Sienna Company developed a specialized banking application software program that jt licenses to various financial institutions through multiple$-$year agreements. On January $1,2024,$ these licensing agreements have a fair value of $$915,000$ and represent Sienna's sole asset. Although Sienna currently has no liabilities, the company has a $$140,000$ net operating loss $($NOL$)$ carry$-$forward because of recent operating losses.

On January $1,2024,$ Paoli, Incorporated, acquired all of Sienna's voting stock for $$1,115,000.$ 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 afuture tax reduction from its Net Operating Loss. Assume an applicable federal income tax rate of $21$ percent.

Required:

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

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

$\backslash$table$[[,$Amount$],[$a$.$ Goodwill,$],[$b$.$ Goodwill,$]]$