Arbitrage Free Tree to Value Bond

CFA Level II Fixed Income
#1

Why is the coupon of 2.8% being used twice in the below rather than just in the numerator/cash flow? This is using the arbitrage free tree to value a bond.

vu,u=0.5×(102.8/1.0456)+(102.8/1.0456)+2.8=101.117

vu,d=vd,u=0.5×(102.8/1.0345)+(102.8/1.0345)+2.8=102.172

vd,d=0.5×(102.8/1.0260)+(102.8/1.0260)+2.8=102.995

#2

Because you get a coupon at time 3 (which is part of the 102.8 in parentheses), and you get a coupon at time 2 (which is added at the end).

This gives the value of the portfolio (bond plus coupon) at each time 2 node; without the additional coupon at the end, you get the value of the bond at each time 2 node.