Question

1. Smith Corporation issued convertible bonds 5 years ago with an original maturity of 30 years, coupon of 4.5%, and annual payment. They were sold at their par value of $1,000 and with a conversion price of $28.57. Common stock at the time was selling for $14 per share. During the last 5 years, the stock price has not exceeded $22 per share. Straight nonconvertible debentures issued at approximately the same time had a coupon rate of 7.2%. During the next 5 years the stock price is expected to reach $35. What would be the value of the bond alone? What would be the value if the bondholder converts the bond?

Answer 1

a) We need to find the value of the bond alone.

Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the expected value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.

We discount the cashflows at 7.2% p.a

We use the financial calculator:

N = 25 Years

PMT = Coupons = 45 per annum

I/Y = 7.2

FV = 1000

Compute PV we get, 690.94

b) If we plan to convert to equity:
Conversion Ratio= Bond Price / Conversion Price = 1000 / 28.57 = 35

Hence Conversion Value if Price reaches 35 = 35 * 35 = 1225.12

Hence we expect to receive 1225.12 after 5 years plus 5 coupons

Hence we find the PV of cashflows

We use the financial calculator:

N = 5 Years

PMT = Coupons = 45 per annum

I/Y = 7.2

FV = 1225.12

Compute PV we get, 1048.90