Question

Wilma is considering opening a widget factory. The unlevered cost of equity for making widgets is 0.10. This factory would cost $10 million to set up, and would produce EBIT of $3 million per year for the foreseeable future. She is thinking of applying for a $3 million subsidized perpetual loan to finance this project. Complying with the auditing requirements of this loan would have a present value of $2 million. This loan would have a rate of 0.04, while the rate she could get from the bank is 0.07. Her tax rate is 0.41. What is the NPV of this project, using the APV method?

Answer 1

Unlevered Cost of Equity = 0.1 or 10% , Initial Investment = $ 10 million, Expected Perpetual EBIT = $ 3 million, Planned Perpetual Loan = $ 3 million, PV of Compliance = $ 2 million, Cost of Debt (Loan Rate) = 0.04 or 4 % and Bank Interest Rate = 0.07 or 7 %

Tax Rate = 0.41 or 41 %

Interest Expense on Perpetual Debt = Bank Interest Rate x Debt = 3 x 0.07 = $ 0.21 million

Interest Tax Shield = 0.41 x 0.21 = $ 0.0861 million

PV of Interest Tax Shield = 0.0861 / Cost of debt = 0.0861 / 0.04 = $ 2.1525 million

Unlevered PV of Perpetual Free Cash Flows = EBIT x (1-Tax Rate) / Unlevered Cost of Equity = 3 x (1-0.41) / 0.1 = $ 17.7 million

Value of Project = 17.7 + 2.1525 = $ 19.8525 million

PV of Compliance = $ 2 million

Total Value of Project = 19.8525 + 2 = $ 21.8525 million

Project NPV = 21.8525 - 10 = $ 11.8525 million