As part of its stock$-$based compensation package, International Electronics granted $22$ million stock appreciation rights $($SARs$)$ to top officers on January $1,2024.$

At exercise, holders of the SARs are entitled to receive cash or stock equal in value to the excess of the market price at exercise over the share price at the date of grant.

The SARs cannot be exercised until the end of $2027($vesting date$)$ and expire at the end of $2029.$

The $$1$ par common shares have a market price of $$66$ per share on the grant date.

The fair value of the SARs, estimated by an appropriate option pricing model, is $$5\mathrm{.}50$ per SAR at January $1,2024.$

The fair value re$-$estimated at December $31,2024,2025,2026,2027,$ and $2028,$ is $$6\mathrm{.}50,$$$5\mathrm{.}50,$$$6,$$$2\mathrm{.}00,$ and $$3\mathrm{.}50,$ respectively.

All recipients are expected to remain employed through the vesting date.

Required:

to $3.$ Prepare the appropriate journal entries pertaining to the SARs on January $1,2024$ and December $31,2024-$December $31,2027.$ The SARs remain unexercised on December $31,2028,$ prepare the appropriate entry.

The SARs are exercised on June $6,2029,$ when the share price is $$70,$ and executives choose to receive the market price appreciation in cash. Prepare the appropriate journal entry$($s$)$ on that date.