Question

Exodus Limousine Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is

a. 5 percent.

b. 15 percent.

Short answer

1. Bond price for 5% yield to maturity is $1,912.80
2. Bond price for 15% yield to maturity is $666.92

Step-by-step solution

Computation of coupon:

$\begin{array}{rcl}\mathbf{Coupon}& \mathbf{=}& \mathbf{Bond}\mathbf{}\mathbf{outstanding}\mathbf{\times }\mathbf{}\mathbf{Interest}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1000}\mathbf{\times }\mathbf{10}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\end{array}$

a. Computation on the basis of 5 percent.

• Par value of bond (P) is $1,000.
• Yield to maturity (r) is 5%.
• Years to maturity (n) is 50.

$\begin{array}{rcl}\mathbf{Bond}\mathbf{}\mathbf{price}& \mathbf{=}& \mathbf{Coupon}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+r\right)}^n}}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{100}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+0.05\right)}^{50}}}\right]}{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{+}\frac{\mathbf{1000}}{{\left(1+0.05\right)}^{\mathbf{50}}}\\ & \mathbf{=}& \mathbf{100}\mathbf{\times }\mathbf{18}\mathbf{.}\mathbf{26}\mathbf{+}\mathbf{87}\mathbf{.}\mathbf{20}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{912}\mathbf{.}\mathbf{80}\end{array}$$\begin{array}{rcl}\mathbf{Bond}\mathbf{}\mathbf{price}& \mathbf{=}& \mathbf{Coupon}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+r\right)}^n}}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{100}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+0.05\right)}^{50}}}\right]}{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{+}\frac{\mathbf{1000}}{{\left(1+0.05\right)}^{\mathbf{50}}}\\ & \mathbf{=}& \mathbf{100}\mathbf{\times }\mathbf{18}\mathbf{.}\mathbf{26}\mathbf{+}\mathbf{87}\mathbf{.}\mathbf{20}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{912}\mathbf{.}\mathbf{80}\end{array}$

b. Computation on the basis of15 percent.

$\begin{array}{rcl}\mathbf{Bond}\mathbf{}\mathbf{price}& \mathbf{=}& \mathbf{Coupon}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+r\right)}^n}}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{100}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+0.15\right)}^{50}}}\right]}{\mathbf{0}\mathbf{.}\mathbf{15}}\mathbf{+}\frac{\mathbf{\$}\mathbf{1000}}{{\left(1+0.15\right)}^{\mathbf{50}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{66}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{92}\\ & \mathbf{=}& \mathbf{\$}\mathbf{666}\mathbf{.}\mathbf{92}\\ & & \end{array}$