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CMS Corporation's balance sheet as of today is as follows: Long-term debt (bonds, at par) $10,000,000...

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 an 4.6% 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?

Select the correct answer. a. $5,756,129

b. $5,756,973

c. $5,755,285

d. $5,754,441

e. $5,753,597

Solutions

Expert Solution

Answer is a. $5,756129

This question requires us to calculate the current value of bond. Current value or market price of bond is basically the present value of all cashflows associated with the bond – namely coupon and maturity value, discounted at market interest rate (or YTM).

In this question, we need to calculate the price of bond, with given characteristics.

The balance sheet has $10,000,000 recorded as long term debt and each bond has a face value of $1,000. So, number of bonds outstanding = 10,000,000/1,000 = 10,000

Let us calculate the price of a single bond first, and then we can calculate the price of total bonds outstanding. Mathematical relation for finding price of a bond is as given below:

Where M is the maturity value ($1000 in our case)

i is the YTM (12% annually -- > 6% semi-annually)

C is the coupon paid (4.6% annually -- > 2.3% semi-annually. Hence $1000 * 2.3% = $23 per semi-annual period)

N is the number of periods to maturity (10 years -- > 20 semi-annual periods)

Substituting these values in mathematical relation above, we get:

P = 23 * 11.46992 + 311.804727

P = 263.808188 + 311.804727

Hence, price of 1 bond = $575.612915

Price of 10,000 bonds = $5,756,129.15 (Market value of debt)

jeff jeffy answered 1 year ago
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