Simulation Analysis Sensitivity analysis becomes unmanageable if we change several factors

Simulation Analysis Sensitivity analysis becomes unmanageable if we change several factors

at the same time. A manageable approach to changing two or more fac- tors at the same time is computer simulation. Simulation analysis allows the financial manager to develop a probability distribution of possible outcomes, given a probability distribution for each variable that may change.

Suppose you are analyzing a project having the following uncertain elements: (1) sales (number of units and price); (2) costs; and (3) tax rate. Suppose further that the initial outlay for the project is known with certainty and so is the rate of depreciation. From the firm’s market- ing research, you estimate a probability distribution for dollar sales. And from the firm’s engineers, production management, and purchasing agents, you estimate the probability distribution for costs, which depends, in part, on the number of units sold. The firm’s economists estimate the probability distribution of possible tax rates.

You have three probability distributions to work with. Now you need a computer simulation program to meet your needs—one that can:

■ randomly select a possible value of unit sales for each year, given the probability distribution; ■ randomly select a possible value of costs for each year, given the unit sales and the probability distribution of costs; and ■ randomly select a tax rate for each year, given the probability distribu- tion of tax rates.

While the computer cannot roll a die, spin a wheel like they do in TV game shows, or select ping-pong balls with numbers as they do with lot- teries, computers can be programmed to randomly select values based on whatever probability distribution you want. For example, Lotus Development Corporation has a program, called @Risk, that allows the financial manager to assume probability distributions for different vari- ables in an analysis and perform a simulation.

Once the computer selects the number of units sold, the cost per unit, and the tax rate, the cash flows as well as its internal rate of return are calculated. You now have one internal rate of return. Then you start all over, with the computer repeating this process, calculating an inter- nal rate of return each time. After a large number of trials, you will have

a frequency distribution of the return on investments. A frequency dis- tribution is a description of the number of times you’ve arrived at each different return. Using the statistical measures of risk, you can evaluate

Capital Budgeting and Risk

the risk associated with the return on investments by applying these measures to this frequency distribution. 1

Simulation analysis is more realistic than sensitivity analysis because it introduces uncertainty for many variables in the analysis. But if you use your imagination, this analysis may become complex since there are interdependencies among many variables in a given year and interdepen- dencies among the variables in different time periods.

However, simulation analysis looks at a project in isolation, focus- ing on the project’s total risk. And simulation analysis also ignores the effects of diversification for the owners’ personal portfolio. If owners hold diversified portfolios, then their concern is how a project affects their portfolio’s risk, not the project’s total risk.