Question

Wilson Oil Company issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point in time as described next:

Real rate of return ........................ 8%

Inflation premium ......................... 3

Risk premium .............................. 4

Total return ............................... 15%

Assume that 10 years later, due to bad publicity, the risk premium is now 7 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity. Compute the new price of the bond.

Short answer

The new price of the bond is $847.80 ($763.80+$84).

Step-by-step solution

Computing current required rate of return-

$\begin{array}{c}\mathrm{Bond}\text{'}\mathrm{scoupon}=\mathrm{Facevalue}\times \mathrm{Interestrate}\\ =\$1,000\times 15\%\\ =\$150\end{array}$

Computing coupon amount-

$\begin{array}{c}\mathrm{Bond}\text{'}\mathrm{scoupon}=\mathrm{Facevalue}\times \mathrm{Interestrate}\\ =\$1,000\times 15\%\\ =\$150\end{array}$

Computing present value of principal where n=30; i= 9%-

$\begin{array}{c}\mathrm{Presentvalueofprincipal}=\mathrm{Facevalue}\times \mathrm{Presentvalueofi}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{84}\\ =\$84\end{array}$

Computing present value of interest where n=30; i= 9%--

$\begin{array}{c}\mathrm{Presentvalueofinterest}=\mathrm{Coupon}\times \mathrm{Presentvalueofi}\\ \mathbf{=}\mathbf{\$}\mathbf{150}\mathbf{\times }\mathbf{5}\mathbf{.}\mathbf{092}\\ \mathbf{=}\mathbf{\$}\mathbf{763}\mathbf{.}\mathbf{80}\end{array}$