3. Suppose you want to buy an 18% coupon bond with a face value of $1,000, maturity of 2.5 years, and yield of 20%.
Further suppose that you want to raise enough money to buy this bond by issuing a pair of zero-coupon bonds: one with a maturity of 6 months, and another with a maturity of 6 years. Both bonds will have a yield of 20%.
If you also want the duration of your liabilities to match the duration of your asset, what should be the price and face values of each of these zero-coupon bonds? (40 points)
(Note: As your first step, you should calculate the exact price and duration of the asset--NOT the price or duration rounded to 3 decimal places--to see exactly what you need to match.)
Price of the 6-month zero-coupon bond:
Price of the 6-year zero-coupon bond:
Face value of the 6-month zero-coupon bond:
Face value of the 6-year zero-coupon bond: