# Introduction to Simulation Models

Simulation models sets out to mimic real life company operations, that is describing the transformation of raw materials and labor to finished products in such a way that it can be used as support for strategic decision making.

A full simulation model will usually consist of two separate models:

- an EBITDA model that describes the particular firm’s operations and
- an generic P&L and Balance simulation model (PL&B).

**The EBITDA model ladder**

Both the deterministic and stochastic balance simulation can be approached as a ladder with two steps, where the first is especially well suited as an introduction to risk simulation and the second gives a full blown risk analysis. In these successive steps the EBITDA calculations will be based on:

- financial information only, by using coefficients of fabrications and unit prices (e.g. kg flour per 1000 bread and cost of flour per kg, etc.) as direct input to the balance model – the direct method and
- EBITDA models to give a detailed technical description of the company’s operations.

The first step uses coefficients of fabrications and their variations give a low effort (cost) alternative, usually using the internal accounting as basis. In many cases, this will often 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.

This step is especially well suited for introduction to risk simulation and the art of communicating risk and uncertainty throughout the firm. It can also profitably be used in cases where time and data is limited and where one wishes to limit efforts in an initial stage. Data and assumptions can later be augmented to much more sophisticated analyses within the same framework. This way the analysis can be successively built in the direction the previous studies suggested.

The second step implies setting up a dedicated EBITDA subroutine to the balance model. This can then 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 EBITDA model can both be a stand-alone model and a subroutine to the PL&B model. The stand-alone EBITDA model can be used to in detail study the firm’s operations and how different operational strategies will or can affect EBITDA outcomes and distribution.

When connected to the PL&B model it will act as a subroutine giving the necessary information to produce the P&L and ultimately the Balance and the – outcomes distributions.

This gives great flexibility in model formulations and the opportunity to fit models to different industries and accommodate for the data available.

**P&L and Balance simulation**

The generic PL&B model – based on the IFRS standard – can be used for a wide range of business activities both:

- describes the firm’s financial environment (taxes, interest rates, currency etc.) and
- acts as a testing bed for financial strategies (hedging, translation risk, etc.)

Since S@R has set out to create models that can give answers to both deterministic and stochastic questions thus the PL&B model is a real balance simulation model – not a simple cash flow forecast model.

All runs in the simulation produces a complete P&L and Balance it enables uncertainty curves (distributions) for any financial metric like ‘Yearly result’, ‘free cash flow’, economic profit’, ‘equity value’, ‘IRR’ or’ translation gain/loss’ etc. to be produced.

People say they want models that are simple, but what they really want is models with the necessary features – that are

easyto use. If something is complex but well designed, it will be easy to use – and this holds for our models.

The results from these analyses can be presented in different forms from detailed traditional financial reports to graphs describing the range of possible outcomes for all items in the P&L and Balance (+ much more) looking at the coming one to five (short term) or five to fifteen years (long term) and showing the impacts to e.g. equity value, company value, operating income etc.

The goal is to find the distribution for the firm’s equity value which will incorporate all uncertainty facing the firm.

*This uncertainty gives both shape and location of the equity value distribution, and this is what we – if possible – are aiming to change:*

- reducing downside risk by reducing the left tail (blue curve)
- increasing expected company value by moving the curve to the right (green curve)
- increasing the upside potential by increasing the right tail (red curve) etc.

**The Data**

To be able to simulate the operations we need to put into the model all variables that will affect the firm’s net yearly result. Most of these will be collected by S@R from outside sources like central banks, local authorities and others, but some will have to be collected from the firm.

The production and firm specific variables are related to every day’s activities in the firm. Their historic values can be collected from internal accounts or from production reports. Someone in the procurement-, production- or sales department will have their records and most always the controllers. The rest will be variables inside the domain of the CEO and the company treasurer.

The variables fall in five groups:

ii. variables describing the firms strategy,

iii. general variables used for forecasting purposes,

iv. direct problem related variables and

v. the firm specific:

The first group will contain – for all countries either delivering raw materials or buying the finished product (s) – variables like: taxes, spot exchange rates etc. For the firm’s domestic country it will in addition contain variables like: Vat rates, taxes on investments and dividend income, depreciation rates and method, initial tax allowances, overdraft interest rates etc.

The second group will contain variables like: minimum cash levels, debt distribution on short and long term loans and currencies, hedge ratios, targeted leverage, economic depreciation etc.

The third group will contain variables needed for forecasting purposes: yield curves, inflation forecasts, GDP forecasts etc. The expected values and their 5 % and 95 % probability limits will be used to forecast exchange rates, interest rates, demand etc. They will be collected by S@R.

The fourth group will contain variables related to sales forecasts: yearly air temperature profiles (and variation) for forecasting beer sales and yearly water temperature profiles (and variation) for forecasting increase in biomass in fish farming.

The fifth group will contain variables that specify the production and costs of production. They will vary according to the type of operations e.g.: operating rate (%), max days of production, tools maintenance (h per 10.000 units) , error rate (errors per 1000 units), waste (% of weight of prod unit), cycle time (units per min), number of machines per shift (#), concession density (kg per m^{3}), feed rates (%), mortality rates (%) etc., etc.. This variable specifies the production and will they be stochastic in the sense that they are not constant but will vary inside a given – theoretical or historic – range.

To simulate costs of production we use the coefficients of fabrication and their unit costs. Both the coefficients and their unit costs will always be of stochastic nature and they can vary with capacity utilization: energy per unit produced (kwh/unit) and energy price (cost per Kwh), malt use (kg per hectoliter), malt price (per kg), maximum takeoff weight (ton), takeoff charge (per ton), specific consumption of wood, (m^{3}/Adt), cost of round wood (per m^{3}), etc., etc.

The uncertainty (and risk) stemming from all groups of variables will be propagated through the P&L and down to the Balance, ending up as volatility in the equity distribution.

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

### 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.

Most companies have some sort of model describing the company’s operations. They are used mostly for budgeting, but in some cases also for forecasting cash flow and other important performance measures.

If the client already has spread sheet models describing the operations, we can build on this. There is no reason to reinvent what has already been done – thus saving time and resources that can be better utilized in other phases of the project.

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.

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.

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 first approach can also be considered as an introduction and stepping-stone to a more complete EBITDA model and detailed simulations.

### 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, key people from the controller group will be adequate for this work and if they do not have the direct knowledge, they usually know whom 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 – depending on the scope of the project.

For S&R, the period 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 second alternative for more complex models. The total time will also depend on the number of analyses that needs to be run and the type of reports that has to be delivered.

The team’s participation in the project also makes communication of the results up or down in the system simpler. Since the input data is collected by templates this gives the responsible departments and persons, ownership to assumptions, data and results. These templates thus visualize the flow of data thru the organization and the interdependence between the departments – facilitating the communication of risk and the different strategies both reviewed and selected.

No knowledge or expertize on uncertainty calculations or statistical methods is required from the clients side. The team will thru ‘osmosis’ acquires the necessary knowledge. Usually the team finds this as an exciting experience.