Yesterday Dexter’s Laboratory paid a dividend of $4.20 a share on its common sto
ID: 2651591 • 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
The answer is computed as follows:
Compute the current price of the share.
Price of the stock = Dividend / (Rate of return - growth) = 4.20 / (0.15-0.05) = 4.20 / 0.10 = $42.
Number of shares issued on conversion = Face value of the bond / Conversion price = $1,000 / $25 = 40 shares.
a.
Price to be paid for the bond = 40 shares * $42 = $1,680.
b.
Compute the annual return earned over the last 10 years if the bond is converted today.
The purchase price of the bond before 10 years = PV(0.06,40,-70,1000) = 1,150.
Current price of the bond = 1680
Capital gain = ($1,680-$1,150)/10 = $530/10 = $53
Total Return = Interest + Capital Gain = $140 +$53 = $193.
Annual internal rate of return = $193/1000 = 19.3%.
c.
Capital Loss = $1,090-$1,1150 = -$60/10 = -$6
Total annual return = Interest + Capital gain = $140 -$6 = $134.
Annual rate of return = $134/1000 = $13.4%.
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