Sharmer Company issues 5%, 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 factors: $$\begin{array}{l}
\begin{array} { r l c c }
&&\text { Present Value of an }\
n = & \mathrm { i } = & \text { Annuity } & \text { Present value of \$1 } \
5 & 5 \% & 4.3295 & 0.7835 \
10 & 3 \% & 8.7521 & 0.7812 \
5 & 6 \% & 4.2124 & 0.7473 \
10 & 3 \% & 85302 & 0.7441
\end{array}
\end{array}$$
A) $1,213,255
B) $957,355
C) $1,000,000
D) $786,745
E) $1,250,000

Question

Sharmer Company issues 5%, 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 factors: $$\begin{array}{l}
\begin{array} { r l c c } 
&&\text { Present Value of an }\
n = & \mathrm { i } = & \text { Annuity } & \text { Present value of \$1 } \
5 & 5 \% & 4.3295 & 0.7835 \
10 & 3 \% & 8.7521 & 0.7812 \
5 & 6 \% & 4.2124 & 0.7473 \
10 & 3 \% & 85302 & 0.7441
\end{array}
\end{array}$$
A) $1,213,255
B) $957,355
C) $1,000,000
D) $786,745
E) $1,250,000

Quizplus · Accepted Answer

The selling price of the bond can be calculated using the present value formula:
PV = PMT x (1 - 1/(1+r)^n) / r + FV/(1+r)^n
where PV is the present value or selling price, PMT is the semiannual interest payment, r is the semiannual market rate (6%/2 = 3%), n is the number of semiannual periods (10 years x 2 periods per year = 20), and FV is the par value ($1,000,000).

Using these values, we get:
PV = $25,000 x (1 - 1/1.03^20) / 0.03 + $1,000,000 / 1.03^20
PV = $957,354.81

Therefore, the best choice is B.

Sharmer Company Issues 5%, 5-Year Bonds with a Par Value