Use the following information to solve problems 1 - 9 Suppose Tesla decides to issue bonds to finance a new production line. Assume the $1,000 face value bond is issued with 10 years to maturity with an annul-pay coupon rate of 5%, and is priced with a yield-to-maturity of 5.5%. 1. Calculate the price of the bond at issuance. 2. Assume the bond is callable beginning in 5 years. Calculate the bond's yield to worst, with the following call schedule: Year 5: \$1,050, Year 6: \$1,040, Year 7: \$1,030, Year 8: $1,020, Year 9: $1,010 3. Calculate the bond's modified duration at issuance. 4. Use modified duration from question 3 to estimate the dollar change in bond value if yields increase by 1% just after issuance. 5. Calculate convexity for the bond at issuance. 6. Estimate the dollar change in the bond value if yields increase by 1% just after issuance using the modified duration and the convexity adjustment. 7. Calculate the actual change in the bond's value if yields increase by 1% just after issuance. Calculate the percent error for the duration approximation and for the duration-with-convexity approximation. What do you conclude? 8. Assume coupons can be reinvested at 6% and in 3 years the bond is priced to yield 6% to maturity. Calculate the 3 -year holding period return and the horizon yield (annual realized return). 9. Suppose a bond portfolio manager (PM) buys $5 million of the Tesla issuance. The PM is concerned that interest rates may rise in the future and wants to fully immunize this portfolio of bonds. The PM wants to use zero coupon bonds that mature in 5.275 years to immunize the portfolio. How much of the zero-coupon bonds does the PM need to transact to immunize the portfolio? Specify whether the PM will take a long or a short position in the zeroes