of the component parts on the final value. We can illustrate this by reference to a rack rented freehold office property. Similar investments are selling All Risks Yields around 5%. The valuer’s assessment is that this does not require any adjustment, as the characteristics of the subject property are very similar to that of the comparables available. Thus the valuation uses an All Risk Yield of 5% on the Market Rental of £10,000. This produces a capital value of £200,000 as illustrated in Figure 1. Implicit (All Risk Yield) Capitalisation Model Market Rent £10,000 YP perp @ 5.00% 20 Capital Value £200,000 Figure 1: Implicit Valuation 3 The Year’s Purchase is the reciprocal of the All Risks Yield. Discounted Cash Flow: Accounting for Uncertainty Page 4 Here it can be seen that the all risk yield produces a multiplier (YP) of 20, which is applied to the current market rent of the property. This rent is expected to increase over time yet the valuation makes no attempt to quantify this expectation. Likewise, there is no indication of the holding period or the overall required rate of return etc. The All Risks Yield includes all these factors but implicitly. Effectively is an all-encompassing aggregation and thus no one variable is considered individually but only as part of the overall attractiveness of the investment. Explicit Valuation Models The basis of the Discounted Cash Flow valuation is that the value of the property investment will be equal to the Gross Present Value (GPV) of the projected rental income flow, at the market’s required rate of return (discount rate). The advantage of the Discounted Cash Flow technique is that it makes the valuation more "transparent". It makes explicit the assumptions (market expectations) on future rental growth, holding period, depreciation, refurbishment, redevelopment, costs of management and transfer, taxation and financing arrangements and thus by making these assumptions explicit, it will allow us to question the certainty of each of the input variables. It should be stressed again, that we are not advocating the discontinuance of using the implicit method where appropriate. What we are doing is to analyse the hidden assumptions implied in the all risk yield method and by so doing question the certainty of each assumption. The Discounted Cash Flow technique, as applied to property, has developed in response to the perceived shortcomings of the all risks yield method, which, although a useful method of analysis and pricing, fails to explain the implicit assumptions contained within it. But each method is trying to assess price. Where there is substantial market information and where the property type is traded extensively, the two methods will produce the same value. Again, we can illustrate this by reference to the example in Figure 1, which had a Market Rent of £10,000 and an All Risks Yield of 5%. The All Risk Yield method implies growth and, although not stated, it must be doing so at a certain level. This can be analysed by reference to investors’ overall required return from this type of property. Most property investors (particularly of prime rack-rented property) will know the level of return they require; remembering that the All Risks Yield is only an initial return figure. Thus, by analysing the market we can determine that investors are requiring an overall return of 8% for this type of property. This is called the Equated Yield. Knowing this, there must be a relationship between the three variables 4 Retrospectively this would be viewed as the total return (income return plus capital return over defined investment period). Discounted Cash Flow: Accounting for Uncertainty Page 5 (initial yield, overall yield and growth). In simple terms, in one year, if an investor accepts an initial return of 57%, but requires an overall return of 8%, then the income must grow by 3% (return) over the year for the 8% return to be reached. This growth is equal to the difference between the overall return and the initial return. In practical terms this growth may either be in the form of an increase in the income flow over the period of the investment, and/or an increase in its capital value. The simple annual growth calculation of deducting the initial yield from the required overall yield is only true where incomes change annually. With UK property, the rent review pattern means that not only does an investor need a certain level of growth each year, as above, but the investor also needs additional growth to compensate for every year that the income is fixed. The formula in Figure 2 calculates this total growth requirement at any given initial yield, overall discount rate (equated) yield and rent review pattern. Thus at 8% equated yield (e) and 5% initial yield or ARY (k) it can be calculated that the annual growth requirement (g) would be 3.30%. Effectively, an investor accepting an initial return of 5% would require 3.30% growth in rental income on average each year (compounded at each rent review) to achieve an overall return (equated yield) of 8%. This does not mean that this is the growth pattern that will actually happen, it simply indicates the level of consistent growth that is required if the investor is to achieve the required target rate at that price. If growth turns out to be lower that this linear average figure, then the investor has paid too much for the property. If growth turns out to be above 3.30%, then the investor will achieve an overall return of above 8%. In the analysis the expected growth is reflected in the income flow, however in practice, there may be accompanying changes in the future exit yield (ARY at resale) over time, which may lead to an increase or decrease in the capital value at resale. FORMULA k = e (SF x p) k = Initial Yield (All Risk Yield)