Question

Using the information below, compute the prices of the following SEMI-ANNUAL payment bonds. Show your computation in every case.

Per value Coupon Rate Yield to Maturity Years to Maturity

$ 5,000 10 12% 20

$ 5,000 10 10 % 20

$ 5,000 10 6 % 20

A) Indicate which bond is selling at discount, par, and premium. (Use the formula)

B) What is the relationship between bond prices and interest rates?

Answer 1

Given that:
For the first bond:
Par value=$5000
Coupon Rate=10%
Yield to Maturity=12%
Years to Maturity=20

As the interest is paid semiannually, the semiannual coupon rate=10%/2=5%
Semiannual yield to Maturity=12%/2=6%
As the interest is paid semiannually, total number of periods=Years to Maturity*2=20*2=40
Semiannual coupon payment=Semiannual coupon rate*Par value=5%*$5000=$250

For the second bond:
Par value=$5000
Coupon Rate=10%
Yield to Maturity=10%
Years to Maturity=20

As the interest is paid semiannually, the semiannual coupon rate=10%/2=5%
Semiannual yield to Maturity=10%/2=5%
As the interest is paid semiannually, total number of periods=Years to Maturity*2=20*2=40
Semiannual coupon payment=Semiannual coupon rate*Par value=5%*$5000=$250

For the third bond:
Par value=$5000
Coupon Rate=10%
Yield to Maturity=6%
Years to Maturity=20

As the interest is paid semiannually, the semiannual coupon rate=10%/2=5%
Semiannual yield to Maturity=6%/2=3%
As the interest is paid semiannually, total number of periods=Years to Maturity*2=20*2=40
Semiannual coupon payment=Semiannual coupon rate*Par value=5%*$5000=$250

Part A:
We have calculated the present value of the bonds and found that,
Present value of the first bond=$4,247.69, this bond is trading at a discount as present value of the bond is less that the par value (Present value<Par value).
Present value of the second bond=$5,000.00, this bond is trading at par as the present value of the bond is equal to the par value (Present value=Par value).
Present value of the third bond=$7,311.48, this bond is trading at a premium as present value of the bond is more that the par value (Present value>Par value).

Part B:
Bond prices and interest rates have an inverse relationship, so when one moves up the other moves down.