Yesterday Dexter’s Laboratory paid a dividend of $4.20 a share on its common sto
ID: 2651641 • Letter: Y
Question
Yesterday Dexter’s Laboratory paid a dividend of $4.20 a share on its common stock. The firm’s
earnings and dividends are expected to grow indefinitely at 5%, and the market requires a 15%
rate of return on Dexter’s common stock. Ten years ago you purchased a convertible debenture
of Dexter’s Lab. At that time, the bond had 20 years left to maturity and its yield to maturity was
12% a year, compounded semi-annually. The $1,000 par value bond pays an annual coupon of
14%, compounded semi-annually. The bond is convertible into Dexter’s common stock at a
conversion price of $25 a share.
{a} What price did you pay for the bond?
{b} What annual internal rate of return did you earn over the last 10 years if you convert the bond
today?
{c} What annual rate of return did you earn over the last 10 years if, instead of converting, you
surrender the bond when it is called today at $1,090?
Explanation / Answer
a) Price to be paid for the bond= 70x 15.05(Compounded PV at 6% for 40 years)+ 1000x .097
= 1053.5 + 97 = 1150.5
b) Conversion price of bond is $25/share
Conversion ratio = 1000/25 = 40, Market price per share= 4.2/.15-.05= Rs.42
Conversion premium= Bond price-(Conversion ratio x market price per share)
= 1150.5- (42x40)= -529.5
If the bond price is selling for less than parity, then this creates an arbitrage opportunity, which is the buying and selling of the same or derived securities to profit from a price discrepancy among the different securities. In this case, if the bond is selling for less than the stock price × conversion factor, then an arbitrageur can make money immediately by selling the stock short, and buying the bond. The stock is sold short because the conversion takes time, and if the arbitrageur waited, the price of the stock might decline. Then the arbitrageur simply converts the bond into shares of stock to cover the short.
Rate of return = 529.5/1150.5x100= 46%
c) Annual internal rate of return = 1090-1000/1000x100= 9%
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