Risk Adjusted Value (RAY)
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 $10 for a dry hole on one and $100 million 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 loss the same as a $10 loss. A key assumption in EPV analysis is that the manager is risk 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 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 $10 million. 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 $12 million, say $9 million, then $8 and so on until the manager said yes, the value eliciting the yes is the certainty equivalent or the indifference value.
Let’s assume that two companies have different, but identical, prospects worth $10 million (EPV), each with a 100% WI, and an offer to farm out to a third party. The first party accepts a guaranteed offer of $6 million, while the second party accepts an offer for $4 million. 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 (3.40).
where r = risk aversion level of firm, Ps = probability of success, R = NPV of success, C = NPV of failure, E = exponential function, and Ln = natural logarithm.
In the Cozzolino (1977) format examples, like those above that are used to solve for r, assuming that RAV is already established, if R, C, RAV, and P are known, the corporate risk aversion can be determined. Without performing 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 eliminate the need to estimate the risk component. By employing the elements of subjectivity and assuming an exponential utility function, Equation 3.41 results.
RAV = m~ — 2 В
where m – mean NPV, s2 = standard deviation of distribution, and В = total monies budgeted for risky investments.
RAV under this format can be based on information typically generated 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 relationships: m relative to s2 and s2 relative to B.
If the mean value of NPV that was calculated from the Monte – Carlo simulation is equal to 10 million dollars, then a standard deviation illustrates 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
For a smaller investor with a budget of only $200 million, RAV becomes
RAV = 10—=-
The breakeven RAV value for В is found by solving
RAV (breekeven) =———— =———- = 11.25.
2 xm 2×10
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.