Three investors invest in the same 10 -year 8% annual coupon bond. They bought the bond at the same price ( $85.503075 for a par value of $100 ) and at the same time. A is a buy-and-hold investor (hold till maturity), B will sell the bond after four years, and C will sell the bond after seven years. 1. What is the yield to maturity of this bond at the time of purchase? 2. After the bond is purchased by the three investors and before the first coupon is received, interest rate goes up to 12%. Calculate: i. What is the change in IOI for each investor? (Hint: Find the difference between the IOI under the original YTM and the IOI under the new yield). ii. What is the capital gain/loss for each investor? (Hint: capital gain/loss = price at sale or maturity - pricesarryig. Carrying value is the hypothetic price of the bond if the bond's yield remains at the initial yield to maturity.) iii. What is net gain or loss for each investor after the interest rate change? 3. What is the Macaulay duration of this bond? 4. For each of these three investors, find their respective duration gap. (Hint: Duration gap=Macaulay duration - investor horizon). 5. Use the answers from 2-4 to discuss how the interest rate change has influenced the value of the investors' investment and why? (Hint: Refer to the discussions on duration gap, market price risk and reinvestment risk at the bottom of page 1 of Lecture 5 to answer this question)