XYZ Company is considering its first and only project. This project calls for an investment of $90 million. Suppose the project is expected to generate annual pre-tax cash flows of $13.5 million in perpetuity. We are also given that the corporate profits are taxed at 22.5%, and that if this project were undertaken by an all-equity firm, its cost of capital would be 12.5% (that is, r_ua = 12.5%).

[I]: Work out the after-tax annual cash flow to the unlevered firm, [denoted UCF], and the NPV of the project for the unlevered firm:

[II]: If this project were undertaken by an unlevered firm, what would happen to the market value of the unlevered firm? (In other words, work out the value of the unlevered firm.)

[III]: Suppose the target debt policy is that the equity to debt ratio is 5/3. Work out the target debt to assets ratio (TDA) and the amount of debt that must be raised in order to ensure that the target debt policy is followed.

[IV]: Work out the APV [Adjusted NPV], and V_L [the value of the levered firm] with this amount of debt.

[V]: Assuming that the cost of debt capital is 4.5%, work out r_E, the cost of equity capital.

[VI]: Now, work out r_WACC, the weighted average cost of capital.

[VII]: Discounting the UCF at the weighted average cost of capital, show that you get the same answers for the NPV of the project from the perspective of the levered firm and for the value of the levered firm as you did in [IV] above.