Question 3. (10 points) You want to buy a 3 year bond with a coupon rate of 22%, annual coupons, and a
face value of 1000. You know that 1 year zero coupon bonds (ZCBs) trade a yield to maturity of 12%, 2
year ZCBs trade at a yield to maturity of 9%, and 3 year ZCBs trade at a yield to maturity of 7.5%.
(a) What is the price of this 3 year 22% coupon rate bond?
(b) What is the yield to maturity on this 3 year 22% coupon rate bond?
(c) What does the market expect the rate on a 1-year zero coupon bond will be two years from now
(what is the implied forward rate)?
(d) What does the market expect the rate on a 2-year zero coupon bond will be one year from now?
(e) Assume you buy the coupon bond and then you decide you do not need money until the end of
three years. As a result, when you receive the coupons in years 1 and 2, you will reinvest them at
the prevailing market rate (assume these will be the forward rates you calculated in parts c and d).
How much money will you have at the end of the 3 years? What rate of return will you receive on
your investment?
Question 3. (10 points) You want to buy a 3 year bond with a coupon rate of 22%, annual coupons, and a
face value of 1000. You know that 1 year zero coupon bonds (ZCBs) trade a yield to maturity of 12%, 2
year ZCBs trade at a yield to maturity of 9%, and 3 year ZCBs trade at a yield to maturity of 7.5%.
(a) What is the price of this 3 year 22% coupon rate bond?
(b) What is the yield to maturity on this 3 year 22% coupon rate bond?
(c) What does the market expect the rate on a 1-year zero coupon bond will be two years from now
(what is the implied forward rate)?
(d) What does the market expect the rate on a 2-year zero coupon bond will be one year from now?
(e) Assume you buy the coupon bond and then you decide you do not need money until the end of
three years. As a result, when you receive the coupons in years 1 and 2, you will reinvest them at
the prevailing market rate (assume these will be the forward rates you calculated in parts c and d).
How much money will you have at the end of the 3 years? What rate of return will you receive on
your investment?
Related questions
Arthur plans to invest 10,000 dollars in a ten-year bond of a technology company: Face Tech. Inc. The bond offers an 8 percent annual coupon and a yield to maturity of 10 percent. He plans to sell the bond in 4 years and invest the proceeds in a 3-year default-free zero coupon bond and cash. All bonds have a face value of $1000 per unit. The yield curve for the default free zero coupon bonds is provided in the following table:
| Default free zero coupon bond with face value of $1000 | Yield to Maturity |
| 1-year Bond | 7% |
| 2-year Bond | 8% |
| 3-year Bond | 9% |
| 4-year Bond | 10% |
| 5-year Bond | 12% |
| 6-year Bond | 13% |
| 7-year Bond | 14% |
| 8-year Bond | 15% |
(a) If Arthur can invest the coupons at an annual rate of 7 percent, and 4 years later, this coupon bond of Face Tech. Inc. can sell at a yield to maturity of 8.5%, what is his annualized holding period return on this bond?
(b) After Arthur collected his proceeds from his investments in Face Tech. Inc. 4 years later, he will use the money to purchase 8 units of a 3-year default-free zero coupon bond and put the rest in cash. What are the percentage weights in the 3-year default-free zero coupon bond and cash (out of Arthur's total proceeds), respectively? Assume that the yield curve on zero coupon bonds stays the same and you can ignore the liquidity premium.
