CMS Corporation's balance sheet as of today is as follows:
$\begin{array}{lr}
\text { Long-term debt (bonds, at par) } & \$ 10,000,000 \
\text { Preferred stock } & 2,000,000 \
\text { Common stock (\$10 par) } & 10,000,000 \
\text { Retained earnings } & 4,000,000 \
\hline \text { Total debt and equity } & \$ 26,000,000
\end{array}$
The bonds have a 4.0% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 12%, so the bonds now sell below par. What is the current market value of the firm's debt?

Question

CMS Corporation's balance sheet as of today is as follows: 
$\begin{array}{lr}
\text { Long-term debt (bonds, at par) } & \$ 10,000,000 \
\text { Preferred stock } & 2,000,000 \
\text { Common stock (\$10 par) } & 10,000,000 \
\text { Retained earnings } & 4,000,000 \
\hline \text { Total debt and equity } & \$ 26,000,000
\end{array}$
The bonds have a 4.0% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 12%, so the bonds now sell below par. What is the current market value of the firm's debt?

Quizplus · Accepted Answer

$\begin{array}{l}
\begin{array} { l } 
\text { Calculate the price of each bond:}\
\text { Coupon rate}\
\text { Par value}\
\text { Maturity (Yrs)}\
\text { Periods/Yr.}\
\text { YTM}\
\
\text { N}\
\text { I/YR}\
\text { PMT}\
\text { FV}\
\end{array}
\begin{array} { l } 
4.0 \%\
\$ 1000\
10\
2\
12.0 \% \
\
20\
6.0\%\
\$ 20.00 \
\$ 1,000 \
 \$ 541.20 \
\end{array}
\end{array}$
 
Determine the number of bonds:
 $\begin{array} { l r } 
\text { Book value or balarice sheet } & \$ 10,000,000 \
\text { Par value } & \$ 1,000 \
\text { Nurnber of bonds = Book value/Par value } & 10,000
\end{array}$ 
Calculate the market value of bonds:
 Mrt value $ = $ PV $ \times $ Number of bonds $ = $ $ \quad $$ \quad $  $ \$ 5,412,032 $

CMS Corporation's Balance Sheet as of Today Is as Follows