It is possible to use the idea of certainty equivalents to evaluate how much individuals would be willing to pay to exchange the type of annuities described in figures 2 and 3 with otherwise similar annuities that shielded them from uncertainty concerning the future evolution of the mortality rates of their respective birth cohorts.

A recent retiree, however, faces a sequence of periods over which uncertainty will apply when making decisions concerning annuities, and in this context no analytical solution to the certainty equivalent problem exists.

Choices in investment and quantity are oligopolistic because the decisions of one insurance firm relate to its rivals' certainty equivalents.

4 can be interpreted as the value of demand information because it represents the difference between certainty equivalents in the presence and absence of demand information.

Instead, our methodology values these options from a risk-averse investor's perspective using utility certainty equivalents.

Prior to T - 1, the computation is similar to Equation (12) but involves next period certainty equivalents

Table 1 shows these

certainty equivalents for persons with two levels of risk tolerance--one is risk neutral and cares only about the expected value of the wealth distribution, the other is "moderately" risk averse.

In that context, Bernoulli unveiled the notion of a

certainty equivalent, a guaranteed cash flow that we would accept instead of an uncertain cash flow and argued that more risk averse investors would settle for lower

certainty equivalents for a given set of uncertain cash flows than less risk averse investors.

1) An alternative approach to deal with uncertainty in capital budgeting is to identify

certainty equivalents for the uncertainty parameters in a project (such as selling price, demand, capital investment) and then discount the

certainty equivalent net cash flows using a risk free rate.

Chapter 10 on risk analysis is probably the most difficult in the book, especially the part that deals with risk-adjusted discount rates and

certainty equivalents.

TABLE III

Certainty Equivalent of a Risky Opportunity With an Expected Return of 10% r

Certainty Equivalents (%) 1 9.

The fist is discounted cash flow valuation, where the value of a business or asset is determined by its cash flows and can be estimated in one of four ways: (a) expected cash flows can be discounted back at a risk-adjusted discount rate (b) uncertain cash flows can be converted into

certainty equivalents and discounted back at a risk-free rate (c) expected cash flows can be broken down into normal (representing a fair return on capital invested) and excess return cash flows and valued separately and (d) the value of the asset or business is fist estimated on an all-equity funded basis and the effects of debt on value are computed separately.