Question

What would you pay for a \(100,000 debenture bond that matures in 15 years and pays \)5,000 a year in interest if you wanted to earn a yield of: (a) 4%? (b) 5%? (c) 6%?

Short answer

The bond price at 4% is $111,118, at 5% is $100,000, and at 6% is $90,288.

Step-by-step solution

Calculation at 4%

$\begin{array}{rcl}\mathrm{Bond}\mathrm{Price}& =& \mathrm{Bond}\mathrm{value}\times \left({\mathrm{PVF}}_{4\%,15}\right)+\mathrm{Interest}\times \left({\mathrm{PVA}}_{4\%,15}\right)\\ & =& 100,000\times 0.55526+5,000\times 11.11839\\ & =& 55,526+55,592\\ & =& \$111,118\end{array}$

Calculation at 5%

$\begin{array}{rcl}\mathrm{Bond}\mathrm{Price}& =& \mathrm{Bond}\mathrm{value}\times \left({\mathrm{PVF}}_{5\%,15}\right)+\mathrm{Interest}\times \left({\mathrm{PVA}}_{5\%,15}\right)\\ & =& 100,000\times 0.48102+5,000\times 10.37966\\ & =& 48,102+51,898\\ & =& \$100,000\end{array}$

Calculation at 6%

$\begin{array}{rcl}\mathrm{Bond}\mathrm{Price}& =& \mathrm{Bond}\mathrm{value}\times \left({\mathrm{PVF}}_{6\%,15}\right)+\mathrm{Interest}\times \left({\mathrm{PVA}}_{6\%,15}\right)\\ & =& 100,000\times 0.41727+5,000\times 9.71225\\ & =& 41,727+48,561\\ & =& \$90,288\end{array}$