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Investment – Strategy @ Risk

Strategy @ Risk

Tag: Investment

Fish farming

When we in 2002 were asked to look into the risk of Cod fish farming, we had to start with the basics; how do cod feed and grow at different locations and what is the mortality at the same locations.

The first building block was Björn Björnsson’s paper; Björnsson, B., Steinarsson, A., Oddgeirsson, M. (2001). Optimal temperature for growth and feed conversion of immature cod. ICES Journal of Marine Science, 58: 29-38.

Together with: Björn Björnsson, Marine Research Institute, Iceland and Nils Henrik Risebro, University of Oslo, Norway we did the study presented in the attached paper – Growth, mortality, feed conversion and optimal temperature for maximum rate of increase in biomass and earnings in cod fish farming. (Growth, mortality, feed conversion and optimal temperature for maximum …..)

This formed the basis for a stochastic simulation model used to calculate the risk in investing in cod fish farming at different locations in Norway.

The stochastic part was taken from the “estimation errors” for the relations between growth, feed conversion, mortality etc. as function of deviation from optimal temperature.

As optimal temperature varies with cod size, temperature at a fixed location will during the year and over the production cycle deviate from optimal temperature. Locations with temperature profiles close to optimal temperature profile for growth in biomass will, other parameters held constant, are more favorable.

The results that came out favorably for certain locations were subsequently used as basis for an IPO to finance the investment.

The use of the model was presented as an article in Norsk Fiskeoppdrett 2002, #4 and 5. It can be downloaded here (See: Cod fish farming), even if it is in Norwegian some of the graphs might be of interest.

The following graph sums up the project. It is based on local yield in biomass relative to yield at optimal temperature profile for growth in biomass. Farming operation is simulated on different locations along the coast of Norway and local yield and its coefficient of variation (standard deviation divided by mean) is in the graph plotted against the locations position north. As we can see is not only the yield increasing as the location moves north, but also the coefficient of variation, indicating less risk in an investment.

The temperature profile for the locations was taken from the Institute of Marine Research publication: Hydrographic normals and long – term variations at fixed surface layer stations along the Norwegian coast from 1936 to 2000, Jan Aure and Øyvin Strand, Fisken og Havet, #13, 2001.

Locations of fixed termografic stations along the coast of Norway.

The study gives the monthly mean and standard deviation of temperature (and salinity) in the surface layer at the coastal stations between Sognesjøen and Vardø, for the period 1936 – 1989.

Monthly mean of temperature in the surface layer at all stations

By employing a specific temperature profile in the simulation model we were able to estimate the probability distribution for one cycle biomass at that location as given in the figure below.

Having the probability distribution for production we added forecasts for cost and prices as well as for their variance. The probability distributions for production also give the probability distribution for the necessary investment, so that we in the end were able to calculate the probability distribution for value of the entity (equity).

21/02/2009
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).

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.

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

15/02/2009
The Probability of Gain and Loss

Every item written into a firm’s profit and loss account and its balance sheet is a stochastic variable with a probability distribution derived from probability distributions for each factor of production. Using this approach we are able to derive a probability distribution for any measure used in valuing companies and in evaluating strategic investment decisions. Indeed, using this evaluation approach we are able to calculate expected gain, loss and their probability when investing in a company where the capitalized value (price) is known.

For a closer study, please download Corporate-risk-analysis.

The Probability Distribution for the Value of Equity

The simulation creates frequency and cumulative probability distributions as shown in the figure below.

We can use the information contained in the figure to calculate the risk of investing in the company for different levels of the company’s market capitalization. The expected value of the company is 10.35 read from the intersection between probability curve and a line drawn from the 50% probability point on the left Y-axis.

The Probability Distribution for Gain and Loss

The shape of the probability curve provides concise information concerning uncertainty in calculating expected values of equity. Uncertainty is reduced the steeper the probability curve, whereas the flatter the curve so uncertainty is more evident. The figures below depicts the value of this type of information enabling calculation of expected gains or losses from investments in a company for differing levels of market capitalization.

We have calculated expected Gain or Loss as the difference between expected values of equity and the market capitalization; the ‘S’ curve in the graph shows this. The X-axis gives different levels of market capitalization; the right Y-axis gives the expected gain (loss) and the left y-axis the probability. Drawing a line from the 50% probability point to the probability curve and further to the right Y-axis point to the position where the expected gain (loss) is zero. At this point there is a 50/50 chance of realising or loosing money through investing in the company capitalized at 10.35, which is exactly the expected value of the company’s equity.

To the left of this point is the investment area. The green lines indicate a situation where the company is capitalized at 5.00 indicating an expected gain of 5.35 or more with a probability of 59% (100%-41%).

The figure to the right describes a situation where a company is capitalized above the expected value.

To the right is the speculative area where an industrial investor, with perhaps synergistic possibilities, could reasonably argue a valid case when paying a price higher than expected value. The red line in the figure indicates a situation where the company is capitalized at 25.00 – giving a loss of 14.65 or more with 78% probability.

To a financial investor it is obviously the left part – the investment area – that is of interest. It is this area that expected gain is higher than expected loss.

11/02/2009
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.

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.

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.).

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.

16/02/2008