Imagine that a start$-$up firm plans to open private dining clubs

on college campuses. The test market will be your campus, and if

the concept proves successful, expansion will follow nationwide.

Nationwide expansion will occur in year $4.$If the firm

expands, it projects opening $20$ dining clubs in year $4$ around the

nation.The start$-$up cost of the test dining club is $$18000($this covers

leaseholder improvements and other expenses for a vacant restaurant

near campus$).$ Assume projected revenues are only sufficient to

exactly cover variable and fixed costs $($excluding depreciation$)$ and

thus the only cashflows over the first $4$ years are tax shields from

depreciation.Also assume that the up$-$front costs can be depreciated in $4$

years in a straight$-$line manner.$$The volatility of the

underlying asset is $30\%$ per annum.$$The interest rate available

is $5\%$ and the tax rate is $34\%.$What is the value of the option

to expand $($keep two decimal places$)?$