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Investments – Strategy @ Risk

Category: Investments

  • You only live once

    You only live once

    This entry is part 4 of 4 in the series The fallacies of scenario analysis

    You only live once, but if you do it right, once is enough.
    — Mae West

    Let’s say that you are considering new investment opportunities for your company and that the sales department has guesstimated that the market for one of your products will most likely grow by a little less than 5 % per year. You then observe that the product already has a substantial market and that this in fifteen years’ time nearly will be doubled:

    Building a new plant to accommodate this market growth will be a large investment so you find that more information about the probability distribution for the products future sales is needed. Your sales department then “estimates” the market yearly growth to have a mean close to zero and a lower quartile of minus 5 % and an upper quartile of plus 7 %.

    Even with no market growth the investment is a tempting one since the market already is substantial and there is always a probability of increased market shares.

    As quartiles are given, you rightly calculate that there will be a 25 % probability that the growth will be above 7 %, but also that there will be a 25 % probability that it can be below minus 5 %. At the face of it, and with you being not too risk averse, this looks as a gamble worth taking.

    Then you are informed that the distribution will be heavily left skewed – opening for considerable downside risk. In fact it turns out that it looks like this:

    A little alarmed you order the sales department to come up with a Monte Carlo simulation giving a better view of the future possible paths of the market development.

    The return with the graph below giving the paths for the first ten runs in the simulation with the blue line giving average value and the green and red the 90 % and 10 % limits of the one thousand simulated outcomes:

    The blue line is the yearly ensemble  averages ((A set of multiple predictions that is all valid at the same time. The term “ensemble” is often used in physics and physics-influenced literature. In probability theory literature the term probability space is more prevalent.

    An ensemble provides reliable information on forecast uncertainties (e.g., probabilities) from the spread (diversity) amongst ensemble members.

    Also see: Ensemble forecasting; a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of dynamic systems. Ensemble forecasting is a form of Monte Carlo analysis: multiple numerical predictions are conducted using slightly different initial conditions that are all plausible given the past and current set of observations. Often used in weather forecasting.));  that is the time series of average of outcomes. The series shows a small decline in market size but not at an alarming rate. The sales department’s advice is to go for the investment and try to conquer market shares.

    You then note that the ensemble average implies that you are able jump from path to path and since each is a different realization of the future that will not be possible – you only live once!

    You again call the sales department asking them to calculate each paths average growth rate (over time) – using their geometric mean – and report the average of these averages to you. When you plot both the ensemble and the time averages you find quite a large difference between them:

    The time average shows a much larger market decline than the ensemble average.

    It can be shown that the ensemble average always will overestimate (Peters, 2010) the growth and thus can falsely lead to wrong conclusions about the market development.

    If we look at the distribution of path end values we find that the lower quartile is 64 and the upper quartile is 118 with a median of 89:

    It thus turns out that the process behind the market development is non-ergodic ((The term ergodic is used to describe dynamical systems which have the same behavior averaged over time as averaged over space.))  or non-stationary ((Stationarity is a necessary, but not sufficient, condition for ergodicity. )). In the ergodic case both the ensemble and time averages would have been equal and the problem above would not have appeared.

    The investment decision that at first glance looked a simple one is now more complicated and can (should) not be decided based on market development alone.

    Since uncertainty increases the further we look into the future, we should never assume that we have ergodic situations. The implication is that in valuation or M&A analysis we should never use an “ensemble average” in the calculations, but always do a full simulation following each time path!

    References

    Peters, O. (2010). Optimal leverage from non-ergodicity. Quantitative Finance, doi:10.1080/14697688.2010.513338

    Endnotes

  • Uncertainty modeling

    Uncertainty modeling

    This entry is part 2 of 3 in the series What We Do

    Prediction is very difficult, especially about the future.
    Niels Bohr. Danish physicist (1885 – 1962)

    Strategy @ Risks models provide the possibility to study risk and uncertainties related to operational activities;  cost, prices, suppliers,  markets, sales channels etc. financial issues like; interest rates risk, exchange rates risks, translation risk , taxes etc., strategic issues like investments in new or existing activities, valuation and M&As’ etc and for a wide range of budgeting purposes.

    All economic activities have an inherent volatility that is an integrated part of its operations. This means that whatever you do some uncertainty will always remain.

    The aim is to estimate the economic impact that such critical uncertainty may have on corporate earnings at risk. This will add a third dimension – probability – to all forecasts, give new insight: the ability to deal with uncertainties in an informed way and thus benefits above ordinary spread-sheet exercises.

    The results from these analyzes can be presented in form of B/S and P&L looking at the coming one to five (short term) or five to fifteen years (long term); showing the impacts to e.g. equity value, company value, operating income etc. With the purpose of:

    • Improve predictability in operating earnings and its’ expected volatility
    • Improve budgeting processes, predicting budget deviations and its’ probabilities
    • Evaluate alternative strategic investment options at risk
    • Identify and benchmark investment portfolios and their uncertainty
    • Identify and benchmark individual business units’ risk profiles
    • Evaluate equity values and enterprise values and their uncertainty in M&A processes, etc.

    Methods

    To be able to add uncertainty to financial models, we also have to add more complexity. This complexity is inevitable, but in our case, it is desirable and it will be well managed inside our models.

    People say they want models that are simple, but what they really want is models with the necessary features – that are easy to use. If something is complex but well designed, it will be easy to use – and this holds for our models.

    Most companies have some sort of model describing the company’s operations. They are mostly used for budgeting, but in some cases also for forecasting cash flow and other important performance measures. Almost all are deterministic models based on expected or average values of input data; sales, cost, interest and currency rates etc.

    We know however that forecasts based on average values are on average wrong. In addition will deterministic models miss the important uncertainty dimension that gives both the different risks facing the company and the opportunities they bring forth.

    S@R has set out to create models that can give answers to both deterministic and stochastic questions, by linking dedicated Ebitda models to holistic balance simulation taking into account all important factors describing the company. The basis is a real balance simulation model – not a simple cash flow forecast model.

    Both the deterministic and stochastic balance simulation can be set about in two different alternatives:

    1. by a using a EBITDA model to describe the companies operations or
    2. by using coefficients of fabrications (e.g. kg flour pr 1000 bread etc.) as direct input to the balance model – the ‘short cut’ method.

    The first approach implies setting up a dedicated Ebitda subroutine to the balance model. This will give detailed answers to a broad range of questions about markets, capacity driven investments, operational performance and uncertainty, but entails a higher degree of effort from both the company and S@R. This is a tool for long term planning and strategy development.

    The second (‘the short cut’) uses coefficients of fabrications and their variations, and is a low effort (cost) alternative, usually using the internal accounting as basis. This will in many cases give a ‘good enough’ description of the company – its risks and opportunities. It can be based on existing investment and market plans.  The data needed for the company’s economic environment (taxes, interest rates etc) will be the same in both alternatives:

    The ‘short cut’ approach is especially suited for quick appraisals of M&A cases where time and data is limited and where one wishes to limit efforts in an initial stage. Later the data and assumptions can be augmented to much more sophisticated analysis within the same ‘short cut’ framework. In this way analysis can be successively built in the direction the previous studies suggested.

    This also makes it a good tool for short-term (3-5 years) analysis and even for budget assessment. Since it will use a limited number of variables – usually less than twenty – describing the operations, it is easy to maintain and operate. The variables describing financial strategy and the economic environment come in addition, but will be easy to obtain.

    Used in budgeting it will give the opportunity to evaluate budget targets, their probable deviation from expected result and the probable upside or down side given the budget target (Upside/downside ratio).

    Done this way analysis can be run for subsidiaries across countries translating the P&L and Balance to any currency for benchmarking, investment appraisals, risk and opportunity assessments etc. The final uncertainty distributions can then be “aggregated’ to show global risk for the mother company.

    An interesting feature is the models ability to start simulations with an empty opening balance. This can be used to assess divisions that do not have an independent balance since the model will call for equity/debt etc. based on a target ratio, according to the simulated production and sales and the necessary investments. Questions about further investment in divisions or product lines can be studied this way.

    Since all runs (500 to 1000) in the simulation produces a complete P&L and Balance the uncertainty curve (distribution) for any financial metric like ‘Yearly result’, ‘free cash flow’, economic profit’, ‘equity value’, ‘IRR’ or’ translation gain/loss’ etc. can be produced.

    In some cases we have used both approaches for the same client, using the last approach for smaller daughter companies with production structures differing from the main companies.
    The second approach can also be considered as an introduction and stepping stone to a more holistic Ebitda model.

    Time and effort

    The work load for the client is usually limited to a small team of people ( 1 to 3 persons) acting as project leaders and principal contacts, assuring that all necessary information, describing value and risks for the clients’ operations can be collected as basis for modeling and calculations. However the type of data will have to be agreed upon depending on the scope of analysis.

    Very often will key people from the controller group be adequate for this work and if they don’t have the direct knowledge they usually know who to ask. The work for this team, depending on the scope and choice of method (see above) can vary in effective time from a few days to a couple of weeks, but this can be stretched from three to four weeks to the same number of months.

    For S&R the time frame will depend on the availability of key personnel from the client and the availability of data. For the second alternative it can take from one to three weeks of normal work to three to six months for the first alternative for more complex models. The total time will also depend on the number of analysis that needs to be run and the type of reports that has to be delivered.

    S@R_ValueSim

    Selecting strategy

    Models like this are excellent for selection and assessment of strategies. Since we can find the probability distribution for equity value, changes in this brought by different strategies will form a basis for selection or adjustment of current strategy. Models including real option strategies are a natural extension of these simulation models:

    If there is a strategy with a curve to the right and under all other feasible strategies this will be the stochastic dominant one. If the curves crosses further calculations needs to be done before a stochastic dominant or preferable strategy can be found:

    Types of problems we aim to address:

    The effects of uncertainties on the P&L and Balance and the effects of the Boards strategies (market, hedging etc.) on future P&L and Balance sheets evaluating:

    • Market position and potential for growth
    • Effects of tax and capital cost
    • Strategies
    • Business units, country units or product lines –  capital allocation – compare risk, opportunity and expected profitability
    • Valuations, capital cost and debt requirements, individually and effect on company
    • The future cash-flow volatility of company and the individual BU’s
    • Investments, M&A actions, their individual value, necessary commitments and impact on company
    • Etc.

    The aim regardless of approach is to quantify not only the company’s single and aggregated risks, but also the potential, thus making the company capable to perform detailed planning and of executing earlier and more apt actions against uncertain factors.

    Used in budgeting, this will improve budget stability through higher insight in cost side risks and income-side potentials. This is achieved by an active budget-forecast process; the control-adjustment cycle will teach the company to better target realistic budgets – with better stability and increased company value as a result.

    This is most clearly seen when effort is put into correctly evaluating strategies-projects and investments effects on the enterprise. The best way to do this is by comparing and Choosing strategies by analyzing the individual strategies risks and potential – and select the alternative that is dominant (stochastic) given the company’s chosen risk-profile.

    A severe depression like that of 1920-1921 is outside the range of probability. –The Harvard Economic Society, 16 November 1929

  • Investment analysis

    Investment analysis

    This type of  analysis gives the client direct information regarding the investments profitability, and its influence on company value.

    An important part of the investment analysis is cost. Especially in complex and demanding projects, there is significant risk related to investing. We have developed a method that clearly assesses and explains the relationship between uncertainty raised by each cost element, and which effect it has on the investment’s total risk.

    In a complex project there is often a set of cost elements that triggers follow-up costs. If one cost element exceed budget, the total cost increase can be significant, even though the isolated increase in the original cost element seemed small.

    We have focused on visualizing for the client, the scope of uncertainty in the investment, and which probability distributions that exist for each single cost element overstep.

    We focus especially on those cost elements that should be subject to strong control and follow-up. Such that the likelihood for excess cost can be reduced.

    We see it as crucial that the client has solid analysis describing and explaining the possible total cost outcomes, and their probability distributions at time of decision. With this method and these results the client can discuss the premises for the investment and decide whether or not carry out the investment with the revealed uncertainties.

    Below we present three graphs that shows the sensitivity in a project related to changes in demand for return on capital. For all three graphs the reference point is set in the projects IRR which is the point where the projects discounted revenues equal the value of the projects discounted cost payments (Project inflow/outflow ratio = 1).

    inflow_outflow-ratio1

    The curves are ideal for comparing investments with different profiles. When the X-axes is equal, curves for different projects can be overlapped to give information on whether one project is better than the other.

    payback1

    It is also possible to estimate the probability distribution for the projects net present value, or its effect on the distribution of company value.

    value-of-investment

  • Real options

    Real options

    In real life both for investment decisions and in valuation of companies there are managerial flexibility in the sense that at future points of time there is flexibility in choosing among alternatives.

    When investing, the simplest example is the choice between to invest after a feasibility study or walk away. In valuation the choice can be at a future point of time to continue operation or disinvest.

    These alternatives are real options available for the decision maker. Recognizing these real options will usually increase (reduce loss) the value of the investment or the company under valuation.

    It is well known that most standard valuation techniques of risk-adjusted discounted cash flow (DCF) analysis fails to capture all sources of value associated with this type of investment, in that it assumes that the decision to invest is irreversible and inflexible, i.e., the investment cash flows are committed and fixed for the life of the project.

    A main contribution of real options analysis is to incorporate managerial flexibility inherent in the project in its valuation. Added flexibility value, overlooked in DCF analysis, comes from managerial decisions that can take advantage of price movements: operating flexibility and investment timing flexibility.

    Strategy @ Risk has the ability to incorporate a client’s specific decision alternative in the simulation model. Thus combining Monte Carlo simulation with decision tree analysis. The four-step process of the real option decision analysis is shown below.

    roaprocess

    Production Plant Case

    The board faces the following situation: The company has a choice between building a plant with production capacity of 150 000 metric tons at a most likely cost of $450 mill. or a smaller plant with a capacity of 85 000 metric tons at a most likely cost of $300 mill..

    The demand for the product is over 100 000 metric tons and rising. The decision between a small and large plant will be taken in year 1 and full production starts in year 2.

    If the decision has been to build the smaller plant (at a higher cost per unit produced) the capacity can be increased by 65 000 metric tons at most likely cost of $275 mill. (Normal distributed with variance of ±25%). The decision to increase capacity will be taken in year 2 if the demand exceeds 110 000 metric tons. It is assumed that the demand is normally distributed with a most likely demand of 100 000 metric tons, and demand varies ±20% (upper and lower 5% limit). The demand later periods is assumed to have an increasing variance and a 30% autocorrelation

    In year 3 and 4 it is considered that there is a 40% chance that if sales has been good (over 110 000 metric tons) a competitor will have entered the market reducing sales by 30 000 metric tons. If the demand falls below 70 000 metric tons the company will disinvest.

    The decisions will be made on the value of the discounted cash flows (20% discount rate).
    The above problem can be presented as a decision tree.

    real-options-web

    The boxes represent the “decision point”. The circles represent chance events. The chance events may be continuous, as is the case with demand forecasts, or discrete, as is the case of a competitor entering the market or not.

    Net Present Value of the Alternatives

    The analysis using both the decision tree and Monte Carlo simulation gives us the net present value of the different alternatives. As shown in the figures to the right, the best alternative is to build a large plant immediately giving a net present value of $679 mill.
    A small plant will give a lower net present value (NPV $626 mill.) even if we increase the capacity at a later stage (NPV $637 mill.).

    plant-alternatives

    In this case it will never be profitable to disinvest at any point of time. This will always give a lower value.In some cases it is difficult to distinguish the best strategy from its alternatives. We will in a later post come back to selection strategies using stochastic dominance.