$1.$ A company borrowed $41,500,000$ TL annually for $10$ years with an annual capital cost of $45\%$ for investment. With the investment made, $1800,000$ units will be produced annually. After the production amount remains constant for the first $10$ years, it will decrease by $2\mathrm{.}25\%$ annually for the second $10$ years. The product will be sold at a price of $20$ TL $/$ Piece. The annual price escalation of the sales price is expected to be $30\%$ for the first $10$ years and $22\%$ for the remaining years. $1$ for one product kg of raw material will be used. The price of the raw material is $2\mathrm{.}2$ TL$/$kg$.$ The annual escalation of the raw material price for the first $10$ years is $45\%$ and the second $10$ years is $20\%.$ A total of $100$ kW electrical power will be consumed in the production system. The company will work $(5,700)$ hours per year. The electricity price is $5$ TL $/$kWh$.$ It is estimated that the electricity price escalation will be $42\%$ annually for the first $5$ years, $35\%$ for the second $5$ years and $20\%$ for the remaining period. $10$ personnel will work in the production system. The average monthly cost of one personnel is $15,000$ TL and the annual escalation is $35\%.$ Major maintenance costs will be incurred every $5$ years. The cost to be incurred in the $5$th year is $5,000,000$ TL$.$ The $5-$year escalation of this cost is $200\%.$ Accordingly;

a$)$ Determine the annual effective value of the cost of capital and the present value of the investment cost.

b$)$ Find the raw material, electricity, labor and income values in the first year.

c$)$ Compound escalation of income and raw material cost that will be valid for the second ten years.

Calculate.

d$)$ Create a cash flow table including investment cost, raw materials, electricity, labor, maintenance and income.

e$)$ Determine whether the investment is economically viable by using the Payback Rate method.