62  Risk and the Cost of Capital 
trying to identify the expected value, managers would be better off knowing that 
the project carries a 60 percent chance of being worth $8,000 and a 40 percent risk 
of losing $2,000. Managers can then examine the scenarios under which each 
outcome prevails and decide whether the upside compensates for the downside, 
whether the company can comfortably absorb the potential loss, and whether 
they can take actions to reduce the magnitude or risk of loss. The theoretical ap-
proach of focusing on expected values, while mathematically correct, hides some 
important information about the range and exclusivity of particular outcomes.
Moreover, some companies don’t apply the expected-value approach cor-
rectly. Few companies discuss multiple scenarios, preferring a single-point 
forecast on which to base a yes-or-no decision. Most companies would simply 
represent the expected cash flows from this project as being $1,000 per year, 
the amount if everything goes well, and allow for uncertainty in the cash 
flow by arbitrarily increasing the discount rate. While you can get to the right 
answer with this approach, it has two flaws. First, there is no easy way to de-
termine the cost of capital that gives the correct value. In this case, using a 16.7 
percent cost of capital instead of 10 percent results in a project value of $6,000 
before the investment and $4,000 after the investment. But the only way to 
know that this is the correct value would be to conduct a thorough scenario 
analysis. Companies sometimes arbitrarily add a risk premium to the cost of 
capital, but there is no way for them to know whether the amount they add 
is even reasonably accurate. Second, the decision makers evaluating a project 
with cash flows of $1,000 per year and a 16.7 percent cost of capital are still 
not thinking through the 40 percent risk that it might generate no cash at all.
If for some reason you must use a single cash flow scenario, you can analyt-
ically estimate the equivalent risk premium for different probability levels of 
failure, as in Exhibit 4.3. The exhibit shows the amounts by which you would 
increase the cost of capital instead of using cash flow scenarios for different 
combinations of the probability of failure, as represented on the vertical axis, 
and the size of loss relative to the base case, as represented by the horizontal 
axis. For example, if there was a 50 percent chance of failure in which case 
the project would be worth 40 percent less than expected, the equivalent risk 
premium would be 1.5 percent. Notice in this exhibit that the risk premiums 
are small relative to what most people expect. To get close to a 3 percent risk 
premium, for example, you’d have to believe there was a 50 percent chance of 
failure and a 60 percent reduction in cash flows associated with failure. To get 
to a 5 percent risk premium, you’d have to believe there is a 50 percent chance 
of failure and more than an 80 percent reduction in cash flows.9
Adding ad hoc risk premiums is a crude way to include project-specific un-
certainty in a valuation. Scenario-based approaches have the dual appeal of bet-
ter answers and more transparency on the assumptions embedded within them.
9 Note that the risk premium will be determined not just by the probability and magnitude of loss, but 
also by the duration of the project or company and pattern of cash flows.