3 The model 3.1 The Firm An all-equity firm initially consists of half a dollar in cash, and is considering the possibility to invest that money in a risky project. At the beginning of the period, one such project becomes vailable. All risky projects return one or zero dollar with equal probabilities one period fror now;we denote this end-of-period cash flow by 0. For simplicity, we assume that the risk of these ects is completely idiosyncratic, and that the correct discount rate, the riskfree rate, is zero Given this, the net present value of any risky project is exactly zero, and so the value of the firm is one half The potential value from a risky project comes from the possibility of acquiring information about it. This can be done in two stages: the firm can gather an imperfect signal about the project's payoff in the first stage, and a perfect signal in the second stage. Before each stage, the firm learns the probability that the project will still exist at the end of that stage. The cost of gathering information in this real options framework is therefore the potential loss of a project that is likely to be good. The qualitative implications of our model extend to real options settings in which the draw back to delaying exercise is foregone revenue from the project or an explicit cost to thering additional information introducing these additional cash hows into the model howey greatly complicates the formal analysis, without contributing intuition. We denote the probability that the project will still exist at the end of the first(second)stage by p( @. We assume that p and q are uniformly distributed on [0, 1] and are independent. These two variables can be thought of as describing the ease with which the firm can learn about the project's profitability. Alternatively they capture the amount of competition that the firm faces when deciding whether to invest in a project immediately or to delay the decision. In that sense, a larger(smaller) probability that the project still exists represents a situation in which few(many)other firms are likely to unde the project before more information can be gathered Upon learning p, the imperfect signal that the firm can gather in the first stage is given by 8=E0+(1 where n has the same distribution as u, but is independent from it, and E takes a value of one ith probability a E(0, 1), and zero otherwise. This signal s is more informative for larger values of a, as the true value of the project is then observed more often. The parameter a can in fact be interpreted as the ability of the individual making the capital budgeting decision, whom we refer3 The Model 3.1 The Firm An all-equity firm initially consists of half a dollar in cash, and is considering the possibility to invest that money in a risky project. At the beginning of the period, one such project becomes available. All risky projects return one or zero dollar with equal probabilities one period from now; we denote this end-of-period cash flow by ˜v. For simplicity, we assume that the risk of these projects is completely idiosyncratic, and that the correct discount rate, the riskfree rate, is zero. Given this, the net present value of any risky project is exactly zero, and so the value of the firm is one half. The potential value from a risky project comes from the possibility of acquiring information about it. This can be done in two stages: the firm can gather an imperfect signal about the project’s payoff in the first stage, and a perfect signal in the second stage. Before each stage, the firm learns the probability that the project will still exist at the end of that stage. The cost of gathering information in this real options framework is therefore the potential loss of a project that is likely to be good. The qualitative implications of our model extend to real options settings in which the drawback to delaying exercise is foregone revenue from the project or an explicit cost to gathering additional information. Introducing these additional cash flows into the model, however, greatly complicates the formal analysis, without contributing intuition. We denote the probability that the project will still exist at the end of the first (second) stage by ˜p (˜q). We assume that ˜p and q˜ are uniformly distributed on [0, 1] and are independent. These two variables can be thought of as describing the ease with which the firm can learn about the project’s profitability. Alternatively, they capture the amount of competition that the firm faces when deciding whether to invest in a project immediately or to delay the decision. In that sense, a larger (smaller) probability that the project still exists represents a situation in which few (many) other firms are likely to undertake the project before more information can be gathered. Upon learning ˜p, the imperfect signal that the firm can gather in the first stage is given by s˜ = ˜εv˜ + (1 − ε˜)˜η, where ˜η has the same distribution as ˜v, but is independent from it, and ˜ε takes a value of one with probability a ∈ (0, 1), and zero otherwise. This signal ˜s is more informative for larger values of a, as the true value of the project is then observed more often. The parameter a can in fact be interpreted as the ability of the individual making the capital budgeting decision, whom we refer 6