An investor must choose between two bonds: Bond A pays \(72 annual interest and has a market value of \)925. It has 10 years to maturity. Bond B pays \(62annual interest and has a market value of \)910. It has two years to maturity.

Assume the par value of the bonds is $1,000.

a.Compute the current yield on both bonds.

b.Which bond should she select based on your answer to part a?

c.A drawback of current yield is that it does not consider the total life of thebond. For example, the yield to maturity on Bond A is 8.33 percent. What isthe yield to maturity on Bond B?

d.Has your answer changed between parts band cof this question in terms ofwhich bond to select?

$\begin{array}{rcl}\mathbf{Current}\mathbf{}\mathbf{yield}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{A}& \mathbf{=}& \frac{\mathbf{Annual}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{A}}{\mathbf{Current}\mathbf{}\mathbf{market}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{A}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{72}}{\mathbf{\$}\mathbf{925}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{0778}\mathbf{}\mathbf{or}\mathbf{}\mathbf{7}\mathbf{.}\mathbf{78}\mathbf{\%}\end{array}$

$\begin{array}{rcl}\mathbf{Current}\mathbf{}\mathbf{yield}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{B}& \mathbf{=}& \frac{\mathbf{Annual}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{B}}{\mathbf{Current}\mathbf{}\mathbf{market}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{B}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{62}}{\mathbf{\$}\mathbf{910}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{0681}\mathbf{}\mathbf{or}\mathbf{}\mathbf{6}\mathbf{.}\mathbf{81}\mathbf{\%}\end{array}$

The period of maturity and current yield affects the price of the bond. In case maturity is the same for different bonds, the higher the current yield lower would be the price. On the contrary, if the current yield is the same for bonds, then the period of maturity would be the factor to influences the price of the bond.

In the given case, both bonds are having different current yields and different maturity periods. But the maturity period for bond A is 10 years and for bond B it is two years only. Furthermore, Bond A is having higher current yield. So based on this, bond A should be given priority as the price of the bond would be lower due to the longer maturity period and higher current yield.

Maturity value = $1,000

$\begin{array}{rcl}\mathbf{Yield}\mathbf{}\mathbf{to}\mathbf{}\mathbf{maturity}\mathbf{}\mathbf{on}\mathbf{}\mathbf{Bond}\mathbf{}\mathbf{B}& \mathbf{=}& \frac{\mathbf{Annual}\mathbf{}\mathbf{Interest}\mathbf{+}{\displaystyle \frac{\mathbf{Maturity}\mathbf{}\mathbf{value}\mathbf{-}\mathbf{Current}\mathbf{}\mathbf{price}}{\mathbf{Maturity}\mathbf{}\mathbf{Period}}}}{{\displaystyle \frac{\mathbf{Maturity}\mathbf{}\mathbf{value}\mathbf{-}\mathbf{Current}\mathbf{}\mathbf{price}}{\mathbf{2}}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{65}\mathbf{+}{\displaystyle \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{910}}{\mathbf{2}}}}{{\displaystyle \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{910}}{\mathbf{2}}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{107}}{\mathbf{\$}\mathbf{995}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{112}\mathbf{}\mathbf{or}\mathbf{}\mathbf{11}\mathbf{.}\mathbf{2}\mathbf{\%}\\ & & \end{array}$

Yes, the recommendation would change between parts b and c. As yield to maturity considers the maturity period, the bond B would be preferred because it provides a higher yield to maturity than the bond A.

As against the current yield, bond B is having higher yield to maturity due to a shorter maturity period. Thus, In this case, bond B would be preferred over bond A.