Question

Bonus Problem 2 (Optional, Harder, 45 marks) (a) (10 marks) We consider a bond that pays n coupons at the end of each coupon period. The length of each coupon period is T. The bondholder receives a redemption value at nth coupon payment date. The redemption value, face value and coupon rate (over a coupon period) are C, F and r respectively (see P.13 of Lecture Note 4). For any k = 0,1,2.,,, n, we let Pk be the bond price at kth coupon payment date (just after the coupon payment). We let j be the effective interest rate over a coupon payment period. We assume that the yield rate remains unchanged over time. Using the pricing formula of the bond, show that for any non-negative integer k and positive integer m, we have Pk+m Pk = rFamij + (1 + i)m provided that k + m sn. Give a financial interpretation to this result. (Note: Do not use any other concepts such as outstanding balance and book value)

Answer 1

The equation is basically determining the current intrinsic value of the bond.

Where, P_k+m is the sum total of future cash inflows in form of interest and (1+j)^m is the effective cost which is used to pull out the present value of the total cash inflows. The other element is the redemption value of the bond - which is again pulled back to PV,.