(20 points) Alex is thinking to open a restaurant. There are two kinds of uncertainty. One is macroeconomic uncertainty. The other is restaurant (net) sale uncertainty. Macroeconomic uncertainty exists only between F0 and t:1_ Once a macroeconomic environment is determined at t=1, it will be kept same afterwards .Restaurant sale uncertainty always exists no matter when he opens the restaurant. If he decides to open a restaurant at a certain point of time, first sale will be realized after 1 year and sale amount will be same every year. Once he opens the restaurant, he cannot close it. He should run the restaurant forever .Current time is t:0. There is 50% chance that macroeconomic environment is positive (negative ) at t:1. If macroeconomic environment is positive, there is 70% probability that sale is 200 every year and 30% probability that sale is 100. If macroeconomic environment is negative, there is 30% probability that sale is 170 and 70% probability that sale is 70. Rent is 110 and occurs at the end of every year _ So, the first rent is at the end of year he decides to open the restaurant .There is an interior design cost which is 400. It happens at the beginning of year when he decides to open the restaurant. For example, if he opens the restaurant at t, first sale and first rent will occur at t+1 but interior design cost occurs at t. Discount rate is 5%. Part (c) ~ (g) are independent from each other . "Original setting" in part (c) ~ (g) means the setting written until this point. (a) (2 points )What is NPV of the restaurant if he opens it t:[)? (b) (3 points) Suppose he waits for 1 year so that macroeconomic uncertainty is resolved and opens the restaurant at t=1. What is NPV in this case ? Would he open the restaurant at t=1 if macroeconomic environment is good? Would he open the restaurant at P1 if macroeconomic environment is bad? Would he prefer open the restaurant at t=0 or t=1? (c) (3 points )Suppose that landlord decided to increase the rent to 140 if Alex waits 1 period and opens the restaurant at t:1. All other conditions are same with the original setting. In this case , what is NPV of the restaurant ? Would he prefer open the restaurant at t=0 or t=1? What is the maximum rent Alex is willing to pay to open the restaurant at t:l rather than to open it at t:0? (d) (3 points) Suppose that interior designer decided to increase the design fee to 800 if Alex opens the restaurant at t:1. All other conditions are same with the original . What is NPV if Alex opens the restaurant at F1 in this case ? Would he prefer open the restaurant at t:0 or t:1? What is the maximum interior design cost Alex is willing to pay to open the restaurant at t:1 rather than to open it at t:0? (e) (3 points) Suppose that Alex can close the restaurant at t:1 if he opens the restaurant at t:0 (if he opens the restaurant at F0 and closes at t:1, first sale and rent will occur at t:1 but not from t:2 and onward). All other conditions are same with the original setting. What is NPV if he opens the restaurant at t:0 with this option to close at t:1? (f) (3 points) Suppose that Alex can close the restaurant at t:1 but now rent is 140. All other conditions are same with the original setting .What is NPV if he opens the restaurant at F0 in this case? Suppose he can open the restaurant only at t:0. What is the maximum rent he is willing to pay with the option of closing it at t:1? (g) (3 points) Suppose that Alex can expand the restaurant at t:1 by twice if he opens it at t:0. Then , sale will be twice .lnstead , rent increases from 110 to 200. (rent of 110 is charged for F1, but from t:2, rent is 200 ). And , additional interior design cost for expansion of 100 occurs at t=1. All other conditions are same with the original setting. What is NPV if Alex opens the restaurant at t:0 with this expansion option