You successfully graduated from TSM and find a job in Toulouse with salary of $3000$ euros after tax. After several years of work you have some savings $(50000$ euros$)$ and you are thinking about open up a small firm of your own now. Here is the relevant information:

$1)$ Your salary now is $3000$ euros per month and is expected to raise by $3\%$ every year.

$2)$ The new firms you plan to establish are estimated to cost roughly $200000$ euros, and you believe you can get a loan from BNP Paribas to finance the remaining $150000$ euros. After contacting with BNP Paribas, they offer you with a $20-$year loan at $5\%($annual rate$).$ The loan is equally paid every month and the interest rate is fixed once the contract is signed.

$3)$ After carefully investigate the market, you believe you can make a relatively precise estimation on your sales. For each month, your firm$$s revenue would be $100000$ euros with a gross profit margin of $20\%.$ Your gross profit per month is estimated to be $20000$ euros. Each month your firm will incur a fixed cost of $15000$ euros $($Salaries$,$ supplies, electricity and etc.$).$ Here, we suppose no corporate tax is taxed on your firm, all remaining profit from firm$$s operation goes directly to you.

$4)$ Your $200000$ euros investment are used to buy equipment and machines, which will gradually depreciate over years. You expect the value of your equipment and machines decrease by $5\%$ each year. That$$s to say, after $20$ years, all your machines and equipment can$$t be sold out for any money. If you sell it after one year, you can get $95\%$ of the original value. After $2$ years you get $90\%.$

a$)$ Suppose you plan to run your firm for $15$ years and then sell all your machines and equipment. Solve your entrepreneurship vs$.$ employment problem. Which option gives you higher return here, continue working or opening your own firm? $(4$pts$)$

b$)$ Do a scenario analysis to see what your choice will be if you plan to run your firm for

$-5$ years.

$-20$ years $(3$pts$)$

c$)$ Describe the possible qualitative considerations that may affect your decision on employment versus entrepreneurship.