Question

A convertible bond is selling for $800. It has 10 years to maturity, a $1000 face value, and a 10% coupon paid semi-annually. Similar nonconvertible bonds are priced to yield 14%. The conversion price is $50 per share. The stock currently sells for $31.375 per share. Determine the bond's option value.

Answer 1

Option value is premium paid to the convertable bond over non convertable bond

1) calculation of bonds straight Value

Value of bond will be present value of cashflows

Face value = 1000

Per period coupon rate =10/2 = 5%

No of periods till maturity = 10×2 = 20

Discount rate is 14% per period is 7%

Value is

50(PVIFA 7% 20P) + 1000(pvif 7% 20p)

= 50(10.594) +1000(0.2584)

Straight Value of bond is = 788.1

But market value of bond is 800

So option value is (800-788.1)= 11.9(for bond)