5. 6. W W B 2year 6% 4% C 3year 3% 5% The coupons are paid annually. Now is year (i. (a) (2 points ) \"mat is the 1year spot interest rate '3' {b} (2 points } What is the 2year spot interest rate ? (c) (2 points ) What is the 3year spot interest rate '3' lEd) (3 points ) Suppose that a new Treasury bond is introduced to the market . It is a zerocoupon bond with 3 years to maturity, and it trades at the 4% yield to maturity. What is the noarbitrage price of the new bond? [e] (7 points ) Describe explicitly the arbitrage trading strategy involving bonds A, B, C, and the new bond , which pays $1 at time t = [I and nothing afterwards. {18 points )You are advising a local municipal treasury on a bridge construction project . The project requires an upfront investment {at time {year 0} of $10M ,with an additional investment in year 1 of $5M. The bridge will become operational two years from now, and will start generating toll revenue. Specifically, the bridge produces no cash flows in year 1, and produces a permtual stream of cash flows of $1M per year in subsequent years. Assume that all cash flows are riskfree. The treasury is nancing this project with a tenyear zero coupon bond . The current term structure of risk free interest rates is flat at 2%. Assume that the treasury is able to nance this project at the risk free interest rate. (a) (3 points} What is the NPV of this project? {b} (3 points ] Suppose that the treasury wants to issue enough bonds to cover the present value of construction costs of this project. Let the face value of each bond be $1,010\". What is the total number of bonds that need to he issued? (c) {5 points ) Compute the modied duration of the bond issued by the treasury {d} {5 points ) Suppose the treasury goes ahead with your suggestion in {b} and starts the project .Rjght after its start (at time 0}, the yield curve unexpectedly rises by 1% across all maturities .'What is the resulting change in the NPV of the project , following the change in interest rates? (e) (2 points } Using the duration based approximation , what would be the change in the value of the outstanding bonds following a 1% rise in interest rates? {18 points} A private equity investment fund has firm XYZ in its portfolio. Your task is to estimate the value of this firm, which does not trade publicly. XYZ is 100% equity financed. It is new year 0, and you have the following data on XYZ: Full-year earnings over year 0 100M Payout ratio in year I] 0% Cost of capital 10%