Case $1$: $($Total $36$ points$)$ Your friend Mark has operated a restaurant for several years, and he is considering opening a new one using a place he owns already. Mark asks you to help him in evaluating the proposed project. You are also provided with the following information: $$a$)$ Mark plans to operate the restaurant for $10$ years. $$b$)$ Mark will need to spend $$200,000$ to decorate the restaurant and purchase some equipment. The cost of decoration and equipment will be depreciated on a straight$-$line basis to zero over ten years. At the end, the equipment can be sold at an estimated market price of $$60,000.$c$)$ Mark$$s own place can be leased out to collect $$45,000$ in rent per year if it is not used for the restaurant. $$d$)$ The proposed restaurant will require a $$35,000$ investment in inventory and Mark expects that his accounts payable will rise by $$10,000$ as well. At the end, the working capital will have been completely recovered. $$e$)$ Mark estimates that $15,500$ customers will visit the new restaurant each year. On average, each customer will spend $$25,$ which is almost identical to those of his current restaurant. $$f$)$ The total fixed operating cost, excluding depreciation, is expected to be $$100,000$ each year, and the variable operating cost, excluding depreciation, is expected to be $25\%$ of the sales each year. $$g$)$ Mark paid $$6,000$ to a consultant to collect information for him. $$h$)$ Mark is negotiating with the bank to borrow half of the decoration expenses, and the commercial lending rate of the bank is $7\mathrm{.}5\%.$i$)$ Mark also assumes that the opening of the new restaurant will result in a decrease of sales of his current restaurant by $$21,000$ per year. $$j$)$ The tax rate is $30\%,$ and the project$$s required rate of return is $11\mathrm{.}5\%.$ After getting this information, you need to evaluate the proposed project by addressing the following questions: $1.$Describe the different kinds of cash flows that should be included in the capital budgeting analysis. Use the project to demonstrate. $7$ points $2.$Should Mark open the new restaurant? Why? $14$ points $3.$How sensitive is the project$$s Net Present Value $($NPV$)$ if a$.$ Fixed costs increase by $10\%?3$ points b$.$ Variable costs decrease by $5\%?3$ points