Question

Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 11 percent to 8 percent:

a. What is the bond price at 11 percent?

b. What is the bond price at 8 percent?

c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent?

Short answer

1. Bond price at 11% yield to maturity is $920.33
2. Bond price at 8% yield to maturity is $1,196.37
3. Percentage return on investment is 29.99%

Step-by-step solution

a.Computing annuity amount 

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathit{A}\mathit{m}\mathit{o}\mathit{u}\mathit{n}\mathit{t}& \mathbf{=}& \mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathit{P}\mathit{a}\mathit{r}\mathit{V}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{\times }\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{e}\mathit{s}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{10}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\end{array}$

a.Computing bond price at 11 percent

• Par value of bond (P) is $1,000.
• Yield to maturity (r) is 11%.
• Years to maturity (n) is 20.

$\begin{array}{rcl}\mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e}& \mathbf{=}& \mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathbf{\times }\frac{\left[1-\frac{1}{{\left(1+r\right)}^n}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\mathbf{\times }\frac{\left[1-\frac{1}{{\left(1+0.11\right)}^{20}}\right]}{\mathbf{0}\mathbf{.}\mathbf{11}}\mathbf{+}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}}{{\left(1+0.11\right)}^{\mathbf{20}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\mathbf{\times }\mathbf{7}\mathbf{.}\mathbf{963}\mathbf{+}\mathbf{124}\mathbf{.}\mathbf{034}\\ & \mathbf{=}& \mathbf{\$}\mathbf{920}\mathbf{.}\mathbf{33}\\ & & \end{array}$

b.Computing bond price at 8 percent

• Par value of bond (P) is $1,000.
• Yield to maturity (r) is 8%.
• Years to maturity (n) is 20.
• $\begin{array}{rcl}\mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e}& \mathbf{=}& \mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathbf{\times }\frac{\left[1-\frac{1}{{\left(1+r\right)}^n}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\mathbf{\times }\frac{\left[1-\frac{1}{{\left(1+0.08\right)}^{20}}\right]}{\mathbf{0}\mathbf{.}\mathbf{08}}\mathbf{+}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}}{{\left(1+0.08\right)}^{\mathbf{20}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\mathbf{\times }\mathbf{9}\mathbf{.}\mathbf{818147}\mathbf{+}\mathbf{214}\mathbf{.}\mathbf{5482}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{196}\mathbf{.}\mathbf{37}\\ & & \end{array}$
  

c. Computigpercentage return on investment

$\begin{array}{rcl}\mathit{P}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}\mathit{R}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}& \mathbf{=}& \frac{\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{8}\mathbf{\%}\mathbf{-}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{11}\mathbf{\%}}{\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{11}\mathbf{\%}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{196}\mathbf{.}\mathbf{37}\mathbf{-}\mathbf{\$}\mathbf{920}\mathbf{.}\mathbf{33}}{\mathbf{\$}\mathbf{920}\mathbf{.}\mathbf{33}}\\ & \mathbf{=}& \mathbf{29}\mathbf{.}\mathbf{99}\mathbf{\%}\\ & & \end{array}$