Question

Fifteen years ago, Roop Industries sold $400 million of convertible bonds. The bonds had a 40-year maturity, a 5.75% coupon rate, and paid interest annually. They were sold at their $1,000 par value. The conversion price was set at $61.20, and the common stock price was $54 per share. The bonds were subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.30% at the time Roop's bonds were issued.

Now suppose that the price of Roop's common stock had fallen from $54 on the day the bonds were issued to $32.50 at present, 15 years after the issue. Suppose also that the interest rate on similar straight debt had fallen from 8.30% to 5.75%. Under these conditions, what is the current price of the straight-bond portion of the convertible bond? Do not round intermediate calculations. Round your answer to the nearest dollar. Enter all amounts as a positive number.

$   per bond

What is the current value if a bondholder converts a bond? Do not round intermediate calculations. Round your answer to the nearest cent.

$   per share

Answer 1

In the above question we need to calculate two things basically: -

· What is the Current price of the straight-bond portion of the convertible bond?

· What is the current value if a bondholder converts a bond?

Let’s have a look at the solution: -

a) Current price of the straight-bond portion of the convertible bond

Put the following in a financial calculator:

FV = 1,000;

N = 40-15 (Time lapsed since issue) = 25 (Time left in the maturity of bond);

PMT = 57.5;

Discount rate = 8.30%,

solve for PV. (By using the Compute function)

Price = 734.62 = 735 (approx.) (Ignore the negative sign in the financial calculator)

b) Current value if bond is converted:

Conversion ratio = par value of bond/conversion price = 1,000/61.20 = 16.34 shares

Current value = number of shares*current share price = 16.34*32.5 = 531.05 = 531 (approx.)

As we can see from the above calculation, the bond is worth more than the converted price i.e. 735>531, so the bond will not be converted.