1. You own a three-year bond with a coupon rate (CR) of 12%, and a yield to maturity (YTM) of 14%. Coupons are paid annually and the bond has a face value of $1,000. Find the duration of this bond.
2. You have a four-year financial instrument that will pay $124 in year 1, $206 in year 2, $308 in year 3, and $423 in year 4. If the appropriate discount rate is 12% p.a., find the duration of this instrument.
3. You have a four-year bond with a 11% and a face value of $1,000. The bond makes annual coupon payments and its yield to maturity is 18% p.a. If the bond's yield to maturity increases by 1% (i.e., by 100 basis points), find the resulting percentage change in the bond's price. For example, if the bond's price changes from $1,000 to $900, then the percentage change in price would be 100x(900 - 1,000)/1,000 = -10.00%. Give the answer as a percent with two decimals, e.g., -7.12%.
4. You have a four-year bond with a coupon rate CR = 6% and a face value of $1,000. The bond makes annual coupon payments and its yield to maturity is 5% p.a. If the bond's yield to maturity decreases by 1% (i.e., by 100 basis points), find the resulting percentage change in the bond's price. For example, if the bond's price changes from $1,000 to $1,100, then the percentage change in price would be 100x(1,100 - 1,000)/1,000 = 10.00%. Give the answer as a percent with two decimals, e.g., 7.12%.
5. You have a stock that is expected to pay a $2 dividend one year from now. Thereafter, you expect annual dividends to experience a constant grow of 8% p.a. forever. If the appropriate discount rate is 18% p.a., what is the duration of this stock?