#Three

The following formula will be needed: (Sum of n and i) -> Pn i=0 x^i = 1x^(n+1) / 1x

(a) (3 points) An asset with price S at time 0 pays some cashflows. The cashflows are worth Ca with probability p and Cb with probability 1 p and are paid annually from time 1 to time T. Provide a formula for the asset price S by assuming that the (annualized) discount rate is r.

(b) (3 points) An asset with price S at time 0 pays some cashflows. The cashflows are worth C, are paid every 6 months, and are perpetual. Provide a formula for the asset price S by assuming that the (annualized) discount rate is r.

(c) (3 points) An asset with price S at time 0 pays some cashflows. Cashflows worth Ca are paid annually from time 1 to time T. In addition, cashflows worth Cb are paid annually from time T + 1 to infinity (perpetuity). Provide a formula for the asset price S by assuming that the (annualized) discount rate is r.

(d) (3 points) An asset with price S at time 0 pays some cashflows. The cashflows are worth C1 with probability p1, C2 with probability p2, and C3 with probability 1 p1 p2. These cashflows are paid every n months (perpetuity). Provide a formula for the asset price S by assuming that the (annualized) discount rate is r.

(e) (3 points) An asset with price S at time 0 pays some cashflows. Perpetual cashflows worth Ca are paid every odd years (1, 3, 5,...). In addition, perpetual cashflows worth Cb are paid every even years (2, 4, 6,...). Provide a formula for the asset price S by assuming that the (annualized) discount rate is r.