PROBLEM $1$

Badger Company offers its top executives an incentive stock option plan. Under the plan, the company grants $100,000$ options to its top four executives on December $31,2023($in equal amounts$).$ Each option allows the executive to buy one share of the company's $$1$ par value. The options vest on $\frac{12}{31}\frac{?}{2026},$ and they expire six years after the grant date.

The exercise price is the market price of the shares on the date of the grant, $$29$ per share.

Badger chooses to recognize forfeitures in the year they occur$-$i$.$e$.,$ they do not estimate forfeitures on the date of grant.

Using an appropriate option pricing model, the fair value of the $100,000$ options on the grant date is $$500,000.$

The following is information about the market value of Badger's common stock $($through $2027)$:

$\backslash$table$[[$Date$,\frac{12}{31}\frac{?}{2023},\frac{12}{31}\frac{?}{2024},\frac{12}{31}\frac{?}{2025},\frac{12}{31}\frac{?}{2026},\frac{12}{31}\frac{?}{2027}$