Question

Question:The yield to maturity for 10-year bonds is as follows for four different bond rating categories:

Aaa 9.40% Aa2 10.00%

Aa1 9.60% Aa3 10.60%

The bonds of Falter Corporation were rated as Aaa and issued at par a few weeks ago. The bonds have just been downgraded to Aa2. Determine the new price of the bonds, assuming a 10-year maturity and semiannual interest payments. (Refer to “Semiannual Interest and Bond Prices” in Chapter 10 for a review if necessary.)

Short answer

Answer

The price per bond is computed as $962.61

Step-by-step solution

Definition of Par Value

The par value is also known as the nominal value which is the face value of the bond or any other financial instrument.

Computation of price of the bond

$\begin{array}{rcl}\mathbf{SemiannualCoupon}& \mathbf{=}& \left(\frac{\mathbf{CouponRate}}{\mathbf{2}}\right)\mathbf{\times }\mathbf{FaceValue}\\ & \mathbf{=}& \left(\frac{\mathbf{0}\mathbf{.}\mathbf{094}}{\mathbf{2}}\right)\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{47}\mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathit{p}\mathit{e}\mathit{r}\mathit{b}\mathit{o}\mathit{n}\mathit{d}\mathbf{=}\mathbf{CouponPayment}\mathbf{\times }\mathbf{\left(}\frac{{\displaystyle 1-{\left(1+r\right)}^{-n}}}{{\displaystyle r}}\mathbf{\right)}\mathbf{+}\frac{{\displaystyle \mathbf{FaceValue}}}{{\displaystyle {\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{r}\mathbf{)}}^{\mathbf{n}}}}\\ & \mathbf{=}& \mathbf{47}\mathbf{\times }\mathbf{\left(}\frac{{\displaystyle 1-{\left(1+0.05\right)}^{-10\times 2}}}{{\displaystyle 0.05}}\mathbf{\right)}\mathbf{+}\frac{{\displaystyle \mathbf{1}\mathbf{,}\mathbf{000}}}{{\displaystyle {\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{)}}^{\mathbf{10}\mathbf{\times }\mathbf{2}}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{962}\mathbf{.}\mathbf{61}\\ & & \\ & & \end{array}$