Consider two bonds. The first is a 6% coupon bond with six years to maturity, and a yield to maturity of 4.5% annual rate, compounded semi-annually. The second bond is a 2% coupon bond with six years to maturity and a yield to maturity of 5.0%, annual rate, compounded semi-annually.
1. Calculate the current price per $100 of face value of each bond. (You may use financial calculator to do question 1 and 2, I'm just unsure how to use it.)
2. Given the data for the first two bonds, now consider a third bond: a zero coupon bond with six years to maturity. Calculate the price per $100 of face value of the zero coupon bond. Calculate the yield to maturity for the zero coupon bond. (Express the yield as annual rate, compounded semi-annually).
HINT: Use the Value Additivity principle to answer part c. Create a synthetic zero- coupon bond, that is, a portfolio of the 6% coupon bond and the 2% coupon bond that has the same cash flows as a 6-year, zero coupon bond.
For both the bonds, coupon is compounded semiannualy
a) First bond
Assuming Face value = 100, Semiannual coupon = 6% / 2* 100 =3
Yield to maturity = 4.5%
Years to maturity = 6 , Number of coupon payment period = 6 * 2 = 12
Using excel, Bond current price = $86.3
Period | Coupon | Yield / discount rate | Discount factor | Present value of cash flow |
1 | 3 | 4.50% | 0.957 | 2.9 |
2 | 3 | 4.50% | 0.916 | 2.7 |
3 | 3 | 4.50% | 0.876 | 2.6 |
4 | 3 | 4.50% | 0.839 | 2.5 |
5 | 3 | 4.50% | 0.802 | 2.4 |
6 | 3 | 4.50% | 0.768 | 2.3 |
7 | 3 | 4.50% | 0.735 | 2.2 |
8 | 3 | 4.50% | 0.703 | 2.1 |
9 | 3 | 4.50% | 0.673 | 2.0 |
10 | 3 | 4.50% | 0.644 | 1.9 |
11 | 3 | 4.50% | 0.616 | 1.8 |
12 | 103 | 4.50% | 0.590 | 60.7 |
Bond present value | 86.3 |
Excel formula:
b) For second bond coupon is 2% (compounded semmiannually) and Yield to maturity is 5%, years to maturity =6%
Using excel, Bond current price = $64.5
Period | Coupon | Yield / discount rate | Discount factor | Present value of cash flow |
1 | 1 | 5.00% | 0.952 | 1.0 |
2 | 1 | 5.00% | 0.907 | 0.9 |
3 | 1 | 5.00% | 0.864 | 0.9 |
4 | 1 | 5.00% | 0.823 | 0.8 |
5 | 1 | 5.00% | 0.784 | 0.8 |
6 | 1 | 5.00% | 0.746 | 0.7 |
7 | 1 | 5.00% | 0.711 | 0.7 |
8 | 1 | 5.00% | 0.677 | 0.7 |
9 | 1 | 5.00% | 0.645 | 0.6 |
10 | 1 | 5.00% | 0.614 | 0.6 |
11 | 1 | 5.00% | 0.585 | 0.6 |
12 | 101 | 5.00% | 0.557 | 56.2 |
Bond present value | 64.5 |
2) Using addition principal
Price of zero coupon bond = average (value of bond 1, value of bond 2)
= average(86.3,64.5)
Price of zero coupon bond = $75.4
Using rate formula to to calculate yield = RATE(6,0,-75.4,100)
Yield on zero coupon = 4.8%
Consider two bonds. The first is a 6% coupon bond with six years to maturity, and...
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