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 7.5% 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. $7,420,400

b. $7,418,701

c. $7,420,967

d. $7,419,834

e. $7,419,268

Answer 1

Solution :-

Par Value of Stock = $1,000

Semiannual Coupon Amount = $1,000 * 7.5% * 6 / 12 = $37.50

Total Semiannual Period = 10 * 2 = 20

Semiannual Yield = 12% / 2 = 6%

Now Price of Bond = $37.50 * PVAF ( 6% , 20 ) + $1,000 * PVF ( 6% , 20 )

= ( $37.50 * 11.47 ) + ( $1,000 * 0.3118 )

= $430.12 + $311.80

= $741.9267

Now Par Value of Long term debt = $10,000,000

Now the current market value of the firm's debt = $10,000,000 * $741.9267 / $1,000

= $7,419,268

Therefore Correct Answer is (E)

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