To value the capped floater, we work backwards through the binomial tree:

Year 1:

• Upper node: Rate = 6.0%, but capped at 5%, so coupon = 5%
• Lower node: Rate = 3.0%, coupon = 3.0%

Year 0:

• Rate = 4.5%, coupon = 4.5%

Valuation:

• At Year 1 upper node: Value = (100 + 5) = 105
• At Year 1 lower node: Value = (100 + 3) = 103
• At Year 0: Value = [0.5 × (105/1.06) + 0.5 × (103/1.03)] + 4.5 = [0.5 × 99.06 + 0.5 × 100] + 4.5 = [49.53 + 50] + 4.5 = 99.53 + 4.5 = 104.03

Present value at Year 0: PV = 104.03 / 1.045 = 99.55

The cap reduces the bond's value compared to an uncapped floater, which would be priced at par (100).