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A 10-year convertible bond with a somewhat high (compared to the current market) 7.5% per annum coupon interest rate was issued 5 years ago at par by Company XYZ, a highly-rated bond issuer. It specifies that for each $1000 of par value, the bond-holder can convert any time into 20 shares of XYZ common stock. XYZ common stock is currently trading at around $65 per share. The bond has 5 years remaining to maturity, but is also callable by the issuer at $1025 for each $1000 of par value. The issuer call can be exercised at any time after the next interest coupon payment date, which is 3 weeks away. The issuer has excess cash and has been paying off/retiring other high interest rate debts recently. Given the information in this paragraph only, what is the approximate current market price of the bond, and why?

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    There are SOOO many factors that affect the answer to your question - what is the viability of the issuing company over the remaining life of the bond, how likely is it the issuer will call after the next payment date, what's the attractiveness of XYZ's stock that would make conversion more desirable than holding the bond to maturity for the coupon rate, and so on. This is just stuff off the top of my head, too, and I'm not really a bond guy. – RiverNet Apr 17 at 17:14
  • This sounds like a homework question. Also, it might be better suited for quant.stackexchange.com – 0xFEE1DEAD Apr 19 at 15:56
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Some considerations:

A 10-year convertible bond with a somewhat high (compared to the current market) 7.5% per annum coupon interest rate was issued 5 years ago at par by Company XYZ, a highly-rated bond issuer.

  • high coupon compared to current market means it's likely to be called
  • highly-rated issuer, i.e. unlikely to default

It specifies that for each $1000 of par value, the bond-holder can convert any time into 20 shares of XYZ common stock. XYZ common stock is currently trading at around $65 per share.

could be converted to 20 * $65 = $1,300

The bond has 5 years remaining to maturity, but is also callable by the issuer at $1025 for each $1000 of par value. The issuer call can be exercised at any time after the next interest coupon payment date, which is 3 weeks away. The issuer has excess cash and has been paying off/retiring other high interest rate debts recently.

issuer is likely to call at $1,025

Given the information in this paragraph only, what is the approximate current market price of the bond, and why?

scenarios:

  1. you convert and immediately sell the shares in the market at $65/share
  2. you hold until the next coupon payment ($37.5) and the issuer calls at $1,025
  3. you hold to maturity and get 5 years' worth of coupons + $1,000 principal

To simplify, we can reject scenario #3. This gives you a range for the bond's current price. Until the stock drops below $53.125 ([1,025 + 37.5]/20), the convertible bond is worth whatever the 20 shares are worth, with a floor at $1,025.

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I think the disconnect here is that a company that is highly-rated probably wouldn't be issuing bonds that would pay a rate much beyond treasury yields, because their credit rating would be on a similar par.

Second, it's difficult to give you a price because of other factors that can't be accounted for here - what is the issuer's financial condition now compared to what it was at the time of issue (is the company at greater, lesser, or no different risk of default), what is the history of the issuer calling any of the bonds to this point, what is the size of the issue (how much is still outstanding), what is the current market appetite for corporate bond debt, what other debt instruments are out there for a comparison basis, and so on.

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