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Exercise 307
(a) The percentage of people who will reply to the first letter in
the North (N), Central (C) and South (S) regions of the country,
respectively.
(b) The average donation of those replying to the first letter in each
of these regions.
(c) The percentage of people who will reply to the reminder in each
of the three regions.
(d) The average donation of those replying to the reminder in each
of the regions.
Probability distributions have been estimated for the different
regions because their different economic conditions are likely to
have a major effect on people’s propensity to donate to the charity.
Figure 11.6 shows the cumulative probability distribution of net
returns (i.e. the total value of donations less the cost of running the
direct-mail appeal). It can be seen that there is approximately a 20%
probability that the net returns will be negative, causing the charity
to lose money. In the simulation the possible losses extended to
nearly $150 000.
The managers of the charity are keen to take action to reduce
this risk, but are not sure where their actions should be directed?
Figure 11.7 shows a tornado diagram for the appeal. The numbers
at the ends of the bars show what are thought to be the highest
and lowest possible values for each factor. For example, the possible
average donation in the North is thought to range from $2 to $17.
(a) Identify the areas where risk management is likely to be most
effective.
(b) Create a set of possible risk management strategies that might
reduce the risk of the charity losing money and increase its
expected return.
Cumulative probability
1.0
0.8
0.6
0.4
0.2
0.0
−200000 −100000 0 100000 200000 300000
Surplus $
Figure 11.6 – Cumulative probability distribution for AB Charity