Question

Stilley Resources bonds have four years left to maturity. Interest is paid annually, and the bonds have a \(1,000 par value and a coupon rate of 5 percent. If the price of the bond is \)841.51, what is the yield to maturity?

Short answer

The bond’s yield to maturity is determined as the 9.73%

Step-by-step solution

Definition of Bond

The maturity date is defined as the date on which the principal amount of debt becomes due for repayment.

Determination of annual yield to maturity

$\begin{array}{rcl}\mathbf{Coupon}& \mathbf{=}& \mathbf{Par}\mathbf{}\mathbf{Value}\mathbf{\times }\mathbf{Coupon}\mathbf{}\mathbf{Rate}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{5}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{50}\end{array}$

$\begin{array}{rcl}\mathbf{Approx}\mathbf{}\mathbf{Yield}\mathbf{}\mathbf{to}\mathbf{}\mathbf{Maturity}& \mathbf{=}& \frac{\left[\mathrm{Annual}\mathrm{Coupon}+{\displaystyle \frac{\left(\mathrm{Face}\mathrm{value}-\mathrm{Present}\mathrm{value}\right)}{\mathrm{Time}\mathrm{to}\mathrm{maturity}}}\right]}{{\displaystyle \frac{\left(\mathrm{Face}\mathrm{value}+\mathrm{Present}\mathrm{value}\right)}{\mathbf{2}}}}\\ & \mathbf{=}& \frac{\left[\$50+\left({\displaystyle \frac{\$1,000-\$841.51}{4}}\right)\right]}{\left({\displaystyle \frac{\$1,000+\$841.51}{2}}\right)}\\ & \mathbf{=}& \mathbf{9}\mathbf{.}\mathbf{73}\mathbf{\%}\end{array}$