Q.53.
I discounted the node two prices as they are given Viz. Without adding a coupon (since this is an in between node, in all probability it should be a dirty price)
However, in the solutions they do add coupons to discount it to node 1.
What’s happening?!!
Would also like to know this one. The interest payments are semuannual, but the coupon is annual. Therefore, shouldnt we add the full coupon at the yearly points, not half the coupon every 6 months?
This bond pays semi-annual coupons. To get the value at node ‘A’ you add the two bond values together 91.73 + 96.17 = 187.90. Then you add the coupon payment of 3 (6% semi-annually) for each bond. 187.9 + 6 {which is 2 x 3} = 193.9. Next you need to discount this number 0.5 years to node A. 7.91% is an annualized rate, so you divide it by 2. 7.91% / 2 = 3.955%… 193.9 / 1.03955 = 186.523015… Divide this by 2 to get your node value of 93.26, or 93.26% of par.
Alternatively,
Upper node = 91.73 + 3 (semi-coupon) = 94.73. Lower node = 96.17 + 3 = 99.17. Upper node + lower node = 193.9… 193.9 / [1+(.0791/2)] = 186.523015… divided by 2 = 93.26