Blue Lakes is considering a new project. The investment cost of $$180$ million will be depreciated straight line over the next $20$ years. Part of the cost will be financed with a new bond issue. Blue Lakes will issue for $$120$ million a bond with a face value of $$120$ million and $20$ annual coupon payments equal to $5\%$ of face value. In addition to the coupons, the debt obligation calls for payment of the face value of $$120$ million at year $20.$ The project generates EBIT with an expected value of $$20$ million for the next $20$ years. The debt obligation will be fulfilled with probability $1,$ implying that the interest expense deductions associated with the tax$-$shield on the new debt have a zero covariance with the return on the market. The EBIT varies with the market, with the implied unlevered asset beta of $1\mathrm{.}2.$ The expected return on the market is $12\%$ and the risk$-$free rate is $6\%.$ The corporate tax rate is $25\%.$ The CFO asks you to evaluate the project using APV.

a$)$ What is the Cash Flow estimate for the next $20$ years? $($use EBIT and CF formula$)$

b$)$ What is the value of Blue Lake as an unlevered firm? Do not include the initial investment cost.

c$)$ What is the value of its expected tax shield?

d$)$ What is the Blue Lake's value with the tax shield?

e$)$ Is this project a go$?$ Compute the NPV