A renewable energy company issues a 3-year floating-rate not…

A renewаble energy cоmpаny issues а 3-year flоating-rate nоte (FRN) to finance the construction of offshore wind turbines. Because investors are concerned about rising interest rates, the company sets a coupon cap so that annual coupon payments cannot exceed a maximum rate. Analysts value the note using a 3-year binomial interest-rate lattice, calibrated from market par and forward rates. Bond details Face Value: $100.00 Reset/Payment Frequency: Annual (coupon paid at each year-end) Reference Rate: The 1-year short rate at the start of each period (from the lattice) Quoted Constant Spread: [s]% (added to the reference rate each year) Coupon Cap: [cap]% (coupon rate cannot exceed this level) Today’s 1-year spot rate: [z1]% 1-year forward rates starting 1 year from today (t=1):• Node B: [f11b]%• Node C: [f11c]% 1-year forward rates starting 2 years from today (t=2):• Node D: [f21d]%• Node E: [f21e]%• Node F: [f21f]% Coupon rule (capped floater): Coupon at each node = min⁡( [short rate at that node]+s,  cap )minbig(,[text{short rate at that node}] + s,; text{cap},big) At maturity (t=3), the bond pays principal $100 plus the capped coupon.   Task:Using the lattice, estimate the price today by backward induction under equal risk-neutral branch probabilities (0.5). Discount each node’s expected cash flow by the local 1-year short rate at that node. Hint: The cap limits upside for investors, so the note should price below the uncapped floater (all else equal).