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Outcome:

Lose Spend nil

Fig. 5.4 Example of a simple decision tree

A single decision node is hardly worth drawing but multiple decisions can jus-

tify the effort. Let us complicate the auction situation. Suppose that we want

to decide whether it is worth spending $50,000 on initial design work prior to

attending the sealed-bid auction of a unique plot of land with great potential

for redevelopment. We have decided that we will submit a bid of $500,000 and

with this bid we consider that we have an evens chance of being the winning

bidder. If we buy the land we will first have to apply for permission to redevelop.

We think there is an 80% chance that this will be forthcoming. If we fail to

gain permission we anticipate being able to sell the plot for $400,000. Having

gained permission, we estimate that we will need to spend a further $500,000

to renovate the buildings. After that we anticipate being able to sell the rede-

veloped site for $1.2m. For the purposes of simplicity we will assume that all

of the financial numbers are already stated in present value terms. Given the

above assumptions, what is the NPV of our proposed strategy?

The following chart shows the decision tree for this situation. The first node

covers the auction and the second the granting of planning permission.

Outcome:

NPV + $150,000

80% Probability 40%

â€“

Yes

50%

â€“

Win No Outcome:

â€“ 20%

NPV â€“ $150,000

Los Probability 10%

eâ€“ Outcome:

50%

NPV â€“$50,000

Probability 50%

Fig. 5.5 Property development decision tree

The way to calculate the value given a decision tree is first to value each of the

individual outcomes. Next we must calculate the probability of each outcome

occurring. To do this one multiplies across. So we are successful in our venture

153 Building block 5: Risk

in 80% of the times we win the auction. Since we only win the auction 50% of

the time we are successful just 40% of the time. Success brings a value gain of

$150,000. 40% of this is $60,000. Winning the auction but not getting permis-

sion happens just 10% of the time and has an associated value loss of $150,000.

10% of this is minus $15,000. Failing to win the property in the sealed bid

auction results in a value loss of $50,000 owing to our initial design work.

This happens 50% of the time so the contribution to overall expected value is

a value loss of $25,000. Overall, our strategy has a value of just $20,000.

In this case we can also use our model to investigate changes in the assump-

tions. Suppose that we decided that the initial design work could be delayed

until after we gained permission to develop. What would this do to value?

The NPV would now be 50% of zero plus 10% of minus $100,000 plus 40% of

$150,000. This is $50,000. So now we know that the impact on value of doing

the initial design before we know for sure that it is needed is $30,000.

Success values

A related concept to decision trees is the idea of success values. A success

value is the value assuming that a successful outcome is achieved. It is easiest

to explain this through a simple example.

I swim a lot and I keep detailed records of how often I swim and how far I

manage each time. These records show that in 2005 I covered a total distance

of 572.5 km whereas in 2006 I only did 546.0 km. How should I explain the

approximately 5% decline in distance covered? Was age finally taking its toll?

I suggest that to think about my swimming it would be best to distinguish

between days when I did swim (we can call this success) and the days when I

did not (failure). A check of the records shows that in 2005 I swam 285 times

with an average distance per swim of 2,009 m while in 2006 I only swam 263

times but each swim averaged 2,076 m. This gives a much more informative

picture. The reduction in overall distance was due to a cut in the number of

times that I swam.

The idea of a success value can be very useful when dealing with situations

where there is a sharp distinction between success and failure. It is not simply

a question of building a better model of what is going on. Some parts of an

organisation need to plan for a successful outcome while other parts need

to know what will happen after allowing for the failures. In my swimming

example, I must clearly plan for individual swimming sets that are about

2 km long. If, however, I am seeking sponsorship per km swum in a year I

must allow for all those days when I donâ€™t even start.

154 The five financial building blocks

The business analogy might be with a property development company.

Suppose a company had 50 separate property development teams each look-

ing at opportunities like the one we developed above. Each team is invited

to submit its budget to the corporate head office. The likelihood is that each

team will submit a budget based on success because it will want to reserve

the necessary capital should its sealed bid be successful and should planning

permission be granted. So 50 plans will come to head office showing a total

initial design spend of $2.5m, a total property purchase spend of $25m and

a redevelopment budget also of $25m. The sales estimate will be a wonderful

$60m. This is clearly unrealistic. Each team is right to be thinking about the

consequences of success but at the corporate level it is appropriate to allow

for the impact of failure. The corporate budget needs to be for initial design

of $2.5m, land purchase of $12.5m, land sales of $2m, redevelopment costs of

$10m and property sales of $24m.11

The key thing to be aware of when dealing with success values is that dif-

ferent teams within an organisation will need to deal with different sets of

assumptions. Some will need to deal with data that are based on the presump-

tion of success. The higher up the organisational pyramid you look, however,

the more important it will be to allow for both success and failure. This applies

to valuations as well as to simple business planning and target setting.

Making appropriate assumptions

Now that we have a better understanding of how risk works we can return

to the question of what makes a good assumption for the purposes of eco-

nomic evaluation. It should be clear that the best basis for assumptions is that

they be expected values. The advantage of this would be that the resultant

NPV would also be an expected value and so would be the technically correct

basis for assessing whether or not the project created value for sharehold-

ers. The calculated NPV would also be suitable for direct comparison with

other expected value NPVs from competing projects if capital investment

was being rationed.

One does, however, need to be aware of the danger of believing too much

in the quality of your assumptions. Expected values are not easy to estimate.

We know in principle what is needed, but the evidence is that people find

it very hard to produce good quality estimates. With one individual esti-

mate it is hard to prove that a particular assumption was wrong unless the

The overall gain is just $1m which is the same as 50 times our individual project NPV of $20,000.

11

155 Building block 5: Risk

assumption was accompanied by a maximum range and the actual outcome

was outside the range. One can only judge the overall quality of a consider-

able number of estimates because it is only then that one can expect the result

to be close to the forecast.12

An alternative to adopting expected value assumptions is to go for most-

likely assumptions. This can have the advantage that each assumption will

appear reasonable and will require less work to assess. Decision-makers tend

to prefer this approach because they can apply their experiences and decide

if they believe that the assumptions can come about. The problem with using

most-likely assumptions is that one cannot give a particular statistical mean-

ing to the calculated NPV. We know that expected value assumptions should

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