Reducing Uncertainty: Market Research, Simulation and Sensitivity Analysis

A beverage company in Lagos plans a new drink. It does not know how many cartons it will sell, what price the market will accept, or whether the cost of sugar will rise.

It cannot make these uncertainties disappear. But it can do three things about them: gather information so that the estimates are better, build a model that plays out many possible futures, and test how far each estimate could be wrong before the plan fails.

This topic covers the difference between risk and uncertainty and the attitudes of decision makers to them; how market research and focus groups reduce uncertainty; how simulation, in particular the Monte Carlo method, works with random numbers; and how sensitivity analysis measures how much each variable could change before a decision becomes wrong. It builds on the earlier topic on one-off contracts, shutdown and further processing.

The next topic covers expected values and the maximax, maximin and minimax regret rules.

Risk, uncertainty and ways of reducing it

Risk and uncertainty

Many business decisions rest on what the decision maker thinks will happen, and the actual result may be better or worse. Uncertainty is the lack of enough reliable information about what will happen, so that estimates of future sales or costs are likely to be inaccurate.

Risk exists when the outcome could be any of several possibilities and a probability can be assigned to each; risk can then be analysed statistically. Risk cannot be removed from a decision, because it is in the situation; the decision maker can analyse it and decide whether it is acceptable.

Reducing uncertainty by research

For an established product, past sales adjusted for trend and for planned changes in price give a reasonable forecast. For a new product there is no benchmark, and the estimate of demand can be very uncertain. Two methods give more reliable information:

• Market research studies a market to obtain information, such as the attitudes and buying intentions of customers. It may test a prototype with target customers, or try to estimate demand directly, by surveys, interviews, observation or test marketing.
• Focus groups are small groups, selected to represent the target market, who are invited to give opinions and ideas about a product or market to a research team. Their views are rich in detail and quick to obtain. But the group is small, the members may influence one another and a dominant voice may mislead, so the findings need care before they are applied to the whole market.

Research costs money and time, and even good research does not remove uncertainty: customers may not do what they say they will. The value of the information should be greater than its cost (see the later topic on the value of information).

Attitudes to risk

• Risk averse. Considers risk and will not choose the riskier option unless the expected return is high enough to justify it. This is the usual assumption about managers.
• Risk neutral. Ignores risk and chooses the highest expected return.
• Risk seeking. Considers risk but will take extra risk in the hope of a higher return.

Simulation and sensitivity analysis

Simulation

Simulation is the imitation of the working of a real system over time. A model is built to represent the key features of the system. The model is then run many times, with different values for the uncertain variables, and the results are used as if they were observed outcomes. A single run tells little; the average and spread of many runs show what is likely.

Simulation is useful when there are many variables, each with uncertain values, and when the links between them are too complicated for a decision tree: queues, inventory control, project and investment appraisal, and replacement problems.

Monte Carlo simulation

In a Monte Carlo simulation a random device decides what happens at each point. The steps are:

1. List the uncertain variables and their possible values with probabilities.
2. Build a cumulative probability column for each variable.
3. Allocate ranges of random numbers in proportion to the probabilities: 20% takes 20 numbers out of 100. Two-digit random numbers run from 00 to 99.
4. Generate random numbers, one for each variable in each run, and read off the value that matches the range in which each falls.
5. Calculate the result of the run (profit, inventory, queue length) from the chosen values.
6. Repeat many times and analyse the results: their average, range and the probability of a loss.

Advantages: it handles many variables at once; it shows the spread of outcomes as well as the average; it needs no assumption of a particular distribution if the probabilities are known; and a computer makes many runs cheap.

Limitations: the model is only as good as the probabilities put into it; the variables may not be independent (price and volume usually are not); it can be costly to build and may give a false sense of precision; and it does not itself give a decision, only information for one.

Sensitivity analysis

Sensitivity analysis starts from the original plan, for example a budget or project appraisal, and changes one key variable at a time (price, volume, material cost, labour cost, fixed cost, completion time) to see the effect on profit or net present value.

It answers two questions: how much would the result change if this estimate were wrong by a given percentage, and by how much must the estimate change before the decision turns from acceptable to unacceptable? The second is the usual calculation:

Sensitivity (%) = profit (or margin of acceptability) ÷ the value of the item that changes × 100. The item is the sales revenue for a change in price, the contribution for a change in volume, and the cost line itself for a cost change.

The variable with the smallest percentage is the most critical, because only a small error would make the plan fail; management should concentrate checking and control on it. Advantages: simple, quick on a spreadsheet, and shows which estimates matter most.

Limitations: it changes one variable at a time, although in practice several move together (a lower price may raise volume); it gives no probability of a change happening; it does not itself say whether the decision should be made; and the size of change to test is a matter of judgement.

Layouts for simulation and sensitivity

1. Random number ranges. List outcomes and probabilities; cumulate; allocate 00 to the first cumulative figure minus 1, and so on, so that the last range ends at 99.
2. Run. For each random number, find the range and outcome; calculate the result.
3. Average. Total of results ÷ number of runs; compare with the expected value.
4. Sensitivity. Base profit; for each variable, profit ÷ the relevant amount × 100; rank.

Money is in naira and each answer is rounded once, at the end.

Worked examples

1. Cumulative probabilities. 20%, 65%, 100%. Ranges: 10 units 00 to 19; 20 units 20 to 64; 30 units 65 to 99.
2. Simulation. 07 → 10; 71 → 30; 43 → 20; 90 → 30; 28 → 20. Total 110, average 22 units a day.
3. Expected value.
   10 × 0.20 + 20 × 0.45 + 30 × 0.35 = 2 + 9 + 10.5 = 21.5 units.
   The simulated average is close; with more runs it would approach the expected value.

1. Ranges. Volume: 8,000 is 00 to 29; 10,000 is 30 to 79; 12,000 is 80 to 99. Price: ₦50 is 00 to 39; ₦55 is 40 to 99. Variable cost: ₦30 is 00 to 24; ₦35 is 25 to 74; ₦40 is 75 to 99.
2. Run 1. 41 → 10,000; 85 → ₦55; 12 → ₦30.
   Contribution (55 − 30) × 10,000 = 250,000
   profit = ₦160,000.
3. Run 2. 08 → 8,000; 22 → ₦50; 90 → ₦40.
   Contribution 10 × 8,000 = 80,000
   profit = ₦(10,000).
4. Run 3. 93 → 12,000; 60 → ₦55; 51 → ₦35.
   Contribution 20 × 12,000 = 240,000
   profit = ₦150,000.
5. Average.
   (160,000 − 10,000 + 150,000) ÷ 3 = ₦100,000.
   Three runs are far too few to rely on; thousands would be run in practice.
   The runs show that a loss is possible when all three variables go the wrong way.

1. Profit.
   Contribution (100 − 60) × 20,000 = 800,000
   less fixed 600,000 = ₦200,000.
2. Price.
   200,000 ÷ revenue 2,000,000 = 10.0% fall.
3. Volume.
   200,000 ÷ contribution 800,000 = 25.0% fall.
4. Materials.
   200,000 ÷ 700,000 = 28.6% rise.
   Labour. 200,000 ÷ 400,000 = 50.0%.
   Variable overhead. 200,000 ÷ 100,000 = 200%.
   Fixed costs. 200,000 ÷ 600,000 = 33.3%.
5. Comment. Price is the most critical variable: a fall of only 10% removes all the profit. Management should be most careful about the selling price estimate, and, since volume is also sensitive, about the market research behind it.

Expect variants: a table of probabilities for demand and a different cost, a two-variable simulation with a given list of random numbers, or a question asking for a discussion of the limits of the method.

Common mistakes

• Wrong random number ranges. Two-digit numbers run 00 to 99, and ranges must not overlap or leave gaps.
• Reading the cumulative column as the range. The range ends at the cumulative figure minus 1.
• Dividing by the wrong base in sensitivity. Price uses revenue; volume uses contribution; a cost uses that cost.
• Calling the simulation average the expected value when only a few runs were done.
• Confusing risk and uncertainty. Risk has estimated probabilities; uncertainty does not.
• Forgetting limitations. Name at least two for each technique.

Quick revision

• Risk has probabilities; uncertainty does not. Reduce uncertainty by market research and focus groups.
• Risk averse, neutral, seeking.
• Monte Carlo: cumulative probabilities, random number ranges, many runs, average and spread.
• Sensitivity: profit ÷ base × 100; the smallest percentage is the most critical; one variable at a time.

How the marks are earned

• Allocate: cumulative probabilities and ranges.
• Calculate: each run and the average, or each sensitivity.
• Comment: what the results show and the limits of the method.

Practice questions

These are original questions, written in the style of the Skills examination. Work each one before you open the answer.

Recall check: multiple choice

Section B style: written questions

Model answers

Spotted a mistake? Tell us and we will check it.