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.
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.
Related questions
Suppose theâ current, zero-coupon, yield curve forâ risk-free bonds is asâ follows:
| Maturityâ (years) | 1 | 2 | 3 | 4 | 5 |
| Yield to Maturity | 4.51 | 4.84 | 5.00â% | 5.12â% | 5.37â% |
a. What is the price per $100 face value of a 3â-year, zero-coupon risk-freeâ bond?
b. What is the price per $100 face value of a 5â-year, zero-coupon, risk-freeâ bond?
c. What is theâ risk-free interest rate for a 3â-year maturity?
Noteâ: Assume annual compounding.
