.provide solutions to the following attachments.

Exercise 33 Table 3 .3 is an extract from a (hypothetical) select life table with a select period of two years. Note carefully the layout each row relates to a xed age at selection. Use this table to calculate (a) the probability that a life currently aged 75 who has just been selected will survive to age 35. (b) the probability that a life currently aged 76 who was selected one year ago will die between ages 35 and 3?, and (C) 4|24m1+1 - Table 3.3. Extrectfrom a (hypothetical) select life table. I In] low 31+: I + 2 25 15 930 15663 15 236 T? 26 15503 15224 14316 T3 '1'? 15050 14244 14310 '19 30 12 576 32 31 11923 33 32 11 250 34 33 10 542 35 34 9 312 36 35 9 064 3'? Exercise 3.4 CMI (Table A23) is based on UK data from 1999 to 2002 for female non-smokers who are term insurance policyholders. It has a select period of ve years. An extract from this table, showing values of q[x_;]+;, is given in Table 3.9. Use this survival model to calculate (3) 2pm] 1 03) sq[73]+2, Company X has zero-coupon debt outstanding with a face value of F > 0 due in exactly one year. This debt does not contain any covenants. The value of the company's assets when the debt comes due will either be 0, 90, or 180 with probabilities 0.2, 0.6, and 0.2, respectively. The current market (and also fair) value of the company's equity is 16. There are no taxes or direct costs of financial distress, all investors are risk neutral, and the risk-free interest rate is zero. The managers of the firm always act in the interests of existing shareholders. When answering each question, state any additional assumptions you may need to make. Show all working/calculations. (a) Determine F, the face value (i.e. promised payment) of the company's debt. [3 marks] Suppose X's managers can choose to costlessly restructure the company's assets so that they will be worth 0 or 180 next year with probabilities 0.7 and 0.3, respectively. (b) Assuming the firm retains its existing assets, graph the expected payoff to X's sharehold- ers as a function of F, i.e. for all feasible face values of debt, 0 S F