Meta Platforms, Inc. $($formerly Facebook, Inc.$)$ had $$18\mathrm{.}385$bn of debt on its balance sheet as of end of $2023,$ it paid $($a$)$ $$0\mathrm{.}446$ billion in interest on its debt and $($b$)$ $$8\mathrm{.}33$ billion in taxes. Suppose Facebook were to issue sufficient debt to reduce its taxes by $$250$ million per year permanently. Assume Facebook's marginal corporate tax rate is $17\mathrm{.}56\%$ and its borrowing cost $($on new debt$)$ is $5\%.$

a$.$ How much of new debt would Meta Platforms need to issue?

b$.$ What is the value of the interest tax shield arising from new debt?