Answer to Question #131459 in Financial Math for agnes

Question

Recently, Midrand Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required annual return is 20 percent, what should the bonds sell for in the market today?

Answer 1

solution

Let the face value of the bond be 1000

years to maturity, $n=10$

Coupon rate, $c=10$ %

Interest payable from year 6 to 10

$=0.1*1000=100$ per year for 5 years.

Redemption amount is the sum of the interest that was supposed to be paid from year 1 to 5 and the face value

Deffered interest payments

$$=0.1*1000*5=500$$

Total redemption amount

$$=1000+500=1500$$

Price of the bond

$$Price=coupons*\frac{1-(1+i)^{-n}}{i}+\frac{redemption}{(1+i)^{n}}$$

The value of the bond at the beginning of year 5, the year when interest payments begin

$$Price=100*\frac{1-(1+0.2)^{-5}}{0.2}+\frac{1500}{(1+0.2)^{5}}$$

$$=901.8776$$

The selling price of the bond today should be

$$=\frac{901.8776}{(1.2)^5} =362.4444$$

answer: assuming the bond has a face value of 1000, it's current price should be 362.44