Sienna Company developed a specialized banking application software program that it licenses to various financial institutions through multiple$-$year agreements. On January $1,2021,$ these licensing agreements have a fair value of $$752,500$ and represent Sienna's sole asset. Although Sienna currently has no liabilities, the company has a $$205,000$ net operating loss $($NOL$)$ carry$-$forward because of recent operating losses.

On January $1,2021,$ Paoli, Inc., acquired all of Sienna's voting stock for $$960,000.$ Paoli expects to extract operating synergies by integrating Sienna's software into its own products. Paoli also hopes that Sienna will be able to receive a future tax reduction from its NOL. Assume an applicable federal income tax rate of $21$ percent.

If there is a greater than $50$ percent chance that the subsidiary will be able to utilize the NOL carry$-$forward, how much goodwill should Paoli recognize from the acquisition?

If there is a less than $50$ percent chance that the subsidiary will be able to utilize the NOL carry$-$forward, how much goodwill should Paoli recognize from the acquisition?