A convertible bond has the following features (rounding allowed in answers): Fac

Question

A convertible bond has the following features (rounding allowed in answers):

Face Value: $1,000

Maturity: 10 years

Annual coupon: $80

Call Price: $1,100

Conversion Price: $50

I. The bond may be converted into how many shares?

II. What is the current value of the convertible as a bond if prevailing interest rates are 9%?

III. What is the current value of the convertible as a stock if the current stock price is $45 per share?

IV. Based on (II) and (III) and assuming a market premium of $50, what should the current price of the bond be?

V. Above, in question IV, if the prevailing interest declines to 7% and all else stays the same, should you sell the bond or hold it? Justify your answer.

Explanation / Answer

1) The number of shares to be converted = Face value / Conversion price

                                                                  = $1,000 / $50 =20

2) Use the excel PV formula to find the current value:

PMT = -$80; FV = -$1000, Rate = 9%, Nper = 10yrs

PV = (Rate, Nper, PMT, FV) = (9%, 10, -80, -1000) = $935.82

3) Total value of the convertible = $45 X 20 = $900

4) The current value of the bond should be( $935.82 + $50 ) = $985.82

     The current value of the stock should be ($900 + $50) = $950

5) Use the excel PV formula to find the current value:

PMT = -$80; FV = -$1000, Rate = 7%, Nper = 10yrs

PV = (Rate, Nper, PMT, FV) = (7%, 10, -80, -1000) = $1,070.24

here, the bond current price is more than the face value, hence the bond should be sold instead of holding.

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