Question

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

Answer 1

$5,412,000

Step-by-step explanation:

Given:

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

Coupon rate = 4%(semi annually)

Par value = $1000

YTM = 12%

Required:

Find the current market value of the firm's debt.

Find the bond price:

Bond price
`= (C * ((1 - ((1)/((1+i)^n)))/(i)) + ((m)/((1+i)^n))`

`= (C * ((1 - ((1)/((1+0.06)^2^0)))/(0.06)) + ((1000)/((1+0.06)^2^0))`

`= 541.20`

Bond price = $541.20

Find number of bonds:

Number of bonds
`= (10,000,000)/(1,000) = 10,000`

Now, to find the current market value of the firm's debt, use:

Current market value of debt = number of bonds × bond price

= 10,000 × 541.20

= $5,412,000

Current market value of the firm's debt = $5,412,000