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Applying simulation to investment decisions 203
It can be seen from these results that simulation enables a more
informed choice to be made between investment opportunities. By
restricting us to single-value estimates the conventional NPV approach
yields no information on the level of uncertainty which is associated
with different options. Hespos and Strassman 7 have shown how the
simulation approach can be extended to handle investment problems
involving sequences of decisions using a method known as stochastic
decision tree analysis.
Utility and net present value
In order to help a decision maker to choose between a number of
alternative investment projects we could obtain a utility function for net
present value. This would involve giving the highest possible NPV a
utility of 1, the lowest a utility of 0 and the use of questions involving
lotteries to determine the utilities of intermediate NPVs. The decision
maker would then be advised to choose the investment project which
had the highest expected utility. The question is, how justified would
we be in converting NPVs to utilities? As we demonstrate below, to use
NPVs we need to make some strong assumptions about the decision
maker’s preferences.
First, the use of the NPV approach implies that the decision maker’s
relative strength of preference for receiving money in any two adjacent
years is the same, whatever those years are. For example, if a 10%
discount rate is used it implies that $1 receivable in one year’s time is
equivalent to receiving about $0.91 today. Similarly, $1 receivable in
10 years’ time is equivalent to receiving $0.91 in 9 years’ time. Now it
may well be that a decision maker has a very strong relative preference
for receiving money now rather than in a year’s time, while his or her
relative preference between receiving a sum in 9 as opposed to 10 years
is much weaker.
Second, if we consider the decision maker’s relative preference for
sums of money between the same pair of years it can be seen that the
NPV method assumes a constant rate of trade-off between the years.
For example (again assuming a 10% discount rate), it assumes that you
would be prepared to give up the promise of $1 in a year’s time in
order to receive $0.91 today, and that you would be prepared to go
on making this exchange, irrespective of the amount of money which
is transferred from next year to this. Again, this may not be the case.
You may be desperate for $10 000 now and be prepared to give up the
promise of £3 in a year’s time for each $0.91 you can receive today. Once