Accounting for convertible zero-coupon bonds

[Roy00]

Hi everyone.

I have been given an assignment on convertible zero-coupon bonds.
I find it quite difficult and I'd like some help.
I hope this is the right place to ask for help on exercises.

The assignment data is taken from a real case.
I quote the text, which is an excerpt from 2009 report of 3M Company:

3M originally sold $639 million in aggregate face amount of these “Convertible Notes” (zero-coupon bonds with maturity 30 years) on November 15, 2002, which are convertible into shares of 3M common stock. The gross proceeds from the offering, to be used for general corporate purposes, were $550 million ($540 million net of issuance costs). Debt issuance costs were amortized on a straight-line basis over a three-year period beginning in November 2002. Debt issue costs allocated to the Notes’ equity component were not material. On February 14, 2003, 3M registered these Convertible Notes in a registration statement filed with the Securities and Exchange Commission. The terms of the Convertible Notes include a yield to maturity of 0.50% and an initial conversion premium of 40 percent over the $65.00 (split-adjusted) closing price of 3M common stock on November 14, 2002. If certain conditions for conversion (relating to the closing common stock prices of 3M exceeding the conversion trigger price for specified periods) are met, holders may convert each of the 30-year zero-coupon senior notes into 9.4602 shares of 3M common stock in any calendar quarter commencing after March 31, 2003.

Question

What journal entry did 3M make when it originally issued the Convertible Notes?
The company follows IFRS as Accounting standard.

My answer

The $639 million of Convertible Notes were issued on November 15, 2002.
Because they are convertible zero-coupon bonds, two facts happens:

• they are necessarily issued at discount;
• there is a share premium because they are convertible.

First of all I compute the present value of the bond.
The market interest rate is given by effective interest rate (or yield to maturity), which is 0.5%.
Therefore, the present value PV of $639 million (the face value) with maturity 30 years is just the discounted face value:

PV = $639 million x (1 + 0.5%)^(-30) = $550 million

which is equal to the gross proceeds that were collected, as expected.

Focusing on the convertible characteristic, the conversion ratio is 9.4602 as stated.
By definition, every Y dollars of Convertible Notes a bondholder receives 9.4602 shares and each share has a conversion price P.
Therefore: Y = P x 9.4602

Given the initial conversion premium of 40% over $65 (the stock price at issuance), we have:

P = stock price at issuance + conversion premium = $65 + $65 x 40% = $91
Y = P x 9.4602 = $91 x 9.4602 = $860.88
Number of notes = Face value / Y = $639 million / $860.88 = 742.265 notes

In the end, the share premium and the bond payable are the following:

Share premium = (Conversion premium) x 9.4602 x (Number of notes)
              = ($65 x 40%) x 9.4602 x (742.265) = $182.57 million

Bond Payable = $639 million – $182.57 million = $456.43 million

Finally, the journal entry is:

Debit Cash                        550
Debit Discount on Bond Payable     89
Credit Bond Payable                      456.43
Credit Share Premium                     182.57

My doubts

I don't know if it is correct. In particulare, I have doubts regarding:

• the value of X (which is the value of a note, or equally the value of 9.4602 shares when conversion is exercised);
• the absence of the debt issuance costs in the journal entry. Moreover, I thought that these costs had to be divided in proportional part to both Bonds Payable and Share Premium and I can't also see this fact.

Sorry for the long post/exercise. I hope you will time to help me.

Thank you really a lot, in advance.

Roy00