Download 1 - public.asu.edu

1.4
Monte Carlo Simulation
Monte Carlo simulation in traditional capital budgeting use repeated random
sampling from probability distributions of crucial primary variables underlying cash flows
to arrive at output distributions or risk profiles of probable cash flows in the project NPV
for a given management strategy. Simulation attempts to imitate a real-world decision
setting by using a mathematical model (consisting of operating equations or identities) to
capture the important functioning characteristics of the project as it evolves through time
encountering random events, conditional on management's preset operating strategy. A
Monte Carlo simulation usually follows these steps:
1. Modeling the project through a set of mathematical equations and identities for all
the important primary variables, including a description of interdependencies among
different variables and across different time periods.
2. Specifying probability distributions for each of the crucial variables, either
subjectively or from past empirical data. Sensitivity analysis should precede simulation to
determine which variables are important so that special care be taken to obtain their
precise probability distributions; and which are not so that a single estimate of the
variables may suffice. To deal with dependencies between two variables, in principle a
single probability distribution can be determined for the independent variable while
several distributions can be specified for the dependent one, each conditional on the
independent variable falling within a given range. In practice this may sometimes place
unreasonable demands on management's ability to furnish realistic estimates.
3. A random sample is then drawn (using a computer random number generator)
from the probability distribution of each of the important primary variables enabling (with
the help of the modeling equations and identities) the calculation of net cash flows for
each period (from which the NPV for the sample can also be determined).
4. The process is repeated many times (until, say, 500 random samplings are
obtained), each time storing the resulting cash flow or NPV sample observations so that
finally a probability distribution for the project's cash flows or of NPV can be generated
(along with its expected value, standard deviation and other statistics).
Although simulation can handle complex decision problems under uncertainty with
a large number of (dynamically interacting) input variables, it is not without its own
limitations.
1. 1. First, even if those responsible for estimating the probability distributions were
unbiased, it would still be very difficult and complex to correctly capture all the
inherent interdependencies. The existence of substantial complexity might then
induce management to delegate model building to experts, with the resulting
danger that management's understanding of and consequently faith in and
commitment to the simulation results may be substantially reduced.
2. 2. Second, when the outcome of simulation is a risk profile of NPV rather than of
the intermediate cash flows, the meaning of an outcome probability distribution of
NPV, is questionable since it is not clear what is the correct discount rate to be
used.
a. a. Quoting Myers (1976): "If NPV is calculated using an appropriate risk
adjusted discount rate, any further adjustment for risk is double-counting.
If a risk-free rate of interest is used instead, then one obtains a distribution
of what the project's value would be tomorrow if all uncertainty about the
project's cash flows were resolved between today and tomorrow. But since
uncertainty is not resolved in this way, the meaning of the distribution is
unclear."
b. b. Also, if a project can have many possible "present values", one for
each point on the distribution, then we can no longer interpret present
value as the price the project would command in competitive capital
markets.
3. 3. Third, even if management wants to base a decision on the probability
distribution or risk profile of NPV, it still has no rule for translating that profile
into a clear-cut decision for action; it can only stare at the expected NPV
(discounted at the riskless interest rate) and its surrounding variance until it
receives inspiration from above on how to trade them off.
4. 4. Fourth, simulation users may be tempted to use as a relevant measure of risk
the variability of project outcomes (i.e., the project's own, or total risk) instead of
its systematic risk, which we saw to be the relevant risk from the point of view of
the firm's shareholders who have opportunities to diversify away part of that risk
by buying other securities in the market; Lewellen and Long (1972) point exactly
to this inability to reveal how the resulting distribution interacts with the
distribution of returns faced by the firm in its other projects or by investors in their
personal portfolios as the major shortcoming of simulation. Furthermore, using the
total variability of the NPV distribution violates value additivity and enables
managers to successfully promote unrelated projects as a group, when each project
alone might be unacceptable.
5. 5. Myers (1976) points to other problems of interpretation of simulation output,
such as the unreliability of extreme values of simulated probability distributions.
6. 6. Finally, Monte Carlo simulation is a forward-looking technique based on a
predetermined (built-in) operating strategy offering roughly symmetric probability
distributions --and as such it may be an appropriate model for path (or history)
dependent problems-- but it cannot handle well the asymmetries in the
distributions introduced by management's flexibility to review its own
preconceived operating strategy when it turns out that, as uncertainty gets resolved
over time, the realization of cash flows differs significantly from initial
expectations. Management in reality can adapt to surprises (e.g., abandon a project
if it turns out to perform surprisingly poorly), but a computer simulation model
cannot: it will faithfully and blindly continue obeying the business-as-usual
operating strategy that was programmed to follow based on management's
expectations and information at the outset. Thus, as will become clear later,
simulation is limited in dealing with the options or free-boundary problems that
enter the valuation of real investment opportunities (such as determining the
optimal timing policies for undertaking or abandoning a project), whose solution
requires a backward induction or dynamic programming approach.
Despite the above shortcomings, in many real-life problems when making use of
dynamic programming is difficult (e.g. when there are many state variables), simulation
and numerical lattice approaches constitute the primary practical approaches to valuation.
The more appropriate role for simulation in traditional capital budgeting would be to
assess the probability distribution not of NPV but of cash flows, from which the expected
value of cash flows and the appropriate risk-adjusted discount rates can be determined and
used to derive a single-value expected NPV that can be used for clear-cut
decision-making. Thus, simulation should not be instead of but rather as an aid to
implementing NPV. When real options are involved, as pointed out later in numerical
methods, simulation may be a powerful tool for determining the relevant "certaintyequivalent" or risk-neutral probability distributions within a backward risk-neutral
valuation process.