Question

Harold Reese must choose between two bonds: Bond X pays \(95 annual interest and has a market value of \)900. It has 10 years to maturity. Bond Zpays \(95 annual interest and has a market value of \)920. It has two years tomaturity.

a.Compute the current yield on both bonds.

b.Which bond should he 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 X is 11.21 percent. Whatis the yield to maturity on Bond Z?

d.Has your answer changed between parts band cof this question?

Short answer

a) 10.50% for bonds X and 10.30% for bond Z

b) Bond X

c) 14.06%

d) Bond Z

Step-by-step solution

Current Yield meaning

The current yield is the rate of interest as per the current market price. It compares the annual interest with the current market price to determine the fluctuation with the normal yield.

a. Computation of current yield

$\begin{array}{rcl}\mathbf{Current}\mathbf{}\mathbf{yield}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{X}& \mathbf{=}& \frac{\mathbf{Annual}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{X}\mathbf{}}{\mathbf{Current}\mathbf{}\mathbf{market}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{X}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{95}}{\mathbf{\$}\mathbf{900}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{105}\mathbf{}\mathbf{or}\mathbf{}\mathbf{10}\mathbf{.}\mathbf{50}\mathbf{\%}\end{array}$

$\begin{array}{rcl}\mathbf{Current}\mathbf{}\mathbf{yield}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{Z}& \mathbf{=}& \frac{\mathbf{Annual}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{Z}}{\mathbf{Current}\mathbf{}\mathbf{market}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{bond}\mathbf{}\mathbf{Z}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{95}}{\mathbf{\$}\mathbf{920}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{1030}\mathbf{}\mathbf{or}\mathbf{}\mathbf{10}\mathbf{.}\mathbf{30}\mathbf{\%}\end{array}$

b. Recommended bond based on current yield

Bond X will selected by the investor because it has higher current yield than Bond Z.

c. Computation of approximate yield to maturity

Let’s suppose maturity value = $1,000

$\begin{array}{rcl}\mathbf{Yield}\mathbf{}\mathbf{to}\mathbf{}\mathbf{maturity}\mathbf{}\mathbf{on}\mathbf{}\mathbf{Bond}\mathbf{}\mathbf{Z}& \mathbf{=}& \frac{\mathbf{Annual}\mathbf{}\mathbf{Interest}\mathbf{+}{\displaystyle \frac{\mathbf{Maturity}\mathbf{}\mathbf{value}\mathbf{-}\mathbf{Current}\mathbf{}\mathbf{price}\mathbf{}}{\mathbf{Maturity}\mathbf{}\mathbf{Period}}}}{{\displaystyle \frac{\mathbf{Maturity}\mathbf{}\mathbf{value}\mathbf{-}\mathbf{Current}\mathbf{}\mathbf{price}}{\mathbf{2}}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{95}\mathbf{+}{\displaystyle \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{920}}{\mathbf{2}}}}{{\displaystyle \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{920}}{\mathbf{2}}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{135}}{\mathbf{\$}\mathbf{960}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{1406}\mathbf{}\mathbf{or}\mathbf{}\mathbf{14}\mathbf{.}\mathbf{06}\mathbf{\%}\end{array}$

d. Recommended bond based on yield to maturity

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

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