The market value of the firm is then the value of its net financial assets plus the value of its capital assets (less any other liabilitiesUnder non-ideal conditions, it may be difficult to write down a complete set of states of nature and associated cash flows. Even if these can be written down, difficulties remain because objective state probabilities are not available. This is perhaps the most fundamental difficulty, since these probabilities must be subjectively estimated. Also an interest rate is not necessarily given. All of these difficulties lead to reliability problems of lack of representational faithfulness and possible bias. The expected present value calculation can still be made, but it is an estimate because the probabilities and other values that go into it are estimates. The expected value of a single roll of a fair die is:

x  1  (1  2  3  4  5  6)  3.5
6

b. First, you would have to write down a set of possible states of nature for the die. One simple possibility would be to define:

State 1: die is fair

State 2: die is not fair.

Then, subjective probabilities of each state need to be assessed, based on any prior information you have. For example, if the person supplying you with the die looks suspicious, you might assess the probability of state 2 as 0.50, say. A problem with this approach, however, is that to calculate the expected value of a single roll, you need an expected value conditional on state 2, and this expected value is not defined when the state is simply “not fair.”

A more elaborate alternative would be to formally recognize that the probability of rolling a 1 can be anything from zero to one inclusive, and similarly for rolling a 2,
3, . . . , 6, subject to the requirement that the six probabilities sum to one. Formally, we can regard a state as a 1 × 6 vector

P = [ p1, p2, . . . , p6], subject