Assume theâ zero-coupon yields onâ default-free securities are as summarized in the followingâ table:
Maturity
1 year
2 years
3 years
4 years
5 years
âZero-Coupon Yields
3.53.5â%
4.04.0â%
4.34.3â%
4.54.5â%
4.94.9â%
What is the price today of aâ two-year, default-free security with a face value of $1,000 and an annual coupon rate of 3%â?
Does this bond trade at aâ discount, atâ par, or at aâ premium?ââ
Noteâ:
Assume annual compounding.
What is the price today of aâ two-year, default-free security with a face value of $1,000
and an annual coupon rate of 3%â?
The price is $. (Round to the nearestâ cent.)
Assume theâ zero-coupon yields onâ default-free securities are as summarized in the followingâ table:
| Maturity | 1 year | 2 years | 3 years | 4 years | 5 years |
| âZero-Coupon Yields | 3.53.5â% | 4.04.0â% | 4.34.3â% | 4.54.5â% | 4.94.9â% |
What is the price today of aâ two-year, default-free security with a face value of $1,000 and an annual coupon rate of 3%â?
Does this bond trade at aâ discount, atâ par, or at aâ premium?ââ
Noteâ:
Assume annual compounding.
What is the price today of aâ two-year, default-free security with a face value of $1,000
and an annual coupon rate of 3%â?
The price is $. (Round to the nearestâ cent.)
Related questions
The following table summarizes prices of variousâ default-free zero-coupon bondsâ ($100 faceâ value):
| Maturityâ (years) | 1 | 2 | 3 | 4 | 5 |
| Priceâ (per $100 faceâ value) | â$95.56 | â$91.05 | â$86.46 | â$81.68 | â$76.57 |
a. Compute the yield to maturity for each bond.
b. Plot theâ zero-coupon yield curveâ (for the first fiveâ years).
c. Is the yield curve upwardâ sloping, downwardâ sloping, orâ flat?
Noteâ: Assume annual compounding.
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.
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.
