What Does A Call Provision Allow The Issuer To Do, And Why Would They Do It? Case Studies Example

A call provision is a special provision in the bond. This special provision gives the bond issuer right to call back the bond that it have issued. Call provision allows the bond issuer to call back the bond from the bondholder i.e. payoff the bond prior to its maturity at a price equal to face value plus some call premium. This price is called call price. This provision gives advantage to the bond issuer in case the interest rate in the market falls. In the case when interest rate falls or declines, the bond issuer can call back its bonds that carry higher interest rates and issue new bonds at a interest rate that is lower than the previous. This provision will help the bond issuer to reduce its interest expense.
Provide the definitions of a discount bond and a premium bond. Give examples.
Discount bond and premium bonds are two types of bonds. Discount bonds are those kinds of bonds that have the selling price below its par value. The selling price of the discount bond is always less than its par value i.e. less than $1000. On contrary to this, premium bonds are those bonds, which have selling price above its par. The selling price of premium bonds are always above its par value. Generally, the bond is a discount bond if the interest rate in the market is higher than that of the coupon rate of the bond and the bond is a premium bond if the interest rate in the market is lower than that of the coupon rate of the bond.

Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zero coupon bond.

There is some difference in the coupon bond and the discount bond. The coupon bond pays certain percent interest on the face value of the bond while the zero coupon bond do not pay interest. The bond with 5 percent coupon is a coupon-paying bond, and this bond pays 5 percent of its face value as the interest to the bondholder. For example, the 5 percent bond will pay $50 annually as the interest to the bondholder if the face value of the bond is $1000. The selling price of the bond with coupon hovers around its par value. On the other hand, zero coupon bond do not pay coupon to the bondholders. The zero coupon bonds are issue at discount i.e. at the price less than its face value. The bondholders get return in their investment as the price of the bond appreciates. Since the bondholder buys the bond at a price lower than its par value, the price of the bond appreciates over time as it approaches towards the maturity. So, the bondholder gets the return in the form of capital appreciation. As the bond matures, the par value is paid to the bondholder, which is higher than the price at which the bond was sold.
Calculate the price of a zero coupon bond that matures in 20 years if the market interest rate is 6.5 percent. use semi-annual compounding:

Given:

Maturity period, N = 20 years = 40 periods (Semiannual compounding)
Interest rate, I = 6.5% = 0.0325 (Semiannual Compounding)
Par value, FV = $1000
Price of the bond, PV=?

We know,

PV= FVN1+iN
PV= 10001+0.032540
PV= 10001+0.032540
PV= 10003.594
PV=$278.23
The price of the discount bond is $278.23.
Compute the price of a 4.5 percent coupon bond with 15 years left to maturity and a market interest rate of 6.8 percent. (Assume interest payments are semi-annual.)

Given

Coupon = 4.5% = 4.5% of par = 4.5%*$1000 = 45. We use $22.5, as it is semiannual compounding.
Maturity, N = 15 years = 30 periods (Semiannual compounding)
Market interest rate, i = 6.8% = 3.4% (Semiannual compounding)
Face value, FV = $1000
Price of the bond =?

We know,

Bond Price=Coupon x 1-1(1+i)Ni+FV(1+i)N
Bond Price=$22.50 x 1-11+0.034300.034+1000(1+0.034)30
Bond Price=$419.05+$366.76
Bond Price=$785.81
So, the price of the bond is $785.81. This bond is the discount bond as its price is below the par.
A 6.85 percent coupon bond with 26 years left to maturity is offered for sale at $1,035.25. What yield to maturity is the bond offering? (Assume interest payments are paid semi-annually.)

Given

Coupon = 6.85% = 6.85% of par = 6.85%*$1000 = $68.5. We use $34.25, as it is semiannual compounding.
Maturity, N = 26 years = 52 periods (Semiannual compounding)
Face value, FV = $1000
Price of the bond, P =$1035.25
Yield to maturity, i =?

We know,

Approximate YTM, i/2 = Coupon+ FV-PNFV+P2
Approximate YTM, i/2 = 34.25+ 1000-1035.25521000+1035.252
Approximate YTM, i/2 = 33.571017.625
Approximate YTM, i/2 = 0.033
YTM = 0.033*2 = 0.066 = 6.6%
So, the yield to maturity is 6.60%.