Question

Using Table 10-1, assume interest rates in the market (yield to maturity) are 14 percent for 20 years on a bond paying 10 percent.

a. What is the price of the bond?

b. Assume five years have passed and interest rates in the market have gone down to 12 percent. Now, using Table 10-2 for 15 years, what is the price of the bond?

c. What would your percentage return be if you bought the bonds when interest rates in the market were 14 percent for 20 years and sold them 5 years later when interest rates were 12 percent?

Short answer

a. Bond price for 14% yield to maturity for 20 years is $735.07

b. Bond price for 12 % yield to maturity for 15 years is $863.78

c. Percentage return on Investment is 17.51%

Step-by-step solution

a. The price of the bond

• Par value of bond (P) is $1,000.
• Yield to maturity (r) is 14%.
• Years to maturity (n) is 20.
• Coupon rate (CR) is 10%.

• $\mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathit{V}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}\mathit{P}\mathit{r}\mathit{i}\mathit{n}\mathit{c}\mathit{i}\mathit{p}\mathit{a}\mathit{l}\mathbf{=}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}$$\mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathit{V}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}\mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathbf{=}\mathit{P}\mathbf{\times }\mathit{C}\mathit{R}\mathbf{\times }\frac{\left[1-\frac{1}{{\left(1+r\right)}^n}\right]}{\mathbf{r}}$
  

  Yield to maturity	PV of Coupons		PV of Principal		Bond Price
  14%	$662.31	+	$72.76	=	$735.07

b. The price of the bond:

• Par value of bond (P) is $1,000.
• Yield to maturity (r) is 12%.
• Years to maturity (n) is 15.
• Coupon rate (CR) is 10%.

$\mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{=}\mathit{P}\mathbf{\times }\mathit{C}\mathit{R}\mathbf{\times }\frac{\left[1-\frac{1}{{\left(1+r\right)}^n}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{P}}{{\left(1+r\right)}^{\mathbf{n}}}$

Time Period in Years to Maturity	Bond Price with 12% Yield to Maturity
15	$863.78

c. Computing percentage return -

$\begin{array}{rcl}\mathit{P}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}\mathit{r}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}& \mathbf{=}& \frac{\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{12}\mathbf{\%}\mathbf{-}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{14}\mathbf{\%}}{\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{14}\mathbf{\%}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{863}\mathbf{.}\mathbf{78}\mathbf{-}\mathbf{\$}\mathbf{735}\mathbf{.}\mathbf{07}}{\mathbf{\$}\mathbf{735}\mathbf{.}\mathbf{07}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{17}\mathbf{.}\mathbf{51}\mathbf{\%}\\ & & \end{array}$