CMS Corporation's balance sheet as of today is as follows: $$\begin{array} { l r }
\text { Long-term debt (bonds, at par) } & \$ 10,000,000 \
\text { Preferred stock } & 2,000,000 \
\text { Common stock ( } \$ 10 \text { par) } & 10,000,000 \
\text { Retained earnings } &\underline{ 4,000,000} \
\text { Total debt and equity } & \underline{\$ 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} { l r } 
\text { Long-term debt (bonds, at par) } & \$ 10,000,000 \
\text { Preferred stock } & 2,000,000 \
\text { Common stock ( } \$ 10 \text { par) } & 10,000,000 \
\text { Retained earnings } &\underline{ 4,000,000} \
 \text { Total debt and equity } & \underline{\$ 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

To calculate the current market value of the firm's debt, we need to calculate the present value of the future cash flows from the bonds. 
The bonds have a par value of $10,000,000 (since they were issued at par), and they mature in 10 years. The coupon rate is 4.0% and is payable semiannually. Therefore, each coupon payment is $20 (=$1,000 x 4.0% x 0.5). 
To calculate the present value of the future cash flows, we need to discount each cash flow by the yield to maturity. The yield to maturity is 12%, so the semiannual discount rate is 6%. The total number of coupon payments is 20 (2 payments per year for 10 years), and the final payment is the maturity value of the bond, which is $10,000,000. 
Therefore, the present value of the coupon payments is: 
$20 x [1 - 1/(1+6%)^20] / 6% = $3,571,968.21 
The present value of the maturity value is: 
$10,000,000 / (1+6%)^20 = $2,840,064.12 
The current market value of the bonds is the sum of these two present values: 
$3,571,968.21 + $2,840,064.12 = $6,412,032.33 
So the current market value of the firm's debt is $6,412,032.33. 
That means the right answer is B.

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