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Construction time and construction cost. You would expect a strong link between the two

because, as the saying goes, â€˜Time is moneyâ€™. If a project is delayed this will almost inev-

itably mean extra costs compared with budget.

Capacity utilisation and average selling prices. Low capacity utilisation could mean

that selling margins would be reduced because companies would be tempted to reduce

selling prices in order to win more sales. So there may well be a correlation between

capacity utilisation and selling prices. We cannot, however, be sure whether low margins

would cause low selling prices. This is because if the raw material prices had risen a lot

this may drive down demand for the product.

Low oil prices and number of people travelling by plane. Low oil prices can translate

into lower ticket prices which in turn can encourage more people to fly.

Hotel occupancy rates and theatre bookings. More people staying in hotels may indicate

more people want to go out in the evening. Some of these people will go to the theatre.

Economic growth and the cost of advertising slots on TV. Greater economic growth will

mean companies can afford more advertising spend. Since the number of advertising

slots is more or less fixed, this will mean that the price per slot will rise.

Sales of baby-clothes and share prices. Share prices will rise if the economy does bet-

ter than expected. When the economy does better than expected people may have more

601 Building block 5: Risk

money to spend on baby-clothes. However, since the arrival of babies is probably more or

less independent of the stock market the correlation would be weak.

A coinâ€™s landing heads six times in a row and then landing tails. Although seven heads

in a row is very unlikely and one might therefore think that sooner or later a tail must

show, there is no correlation between one coin toss and another.

11. You are evaluating a project to mine iron ore. The first cut economics show a substantial

NPV of $1,500m. There are, however, risks concerning the ore body. The first risk concerns

its size because as yet a full geological survey has not been carried out. The second risk

concerns the presence of certain trace elements in the ore. If these are present the cost of

purification would rise very substantially.

As regards the first risk of the ore body size, your first-cut economics are based on a

most likely quantity of ore in place. Should you go ahead and construct the mine in the

usual way, the uncertainty band around the $1,500m NPV is from a worst-case of zero

(10% chance) to the most-likely (75% chance) of $1,500m to an upside case with a value

of $2,000 (15% chance). You have three choices. (1) Do nothing and accept the risks. (2)

Build the facilities in two stages with the second stage adjusted to suit the quantity of ore

in place which will be obvious once the mine comes on stream. This would lower both the

most-likely case NPV and the upside NPV by $100m. However, the downside case would

improve to $800m. (3) Carry out a traditional geological survey at a cost (stated in present-

value-equivalent terms) of $50m. This survey would warn of the downside case and allow

you to lower the construction costs such that the new downside NPV was $1,000m. This

NPV is excluding the cost of the survey and would occur two years later than the NPV in

the do-nothing case.

The trace elements are assessed only to have a 5% chance of being present. If they are

present it would be necessary to construct an additional purification stage. This would cost

$500m (stated in present-value terms) and would delay the NPV by three years. We could

build the purification unit as part of the main project. If we did so its cost would be reduced

by a half and the build would not delay the project at all. We could delay the entire pro-

ject for two years to carry out the necessary sample tests to see if the trace elements were

present. The sample tests would cost $40m to carry out. If they showed that unacceptable

quantities of trace elements were present we would then build the purification unit as part

of the project.

What recommendations would you make to the project team in relation to these

risks? What value would you put on this opportunity at this time? You should assume a

CoC of 9%.

First we will deal with the ore body risk. The base case NPV is not an expected value. The

â€˜correctâ€™ NPV can be calculated in two ways.

Either 10% Ã— $0m + 75% Ã— $1,500m + 15% Ã— $2,000m = $1,425m

Or $1,500 â€“ 10% Ã— $1,500 + 15% Ã— $500 = $1,425m

This is the expected value if we simply accept the ore body risk but before we allow for

the trace element risk.

The expected value of the two stage construction approach is:

10% Ã— $800m + 75% Ã— $1,400m + 15% Ã— $1,900m = $1,415m

602 Individual work assignments: Suggested answers

The incremental effect of the approach can also be calculated directly using the impact

times probability approach. In this instance there are two impacts and two probabilities

which together sum to 100%. The calculation is:

10% Ã— $800m â€“ 90% Ã— $100m = â€“$10m

This way of mitigating the risk does not add to value and so should not be

recommended.

The survey approach would cost $50m and delay the NPVs by two years. I will first look

at the impact of the survey and then study the effect of the delay as a separate step.

The benefit of the survey approach is $1,000m but this only happens 10% of the time

(when we commit to the survey we do not know what the result will be so we must con-

tinue to use the same assumption about the likelihood of the downside). Since 10% of

$1,000 is $100, the net gain of carrying out the survey is $50m, meaning that the expected

value of following this approach is $1,475m. This, however, is before allowing for the

two year delay. This happens irrespective of the outcome. It is quite clear that applying

a 9% discount rate for two years will lower the NPV by more than the $50m gain so this

approach should also be rejected. The conclusion in regard to the ore body size is to live

with the risk.

Now we turn to the trace element effect. This is anticipated to occur 5% of the time.

There is an additional capital cost of $500m (which, conveniently, was stated in value

terms). Also there is a three year delay. With a 9% CoC the discount factor for three years

is 0.772. This means that the value loss owing to delay is:

(1â€“0.772) Ã— $1,425m = $325m

So the total value impact of delay is $825m (i.e. delay cost plus extra capital cost). Since

the trace elements are anticipated just 5% of the time the impact is $41m. The resultant

expected value is $1,384m.

If we built the purification unit as part of the main unit it would cost just $250m. This

is much more than the risked impact of the trace elements so clearly we should not do this

either. The second option to mitigate the risk costs $40m and also delays the project. Once

again, we do not need to do all the maths to work out what to do. It is very clear that this

proposal would not create value and so it can be rejected.

We can conclude that the value of the opportunity at this time is $1,384m.

This final exercise should have indicated the particular benefit of the risk monetisation

approach. Calculations are greatly simplified if you do not always have to work out the

expected value of all possible outcomes. Answers are often obvious and a technique that

allows one to focus on the impact of a risk can save a lot of time.

The exercise should also have shown why one starts with a rough-cut NPV calculation.

If we had tried to build a model that would allow all possible outcomes to be tested the

work involved might have been great. If short cuts exist, then I would suggest you use

them!

Glossary

Abbreviated financial summary (AFS)

A simplified way of presenting the three main accounting statements (income statement, bal-

ance sheet and cash flow statement) alongside a value calculation such that the link between

accounts and value is made very clear. This book suggests adoption of the AFS layout as the

standard means of carrying out all valuations.

ABCDE valuation

A method of valuing a company which is explained in the book. In the model, A stands for

Asset value; B for Business development value; C is for Costs; D is for Debt and other liabil-

ities; with the result being E the Equity valuation.

Amortisation (also called depreciation in the UK)

An accounting term for the charge which results when the capital cost of a fixed asset is

spread out over its estimated useful life. Note that although this charge serves to lower profit,

it does not lower the generation of cash in the period.

Assumptions register

A list of all of the assumptions which have been made as part of the preparation of an invest-

ment case. The suggestion is that decision-makers review the assumptions and then study the

economic indicators that they imply.

Balance sheet

A summary of the assets and liabilities of a company at the end of any financial period. It

is said to show what a company owns and what it owes. It is called a balance sheet because

a consequence of the conventions which are used to prepare it is that the assets which are

owned must equal the sum which has been invested in them. This balancing sum is called

the liabilities.

Beta factor (Î²)

One of the key parameters in the capital asset pricing model (CAPM). Beta (the Greek letter

Î²) is a measure of the risk inherent in any share which cannot be removed through the phe-

nomenon called portfolio diversification. It is calculated via the co-variance of a share price

with the market index.

Bundling

This refers to showing the overall effect of two or more related but actually distinct invest-

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