Marwick Corporation issues 8%,5-year bonds with a par value of $1,000,000 and semiannual interest payments.On the issue date,the annual market rate for these bonds is 6%.What is the bond's issue (selling)price,assuming the following Present Value factors:
$\begin{array} { r l c c }
&&\text { Present Value of an}\
\mathrm {n } = & \mathrm { i } = & \text { Annuity } & \text { Present value of } \$ 1 \
5 & 8 \% & 3.9927 & 0.6806 \
10 & 4 \% & 8.1109 & 0.6756 \
5 & 6 \% & 4.2124 & 0.7473 \
10 & 3 \% & 8.5302 & 0.7441
\end{array}$

Question

Marwick Corporation issues 8%,5-year bonds with a par value of $1,000,000 and semiannual interest payments.On the issue date,the annual market rate for these bonds is 6%.What is the bond's issue (selling)price,assuming the following Present Value factors:
$\begin{array} { r l c c } 
&&\text { Present Value of an}\
 \mathrm {n } = & \mathrm { i } = & \text { Annuity } & \text { Present value of } \$ 1 \
5 & 8 \% & 3.9927 & 0.6806 \
10 & 4 \% & 8.1109 & 0.6756 \
5 & 6 \% & 4.2124 & 0.7473 \
10 & 3 \% & 8.5302 & 0.7441
\end{array}$

Quizplus · Accepted Answer

The bond's issue price can be calculated by adding the present value of the annuity (interest payments) and the present value of the principal (par value at maturity). Given the annual market rate of 6% and semiannual payments, we use the 5 years and 6% row for calculations. The bond pays semiannual interest of $40,000 (0.08 * $1,000,000 / 2). The present value of the annuity (interest payments) is $40,000 * 4.2124 = $168,496. The present value of the principal ($1,000,000) is $1,000,000 * 0.7473 = $747,300. Adding these together gives $168,496 + $747,300 = $915,796. However, this calculation does not match any of the provided options, indicating a mistake in the calculation process. Correctly, the present value of the annuity is $40,000 * 8.1109 (since we have 10 periods, not 5, due to semiannual payments) = $324,436, and the present value of the principal is $1,000,000 * 0.6756 = $675,600. Adding these gives the correct issue price: $324,436 + $675,600 = $1,000,036, which closely matches option D when considering rounding and the correct factors for 10 periods at 4% (semiannual equivalent of the annual 6% rate). The correct calculation approach involves recognizing the semiannual nature of the payments and using the 10-period factors, but the final explanation mistakenly used incorrect factors and calculations. The correct issue price calculation should involve using the appropriate present value factors for a semiannual period, leading to a conclusion that matches one of the provided options accurately.

Marwick Corporation Issues 8%,5-Year Bonds with a Par Value of $1,000,000