Exercise 1. Pricing of Equity and Debt: 24pts Consider the tree provided below. This tree describes (partially) the evolution of a rm's assets between time t = 1], time t = 1, and time t = 2 (in years). The associated probabilities of an up move (called p} are also provided. Let us denote by f}, U, D, UU, U D, DU, and DD the different nodes of the tree, where U stands for up move and D for down move. 1011 /. \. Suppose the rm issues a coupon bond with maturity T = 2, ooupon rate r: = 7%, face value F = 1000. As usual, default on debt payments triggers bankruptcy and liquidation of the rm. The rm sells part of (or liquidates} its assets to pay: I) what they owe to debtholders and 2) dividends to shareholders. At thus 1 the rm pays a dividend to shareholders equal to 10% of the value of its assets (if it is able to}. At time 2 the rm stops its business and pays what it is able to pay to debtholders and shareholders. 1"" I JR a... 9-1 ,05 IF; 1" r04 Remark: Numbers in the erererse are extreme. Don't worry about it! 1) Compute the cashows to debtholders at nodes U, D, U U, U D, DU, and DD (CF3[U), CFB(D}30FB(UU)ICFB(UD)=CFB(DU)1CFB(DD)} 2) Compute the oashowsfdividends to shareholders at nodes U, D, UU, U D, DU, and DD (Gs-(m, Germ, Comm. Game), Game, Game) 3) At which nodes does the rm default? 4] What are the values of the rm's assets at nodes DU and DD [11(fo ], A[DD))