1. **Problem Statement:** We have two projects with different possible firm market values in two years and a debt face value of 20 million payable in two years. 2. **Given:** - Project 1 outcomes: 50 million or 0 - Project 2 outcomes: 25 million or 15 million - Debt face value: 20 million 3. **Formulas and Rules:** - Bondholders get the minimum of the firm's market value and the debt face value because they are paid first. - Shareholders get the residual value after bondholders are paid, i.e., $\text{Shareholders payoff} = \max(0, \text{Firm value} - \text{Debt})$. 4. **Calculations:** **a. Payoffs to bondholders:** - Project 1: - If firm value = 50, bondholders get $\min(50, 20) = 20$ - If firm value = 0, bondholders get $\min(0, 20) = 0$ - Project 2: - If firm value = 25, bondholders get $\min(25, 20) = 20$ - If firm value = 15, bondholders get $\min(15, 20) = 15$ **b. Payoffs to shareholders:** - Project 1: - If firm value = 50, shareholders get $\max(0, 50 - 20) = 30$ - If firm value = 0, shareholders get $\max(0, 0 - 20) = 0$ - Project 2: - If firm value = 25, shareholders get $\max(0, 25 - 20) = 5$ - If firm value = 15, shareholders get $\max(0, 15 - 20) = 0$ **c. Preferences:** - Shareholders favor Project 1 because it offers a higher potential payoff (up to 30) despite the risk of getting nothing. - Bondholders favor Project 2 because it offers more certainty and a higher minimum payoff (at least 15). **Final answers:** - Bondholders payoffs: - Project 1: 20 or 0 - Project 2: 20 or 15 - Shareholders payoffs: - Project 1: 30 or 0 - Project 2: 5 or 0 - Shareholders prefer Project 1; Bondholders prefer Project 2.