Investments, tenth edition

A

Conversion Value

Stock Price

B

Convertible Bond Value

Straight Debt

Conversion Value

Convertible Bond Value

Stock Price

C

 Figure 20.12 

Value of a convertible bond as a function of stock price.  Panel A,  

Straight debt value, or bond floor.  Panel B,  Conversion value of the bond. 

Panel C,  Total value of convertible bond.  

Bond A

Bond B

Annual coupon

$80

$80

Maturity date

10 years

10 years

Quality rating

Baa

Baa

Conversion ratio

20

25

Stock price

$30

$50

Conversion value

$600

$1,250

Market yield on 10-year Baa-rated bonds

8.5%

8.5%

Value as straight debt

$967

$967

Actual bond price

$972

$1,255

Reported yield to maturity

8.42%

4.76%

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P A R T   V I

  Options, Futures, and Other Derivatives

 Bond   A  has a conversion value of only $600. Its value as straight debt, in contrast, is 

$967. This is the present value of the coupon and principal payments at a market rate for 

straight debt of 8.5%. The bond’s price is $972, so the premium over straight bond value is 

only $5, reflecting the low probability of conversion. Its reported yield to maturity based 

on scheduled coupon payments and the market price of $972 is 8.42%, close to that of 

straight debt. 

 The conversion option on bond  B  is in the money. Conversion value is $1,250, and the 

bond’s price, $1,255, reflects its value as equity (plus $5 for the protection the bond offers 

against stock price declines). The bond’s reported yield is 4.76%, far below the compa-

rable yield on straight debt. The big yield sacrifice is attributable to the far greater value of 

the conversion option. 

 In theory, we could value convertible bonds by treating them as straight debt plus call 

options. In practice, however, this approach is often impractical for several reasons:

    1.  The conversion price frequently increases over time, which means the exercise 

price of the option changes.  

   2.  Stocks may pay several dividends over the life of the bond, further complicating the 

option-valuation analysis.  

   3.  Most convertibles also are callable at the discretion of the firm. In essence, both 

the investor and the issuer hold options on each other. If the issuer exercises its 

call option to repurchase the bond, the bondholders typically have a month during 

which they still can convert. When issuers use a call option, knowing bondholders 

will choose to convert, the issuer is said to have  forced a conversion.   These  condi-

tions together mean the actual maturity of the bond is indeterminate.