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RISK ANALYSIS 493

In risk analysis we are concerned with both the probability of a loss and the
magnitude of a loss. Although the base-case scenario looks appealing, PortaCom
might be interested in what happens if the estimates of the direct labour cost per
unit, parts cost per unit and first-year demand do not turn out to be as expected
under the base-case scenario. For instance, suppose that PortaCom believes that
direct labour costs could range from E43 to E47 per unit, parts cost could range
from E80 to E100 per unit and first-year demand could range from 1500 to 28 500
units. Using these ranges, what-if analysis can be used to evaluate a worst-case
scenario and a best-case scenario.
The worst-case value for the direct labour cost is E47 (the highest value), the
worst-case value for the parts cost is E100 (the highest value) and the worst-case
value for demand is 1500 units (the lowest value). Thus, in the worst-case scenario,
c 1 ¼47, c 2 ¼100 and x¼1500. Substituting these values into equation (12.1) leads to
the following profit projection:

Profit ¼ð249 47 100Þð1500Þ 1 000 000 ¼ 847 000
So, the worst-case scenario leads to a projected loss of E847 000.
The best-case value for the direct labour cost is E43 (the lowest value), the best-
case value for the parts cost is E80 (the lowest value) and the best-case value for
demand is 28 500 units (the highest value). Substituting these values into equation
(12.1) leads to the following profit projection:
Profit ¼ð249 43 80Þð28 500Þ 1 000 000 ¼ 2 591 000

Problem 2 will give you So, the best-case scenario leads to a projected profit of E2 591 000.
practise using what-if At this point the what-if analysis provides the conclusion that profits could range
analysis.
from a loss of E847 000 to a profit of E2 591 000 with a base-case scenario value of
E710 000. Although the base-case profit of E710 000 is possible, the what-if analysis
indicates that either a substantial loss or a substantial profit is also possible. Other
scenarios that PortaCom might want to consider can also be evaluated. However, the
difficulty with what-if analysis is that it does not indicate the likelihood of the various
profit or loss values. In particular, we do not know anything about the probability of a
loss.

Simulation
Using simulation to perform risk analysis for the PortaCom problem is like playing
out many what-if scenarios by randomly generating values for the probabilistic
inputs. The advantage of simulation is that it allows us to assess the probability of
a profit and the probability of a loss.
Using the what-if approach to risk analysis, we selected values for direct labour
cost per unit (c 1 ), parts cost per unit (c 2 ) and first-year demand (x), and then
calculated the resulting profit. Applying simulation to the PortaCom problem
requires generating values for these variables that are representative of what we
might observe in practice. To generate such values, we must know the probability
distribution for each variable. Let’s assume that further analysis by PortaCom led to
the following probability distributions for the direct labour cost per unit, the parts
cost per unit and first-year demand:

One advantage of Direct Labour Cost PortaCom believes that the direct labour cost will range from
simulation is the ability to E43 to E47 per unit and is described by the discrete probability distribution shown in
use probability Table 12.1. Thus, we see a 0.1 probability that the direct labour cost will be E43 per
distributions that are
unique to the system unit, a 0.2 probability that the direct labour cost will be E44 per unit and so on. The
being studied. highest probability of 0.4 is associated with a direct labour cost of E45 per unit.

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