Shimano Industries has come up with a new mountain bike prototype and is ready to go ahead with pilot production and test marketing. The pilot production and test marketing phase will last for one year and cost $500,000 (at t=0). Your management team believes that there is a 50% chance that the test marketing will be successful and that there will be sufficient demand for the new mountain bike. If the test-marketing phase is successful, then Shimano Industries will invest $3 million in year one (t=1) to build a plant that will generate expected annual after-tax cash flows of $400,000 in perpetuity beginning in year two (t=2,3,4,). If the test marketing is not successful, Shimano can still go ahead and build the new plant, but the expected annual after-tax cash flows would be only $200,000 in perpetuity beginning in year two (t=2,3,4,). Shimano has the option to stop the project at any time and sell the prototype mountain bike to an overseas competitor for $300,000. Shimano's cost of capital is 10%. a) What is the NPV of the Shimano Industries Mountain Bike Project assuming that Shimano can sell the prototype in year one for $300,000. What decision would Shimano have to make? (9 marks) b) What is the NPV if Shimano does not have the ability to sell the prototype in year one for $300,000. What is the type of real option we are dealing with here? (5 marks) c) Shimano decides to ignore the pilot production and test marketing and goes ahead with building their $3 million manufacturing plant immediately (t=0) with the probability of high or low demand still being 50% each. What is the value of this option to build the plant immediately and ignore the pilot production and test marketing? (6 marks