All four members of our group contributed to this assignment. We held group meetings to discuss and also collaborated to solve the questions. Ryan contributed to both Q1 & 2 and was mainly responsible for leading the coding of the assignment. Nicholas was mainly responsible for the initial setting up of Q1 in python and subsequent troubleshooting. Jessie contributed to Q1 in developing codes and plotting the graphs. Cameron was mainly responsible for the economic interpretation of the results in Q2. Question 1 The optimal for which ′(()) = 1 is 7.25, and () = 26.40. (See python file for details) Question 2 We chose L and gamma as our two parameters to analyze the effect of their variability on the firm’s debt and credit line. Liquidation Payoff (L) In the model, L represents the liquidation payoff to the principal (lender) which they receive when the contract is terminated. L acts as a boundary condition in the solution to the optimal contract because the principal must terminate the contract in order to hold the agent’s value to R; meaning b(R) = L. Consistent with the results in Demarzo and Sannikov (2006), we find that as we increase the liquidation payoff, the implied credit line becomes shorter, and the amount of debt increases. This is due to the declining inefficiency of liquidation, implying a shorter credit line provides less financial flexibility for the project, and debt increased to offset the decreased credit line. Below are the numerical values of debt and the credit line for our tested values of L: Liquidation Value Debt Credit Line 10 59.25 27.16 25 60.39 26.40 50 63.09 24.60 To summarize, the combined graph above shows the pattern the credit line becomes shorter, and debt increases
to offset the reduction. D eb t Credit Line D eb t Credit Line D eb t Credit Line Gamma ( ) The agent uses their money either for consumption or private savings. Gamma represents the consumption discount rate of the risk neutral agent. As long as the private savings growth rate is less than the consumption discount rate, the agent has no incentive to delay reporting or consumption. In the model of the optimal contract, the agent will earn interest at their discount rate gamma when paying off the credit line, though earn interest r < on accumulated cash, therefore they have an incentive to pay dividends once the credit line is repaid. When the value of gamma increases, representing an increase in the discount rate of consumption, the credit line will always go down given it becomes costlier for the agent to delay their consumption. The effect on debt is less straightforward. When gamma is relatively small, the amount of debt increases as gamma increases given the agent has more capacity to borrow through debt with a smaller line of credit. When gamma is relatively high, however, an increase in gamma leads to a decrease in the amount of debt given the reduced profitability due to the agent’s impatience – thus restricting their debt capacity. Below are the numerical values of debt and the credit line for each value of gamma: Gamma Debt Credit Line 0.119 61.79 32.11 0.12 61.94 31.72 0.15 60.39 26.40 0.20 56.38 21.81 Note the value of debt is increasing in gamma for small values of gamma before beginning to decrease. To summarize, the combined graph above shows the pattern that debt is increasing in gamma for small values of gamma, then decreasing in gamma for large values of gamma. D eb t Credit Line D eb t Credit Line D eb t Credit Line