CMS Corporation's balance sheet as of today is as follows:
Long-term debt (bonds,at par)
$10,000,000
Preferred stock
2,000,000
Common stock ($10 par)
10,000,000
Retained earnings
4,000,000
Total debt and equity
$26,000,000
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

Quizplus · Accepted Answer

To calculate the current market value of the bond you need to use the present value formula:
PV = C/(1 + r/2)^(2*t) + C/(1 + r/2)^((2*t)-1)+ ......+ C+ M/(1 + r/2)^(2*t)

Where:
Pv = present value of bond
C= coupon payment
r= required rate of return
t= time to maturity in years
M= par value

In this case,
Coupon payment (C) = 4% of par value = $40
Required rate of return (r) = YTM = 12%
Time to maturity (t) = 10 years
Par value (M) = $1,000

Using the formula above, the present value of the bond can be calculated as:
PV = 40/(1+0.06)^1 + 40/(1+0.06)^2 + ... + 40/ (1+0.06)^20 + 1,000/(1+0.06)^20 = $5,412,032

Therefore, the current market value of the firm's debt is $5,412,032.

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