On January 1,a company issues bonds dated January 1 with a par value of $200,000.The bonds mature in 3 years.The contract rate is 4%,and interest is paid semiannually on June 30 and December 31.The market rate is 5%.Using the present value factors below,the issue (selling)price of the bonds is:
$$\begin{array} { c c c c }
&&{ \text { Present Value of arn } } \
\mathrm { n} = & \mathrm { i } = & \text { Annuity } & \text { Present value of } \$ 1 \
3 & 4.0 \% & 2.7751 & 0.8890 \
6 & 2.0 \% & 5.6014 & 0.8880 \
3 & 5.0 \% & 2.7232 & 0.8638 \
6 & 2.5 \% & 5.5081 & 0.8623
\end{array}$$

Question

On January 1,a company issues bonds dated January 1 with a par value of $200,000.The bonds mature in 3 years.The contract rate is 4%,and interest is paid semiannually on June 30 and December 31.The market rate is 5%.Using the present value factors below,the issue (selling)price of the bonds is:
$$\begin{array} { c c c c } 
&&{ \text { Present Value of arn } } \
\mathrm { n} = & \mathrm { i } = & \text { Annuity } & \text { Present value of } \$ 1 \
3 & 4.0 \% & 2.7751 & 0.8890 \
6 & 2.0 \% & 5.6014 & 0.8880 \
3 & 5.0 \% & 2.7232 & 0.8638 \
6 & 2.5 \% & 5.5081 & 0.8623
\end{array}$$

Quizplus · Accepted Answer

The issue price of the bonds is calculated by finding the present value of the bond's future cash flows, which include the semiannual interest payments and the principal amount to be repaid at maturity. The market rate of interest (5%) is used for discounting because it represents the return required by investors. Since interest is paid semiannually, the market rate per period is 2.5% (5% annual rate divided by 2), and the number of periods is 6 (3 years times 2 periods per year).1. Calculate the present value of the semiannual interest payments: The semiannual interest payment is $200,000 * 4% / 2 = $4,000. Using the present value of an annuity factor for n=6 and i=2.5%, the present value of the interest payments is $4,000 * 5.5081 = $22,032.40.2. Calculate the present value of the principal amount: The principal amount ($200,000) is paid at the end of the bond's term. Using the present value of $1 factor for n=6 and i=2.5%, the present value of the principal is $200,000 * 0.8623 = $172,460.3. Add the present values to find the issue price of the bonds: $22,032.40 + $172,460 = $194,492.40.

On January 1,a Company Issues Bonds Dated January 1 with a Par