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$($Cash$-$flow analysis$)$ Poseidon is considering opening a shipping line from Athens to Rhodes. In order to open the shipping line, Poseidon will have to purchase two ships that cost $1,000$ gold coins each. The life span of each ship is $10$ years, and Poseidon estimates that each ship will earn $300$ gold coins in the first year and that the earnings will increase by $5\%$ per year. The annual costs of the shipping line are estimated at $60$ gold coins annually, Poseidon's interest rate is $8\%,$ and he is charged by Zeus a tax rate of $50\%.$ Depreciation is not an expense for tax purposes.

a$.$ Will the shipping line be profitable?

b$.$ Due to Poseidon's good connections on Olympus, he can get a tax reduction. What is the maximum tax rate at which the project will be profitable?