Question

Barry’s Steroids Company has $1,000 par value bonds outstanding at 16 percent interest. The bonds will mature in 40 years. If the percent yield to maturity is 13 percent, what percent of the total bond value does the repayment of principal represent?

Short answer

The percentage of the principal as a percentage of bond price is 0.6127%

Step-by-step solution

Computation of coupon

$\begin{array}{rcl}\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{c}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}& \mathbf{=}& \mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathit{o}\mathit{u}\mathit{t}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{d}\mathit{i}\mathit{n}\mathit{g}\mathbf{\times }\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{e}\mathit{s}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{16}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{160}\\ & & \end{array}$

Computation of Total bond price-

$\begin{array}{rcl}\mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}& \mathbf{=}& \mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathbf{\times }\frac{[1-\frac{1}{{\left(1+r\right)}^n}]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{r}\mathbf{)}}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{160}\mathbf{\times }\frac{[1-\frac{1}{{\left(1+0.13\right)}^{40}}]}{\mathbf{0}\mathbf{.}\mathbf{13}}\mathbf{+}\frac{\mathbf{\$}\mathbf{1000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{13}\mathbf{)}}^{\mathbf{40}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{160}\mathbf{\times }\mathbf{7}\mathbf{.}\mathbf{634}\mathbf{+}\mathbf{7}\mathbf{.}\mathbf{53}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{228}\mathbf{.}\mathbf{97}\\ & & \end{array}$

Computation of the principal as a percentage of bond price-

$\begin{array}{rcl}\mathit{P}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}& \mathbf{=}& \frac{\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{i}\mathbf{p}\mathbf{a}\mathbf{l}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}}{\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{228}\mathbf{.}\mathbf{97}}\\ & \mathbf{=}& \mathbf{81}\mathbf{.}\mathbf{37}\mathbf{\%}\\ & & \end{array}$