Jupiter Corp., an all$-$equity firm is considering a $$3\mathrm{.}0$ million investment that will be depreciated according to the straight$-$line method over its six$-$year life. The project is expected to generate additional revenue of $$1,000,000$ per year for six years along with cash expenses of $$400,000$ per year. The investment will not change the risk level of the firm. The corporate tax rate is $30\%$ and the firm$$s current cost of equity is $12\%.$

a$)$ Write out the equation for the APV of this all equity financed project. You do not have to solve for the APV value, just identify all of the annual cash flows along with the appropriate discount factors $($PVIFA or PVIF$).$

b$)$ The company can obtain a six$-$year, $8\%$ annual interest loan to finance the project. All principal will be repaid in one balloon payment at the end of the sixth year. Using the APV method, describe all of the financing effect cash flows associated with the analyzing the decision. There are no floatation costs associated with the financing. Please create one equation to represent the value of the unlevered project and another equation representing the value of the financing effects.