Question

2. The following questions are based on a $1,000 face value coupon bond with a coupon rate of 10% a. Suppose the bond has one year to maturity and you buy it for $1,018.52. What is the yield to maturity on the bond? Is the yield to maturity above or below the coupon rate of 10%? Why? b. Since the equation is often considered too difficult to solve, simply write down the equation that one would have to solve to find the yield to maturity if the bond has two years to maturity, and you paid $965 for the bond. If this equation was solved, would the resulting yield to maturity be above or below the coupon rate of 10%? Why?

Answer 1

1) The formula to calculate YTM could be given as
YTM = ( C + ( F - P ) /n) / ( ( F + P ) /2 )
C = Coupon or Interest Payment
F = Face Value
P = Current Market Price
n = Years to Maturity

( 100 + ( 1000 - 1018.52 ) / 1 ) / ( ( 1000 + 1018.52 ) / 2 )
= 194 / 2403
= 0.08 or 8%

The YTM of this bond is below the coupon rate of 10%. The YTM is nothing but the discount rate whicj equates the present value of the bond to its current market price. The current market price is higher than the face value of the bond in this case so the YTM will be obviously lower than the coupon rate.

2) YTM = ( C + ( F - P ) /n) / ( ( F + P ) /2 )
C = Coupon or Interest Payment
F = Face Value
P = Current Market Price
n = Years to Maturity

( 100 + ( 1000 - 965 ) / 2 ) / ( ( 1000 + 965 ) / 2 )
= 0.1196 or 11.96%

The YTM of this bond will be higher because the current market price is lower than the face value. The YTM needs to higher to euqate the present value of the bond to market price.

3) The price of the bond can be calculated by following formula

If the coupon payment is $7 for the face value of $100 bond then
( 7 / ( 1.07 ) ) + ( 107 / ( ( 1.07 ) ^ 2 ) ) = 100
When the YTM and interest rate is the same then the market price of the bond will be equal to its face value.

4) If the YTM and interest rate is the same then the bond will trade at face value.

5) The bond price tends to have negative relationship with the interest rate which means if the interest rate rises then the bond price will fall. The market price of the bond is the present value of all of its cash flow such as coupon payment and principal. If the interest rate rises then the discount factor will lower the bond price.

First four questions have been answered according to the HOMEWORKLIB RULES.