Question

1. Chico Samu and Doudou Lukusa would like Me. Djuma to accurately assess the capital structure of their firm because they want to convert their balance sheet figures from historical book values to market values. Their balance sheet (book values) as of today is as follows:

Long-term debt (bonds, at par)	$30,000,000
Preferred stock	3,000,000
Common stock ($10 par)	15,000,000
Retained earnings	2,000,000
Total debt and equity	$50,000,000

The bonds have a 7.0% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 15 years from today. The yield to maturity is 12%, so the bonds now sell below par. What is the current market value of Chico and Doudou’s debt?

Answer 1

Formula for YTM (Yield to Maturity):

(C+( FV-P)/t) / (FV+ P)/2

Where,

• C – Interest/coupon payment
• FV – Face value of the bond
• P – price of the bond
• t – no. of years till maturity

As per the question, let the current market price of bond be P

Coupon= 1000*0.07/2 (since, semiannual payments)

t= 15 yrs*2= 30 periods (semiannual payments)

   (C+( FV-P)/t) / (FV+ P)/2 = 0.12

(35 + (1000-P)/ 30) / (1000+P)/2 = 0.12

   (35 + (1000-P)/ 30) = 0.06* (1000+P)

Solving for P in the equation, we get, P= 89.29/ bond (approx)

hence, Market value of debt today= No. of bonds outstanding*price= (30,000,000/1000) * 89.29 = $ 26,78,700