Please refer to $"01$:$10$:$30$ Valuing a start$-$up$"$ in this module's lecture recording for

illustration.

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 $$13000($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$)?$