Project Management in the Oil and Gas Industry

2.6 Risk Adjusted Value (RAV)
Three elements contribute to project ranking: expected return, risk, and 
loss of funds. One problem concerns trading off each value. Return may 
indicate one ranking, risk another, and so on. The EPV and risk weighted 
values, however derived, include each of these components. Compare two 
projects, each with the same EMV. If the manager could lose ten dollars for 
a dry hole on one and 100 million dollars on the second, EPV would imply 
that we would be indifferent between the two. Yet, in the real world, few 
managers would treat a potential 100 million dollar loss the same as a ten 
dollar loss. A key assumption in EPV analysis is that the manager risk is 
neutral and the firm has unlimited capital. Neither assumption holds true 
in the real world. 
Extending EPV to reality requires the concept of certainty equivalence. 
By definition, certainty equivalent is the value a manager would just be 

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Project Economic Analysis 79
willing to accept in lieu of the risky investment. This point defines the 
value at which the manager is indifferent between the two alternatives. 
To illustrate, consider an investment with an EPV of ten million dollars. 
EPV includes a return, chance of success, and a potential loss. The actual 
outcome could be higher or lower than this value. Should someone start 
offering the manager a guaranteed amount less than twelve million dollars, 
say nine million, then eight million, and so on until the manager said yes, 
the value eliciting the yes is the certainty equivalent or the indifference 
value.
Two companies have different, but identical prospects worth ten million 
dollars (EPV), each with a 100 percent WI, and an offer to farm-out to a 
third party. The first party accepts a guaranteed offer of six million dollars, 
while the second party accepts an offer for four million dollars. Why would 
the indifference points differ? Because most managers are risk adverse, 
contrary to the primary assumption of EPV and the degree of risk aversion 
depends on two basic components: the wealth of the firm (hence, freedom 
from bankruptcy) and the budget level. In this example, both firms are 
risk averse because they would accept a lower amount to reduce risk. Had 
either accepted the EPV they would be risk neutral, and occasionally we 
see investors who would want more (a true risk taker). 
Cozzolino (1977) introduced the term risk adjusted value to integrate 
these concepts, as defined in Equation 2.40. 
RAV
r
Ln P e
P e
s
r R C
s
rC
1
1
(
)
(
)
(2.40)
where r equals risk aversion level of the firm, P
s 
equals probability of 
success, R equals NPV of success, C equals NPV of failure, E equals expo-
nential function, and Ln equals natural logarithm.
In the Cozzolino (1977) format examples, like those above that are used 
to solve for r, assume that RAV is already established. If R, C, RAV, and P 
are known, the corporate risk aversion can be determined. Without per-
forming an example, larger values for r imply more risk aversion, while 
smaller values reflect lower risk aversion. Evidence suggests that an inverse 
relationship exists between capital budget size and risk aversion level. 
Smaller companies tend to be more risk averse and, thus, tend to spread 
their risk across as many projects as possible. 
This basic format has been extended by Bourdaire et al. (1985) to elimi-
nate the need to estimate the risk component. By employing the elements 
of subjectivity and assuming an exponential utility function, Equation 2.42 
results. 

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80 Project Management in the Oil and Gas Industry
RAV
m
s
B
2
2
(2.42)
where m equals the mean NPV, s
2
=equals the standard deviation of distri-
bution, and B equals total monies budgeted for risky investments.
RAV, under this format, can be based on information typically gener-
ated in the evaluation. RAV also depends on the estimated value relative 
to the dispersion of the NPV outcome. More importantly, high dispersion 
projects may be ranked above projects with lower standard deviation if the 
dispersion relative to the budget is low. RAV depends on two basic rela-
tionships: m relative to s
2
and s
2
relative to B. 
If the mean value of NPV that was calculated from the Monte-Carlo 
simulation is equal to ten million dollars, then a standard deviation illus-
trates the dominance of the dispersion term, since $10 – (15)
2
will be a very 
negative value. Now, suppose that the investor is a large oil company with 
a budget of $1,000 million. The RAV of the project is
RAV
million
10
225
2 1000
9 9
$ .
.
For a smaller investor with a budget of only $200 million, RAV becomes
RAV
million
10
225
2 200
9 4
$ .
.
The breakeven RAV value for B is found by solving
RAV breakeven
s
m
(
)
.
.
2
2
225
2 10
11 25
We are not aware of anyone presently ranking on RAV, although more 
people are discussing it. Like other ideas portrayed in this book, we believe 
it should be included as part of the evaluation for a period of time. If RAV 
aids in decision-making, then include it permanently.

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