Question

A convertible bond pays interest annually at a coupon rate of 5% on a par value of $1,000. The bond has 10 years maturity remaining and the discount rate on otherwise identical non-convertible debt is 6.5%. The bond is convertible into shares of common stock at a conversion price of $25 per share (i.e. the bond is exchangeable for 40 shares). Today's closing stock price was $20. What is the floor value of this bond?

Answer 1

straight bond value =

present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 6.5% , 10 years)

PVIFA( 6.5% , 10 years) = present value interest rate factor of annuity

= [((1+YTM)ⁿ - 1)/((1+YTM)ⁿ*YTM)] = [((1.065)¹⁰ - 1)/((1.065)¹⁰*0.065)] = 7.18883022

Present value(PV) of coupons = C*PVIFA( 6.5% , 10 years) = 50*7.18883022 = 359.44151114

PV of maturity amount = par value/(1+YTM)ⁿ = 1000/(1.065)¹⁰ = 532.72603552

Straight Debt Value = 359.44151114 + 532.72603552 = $892.167546 or $892.17

conversion value = today's closing stock price*no. of shares to be received after conversion = 20*40 = $800

since straight debt value > conversion value

floor value = straight debt value = $892.17