Verify the expected net income for P.V. Ltd. for year 1 in Example2.2 by calculating the expected value of ex post net income. How much is expected net income for year 2? Show calculations. Explain why expected net income is also called “accretion of discount.”

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Example 2.2 Illustration of the Present Value Model Under Uncertainty Let us continue Example 2.1 taking into account that the economy can be in a "bad" state or a "good" state during each year. If it is in the bad state, cash flows will be $100 for the year. If it is in the good state, however, cash flows will be $200 for the year. Assume that during each year the bad state and the good state each occur with proba- bility 0.5. Our assumption that state probabilities are the same each year implies that the state realizations are independent. That is, the state realization in year 1 does not affect the probabilities of state realization in year 2. Uncertain future events such as the state of the economy are called states of nature, or states for short. Thus the states in this example are, for each year: State 1: Economy is bad. State 2: Economy is good. Note that no one can control which of the states is realized-this is why they are called states of nature. Other examples of states that affect cash flows are weather, government policies, strikes by suppliers, equipment breakdowns, etc. In any realistic situation there will be a large number of possible states. However, our two-state example is sufficient to convey the idea-states of nature are a conceptual device to model those uncertain, uncontrollable future events whose realizations affect the cash flows of the firm. While at time 0 no one knows which state will occur, we assume that the set of possible states is publicly known and complete. That is, every possible future event that can affect cash flows is known to everyone. Thus, while no one knows for sure which state will occur, it is known that whatever state does happen must be an element of the set. Furthermore, we assume that the state realization is publicly observable-everyone will know which state actually happens. Finally, we assume that the state probabilities are objective and publicly known. By objective we mean that if we imagine a long-run sequence of repetitions of our two-period economy, the bad state will occur with relative frequency 0.5 (or whatever other state probability we were to assume). Think by analogy