Question

A bond has the following terms: January 1, 2000, settlement date January 1, 2020, maturity date 10 percent semiannual coupon 12 percent yield $100 redemption value Frequency is semiannual 30/360 basis =PRICE("1/1/2000","1/1/2020",10%,12%,100,2,0)=84.954

Bond Problems 1. Calculate the price of a 20-year 10% coupon bond with a par value of $1,000. The bond should be price to provide a yield to maturity of 11%. Interest payments are paid semiannually.

2. Calculate the price of a 20-year 10% coupon bond with a par value of $1,000 if the yield to maturity is 9%. Interest payments are paid semiannually.

3. Calculate for each of the bonds below the price per $1,000 of par value assuming semiannual coupon payments.

Bond Coupon Rate Years to Maturity Required Yield

A 8% 9 7%

B 9% 20 9%

C 6% 15 10%

D 0% 14 8%

4. Consider a bond selling at par with a coupon rate of 6% and ten years to maturity. What is the price of this bond if the required yield is 15%? What is the price of this bond if the required yield increases from 15% to 16%, and by what percentage did the price of this bond change? What is the price of this bond if the required yield is 5%? What is the price of this bond if the required yield increases from 5% to 6%, and by what percentage did the price of this bond change? What can you say about the relative price volatility of a bond in high compared to low interest rate environments?

5. Show the cash flows for the four bonds below, each of which have a par value of $1,000 and pays interest semiannually. Calculate the yield to maturity for the four bonds.

Bond Coupon Rate Years to Maturity Price

W 7% 5 $884.20

X 8% 7 $948.90

Y 9% 4 $967.70

Z 0% 10 $456.39

Answer 1

(1) (a) Settlement Date: 1 Jan 2000 and Maturity Date 1 Jan 2020, Tenure = 20 years or (20 x 2) = 40 half-years, Redemption Value = Face Value = $ 100, Coupon = 10 % per annum payable semi-annually, Yield = 12 %per annum

Semi-Annual Coupon = 0.5 x 0.1 x 100 = $ 5

Therefore, Bond Price = 5 x (1/0.06) x [1-{1/(1.06)^(40)}] + 100 / (1.06)^(40) = $ 84.9537 ~ $ 84.95

(b) Tenure = 20 Years, Coupon Rate = 10 %, Payment Frequency: Semi-Annual, Yield = 11% and Face Value = $ 1000

Semi-Annual Coupon = 0.5 x 1000 x 0.1 = $ 50

Therefore, Bond Price = 50 x (1/0.055) x [1-{1/(1.055)^(40)}] + 1000 / (1.055)^(40) = $ 919.769 ~ $ 919.77

NOTE: Please raise separate queries for solutions to the remaining unrelated questions as one query is restricted to the solution of only one complete question with up to four sub-parts.