On January $1,20$X$1,$ when its $$30$ par value common stock was selling for $$80$ per share, Gierach Corporation issued $$10$ million of $4\%$ convertible debentures due in $10$ years. The conversion option allowed the holder of each $$1,000$ bond to convert the bond into five shares of the company$$s $$30$ par value common stock. Cash settlement upon conversion is not permitted. The debentures were issued for $$10$ million. Without the conversion feature, the bonds would have been issued for $$8\mathrm{.}5$ million.

On January $1,20$X$3,$ the company$$s $$30$ par value common stock was split three for one. On January $1,20$X$4,$ when the company$$s $$10$ par value common stock was selling for $$90$ per share, holders of $40\%$ of the convertible debentures exercised their conversion options.

Required:

Following U$.$S$.$ GAAP, prepare a journal entry to record the original issuance of the convertible debentures.

How much interest expense would the company recognize on the convertible debentures in $20$X$1?$

Prepare a journal entry to record the exercise of the conversion option using the book value method.

Prepare the entry to record the exercise of the conversion option using the market$-$value method.