Happy Times, Incorporated, wants to expand its party stores into the Southeast. In order to establish an immediate presence in the area, the company is considering the purchase of the privately held Joe's Party Supply. Happy Times currently has debt outstanding with a market value of $$170$ million and a YTM of $6\mathrm{.}5$ percent. The company's market capitalization is $$410$ million and the required return on equity is $13$ percent. Joe's currently has debt outstanding with a market value of $$32$ million. The EBIT for Joe's next year is projected to be $$15$ million. EBIT is expected to grow at $7$ percent per year for the next five years before slowing to $5$ percent in perpetuity. Net working capital, capital spending, and depreciation as a percentage of EBIT are expected to be $6$ percent, $12$ percent, and $5$ percent, respectively. Joe's has $2$ million shares outstanding and the tax rate for both companies is $23$ percent.

a$.$ What is the maximum share price that Happy Times should be willing to pay for Joe's? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ After examining your analysis, the CFO of Happy Times is uncomfortable using the perpetual growth rate in cash flows. Instead, she feels that the terminal value should be estimated using the EV$/$EBITDA multiple. The appropriate EV$/$EBITDA multiple is $11.$ What is your new estimate of the maximum share price for the purchase? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$.$ Maximum share price

b$.$ Maximum share price