Please explain step by step how to solve these problems.

The San Francisco Yacht Company (SFYC), a prominent sailboat builder in San Francisco, is considering developing and marketing a new line of personal sailboards whose design would be based on the winged keel technology it developed for use in its 12-meter Americas Cup racing yachts. The new sailboard line would be positioned for the upscale personal recreation market. The project requires an initial investment of $20 million for development and production costs. The success of the project depends highly on whether its sister-product, the 12-meter racing yacht, is successful in its Americas Cup bid. If the racing yacht is successful and wins the Americas Cup (30% probability) then the positive press for the company will boost demand for the sailboard line, and annual cash after-tax cash flows will be $15 million per year for 3 years. If the yacht is successful, but does not win the Americas cup (40% probability) then after-tax cash flows will be $8 million per year for 3 years. If the yacht performs badly (30% probability) then the after-tax cash flows will be only $1 million per year for 3 years. SFYCs cost of capital is 10%.

Part a) What is the expected NPV of the project?

Part b) Because SFYC owns the winged keel patent, it can wait until after the Americas Cup results are known (one year from now) before undertaking the sailboard project. If it waits, the initial investment will be the same, and SFYC will know which series of cash flows it will receive. The advantage of waiting is that SFYC will know if the bad state of the world, in which the yacht performed badly, has occurred and can choose not to invest if that occurs. Use a decision tree analysis to find the expected net present value of this investment timing decision assuming SFYC delays adopting the project, and only adopts it in the states of the world where the outcome is favorable - that is, it only adopts the project if the NPV of that branch is positive. Assume that the initial investment in Year 1, if the project is undertaken, is known with certainty and is discounted at the risk free rate of 6%.

Part c) Instead of using a decision tree analysis, use the Black-Scholes Option Pricing Model to analyze this investment timing option. Assume the variance of the projects returns is ² = 0.45. Hint: One of the inputs to the model is P, the value of the asset underlying the project. Remember that P is the expected present value of the projects cash flows when you include both the good cash flows and the bad cash flows, but dont include the initial investment.