10. (Multiperiod harmony theorem o) its possible cash flow streams. This The value of a firm is the maximum present value of can be expressed as x1 X V = max + + + + (1+52)2 (+)" where the maximization is with respect to all possible streams xp, ,, and the 's are the spot rates Let be the first cash flow in the optimal plan. If the firm chooses an arbitrary plan that results in an initial cash flow of xo (distributed to the owners), the value of the firm after year is V(x)=maxx + { x + ++ 1+ (1+)? (+) where now that maximum is with respect to all feasible cash flows that start with xp and the s's are the spot rates after 1 year An investor purchasing the firm at its full fair price has initial cash flow .ro - V and achieves a value of V(x) after 1 year Hence the I-year total return to the investor is R V(x0) Vo-xo The investor would urge that x be chosen to maximize R. Call this value * Assuming that interest rates follow expectation dynamics and that Vo) > 0, show tha: the maximum R is 1+ and that this return is achieved by the same x that determines Vo