Question 16.P.1: Assume a $1,000, 20-year convertible bond that has a contrac...
Assume a $1,000, 20-year convertible bond that has a contractual interest rate of 0.10. Straight debt pays 0.12. The corporate tax rate is 0.46.
The stock price at time of issue is $20. The bond is callable at a price of $1,100 after one year.
(a) If the conversion premium at time of issue is 0.25, the conversion price per share
is ______________. The bond is convertible into _______________ shares.
(b) A zero-tax investor will earn more than 0.12 if the bond is called prior to ______________ years.
(c) Assume that a 0.10 bond is convertible into 25 shares of common stock currently selling at $40 per share. The stock is paying a $3-per-share dividend. The bond is being issued at a price of $1,000.
Would you buy the common stock or the convertible bond, assuming you (an individual) are going to buy one or the other? Explain.
(a) $20(1.25) = $25 conversion price.
\frac{\$1000}{\$25}=40 shares.
(b)
n=\frac{\ln [(Ck_{i}/B(k_{i}-k) )+1 ]}{\ln (1+k_{i} )} =\frac{\ln [(\$100(0.12)/\$20)+1]}{\ln 1.12} =\frac{\ln 1.6}{\ln 1.12}=\frac{0.47}{0.1133}= 4.15 years.The basic formulation is
C(1+k_{i} )^{-n} -B(k_{i}-k ) B (n,k_{i} )=0
(c) Buy the bond. It is at least as good as the common stock costing the same for the same number of shares, plus:
(1) $100 interest > $75 dividend today.
(2) Downside protection.
(3) Same upside potential.