# Clark Co. issues $400,000 of 8% bonds due in 10 years with interest payable semiannually. At the... ## Question: Clark Co. issues$400,000 of 8% bonds due in 10 years with interest payable semiannually. At the time of issue, the market rate for such bonds is 9%.

What is the issue price of the bond?

## Present Value:

Time Value of money is significant for the stakeholders, especially the investors and creditors. This shows the current valuation of future earnings/ money to be received based on an assumed rate of return. It only implies that the value of money today is not the same as the value of money to be received in the future and those received before considering the time and inflation movements. In relation to bond, its trading market price is the present value of its future interest payments and face value discounted at the prevailing market rate.

{eq}Bond~value=\displaystyle C*\frac{1-(1+\frac{r}{m})^{-nm}}{\frac{r}{m}}+\frac{FV}{(1+\frac{r}{m})^{nm}}\\ whereas:\\ C=coupon~payment\\ r=interest~rate\\ n=number~of~year~until~maturity\\ m=periodicity\\ FV=par~value\\ {/eq}

We need to calculate the semi annual coupon of the bond, then:

{eq}\begin{align*} Coupon~payment&=\frac{C_{r}*FV}{m}\\ &=\frac{.08*400,000}{2}\\ &=\frac{32,000}{2}\\ &=16,000\\ \end{align*} {/eq}

The semi-annual coupon payment of the bond is 16,000.00 Since, the interest payment of the bond were paid semi-annually, then its periodicity is 2, {eq}\begin{align*} Bond~value&=16,000*\frac{1-(1+\frac{.090}{2})^{-10*2}}{\frac{.09}{2}}+\frac{400,000}{(1+\frac{.09}{2})^{10*2}}\\ &=16,000*\frac{1-(1.0450)^{-20}}{.045}+\frac{400,000}{(1.045)^{20}}\\ &=16,000*\frac{1-.4146}{.045}+\frac{400,000}{2.4117}\\ &=16,000*\frac{.5854}{.045}+165,857.14\\ &=16,000*13.0079+165,857.14\\ &=373984.13 \end{align*} {/eq} The issue price of the 10 year bond is373,984.13