Question

Suppose that XYZ Corp is considering financing a project with only equity. The project’s unlevered cost of capital is 10%. The project will require a $1000 initial investment today and pay incremental free-cash-flows of $100 in perpetuity starting the end of the next year. If the firm were to finance the project with debt so that its D/E ratio is 0.50 how will the NPV of the project change? Assume the interest rate on the new debt will be 3%, and the firm faces a 21% tax rate. Round your answer to two decimals.

Answer 1

NPV of the project today

Initial outflow = $1000

PV of incremental cash inflows at the end of the next year = Cash flow / Discount rate = 100/10% = $1000

PV of cash inflow today = 1000PVAF_{(10%,2 year)} = 826.45

NPV of project today = PV of inflow - initial outflow = 826.45 - 1000 = - $173.55

If the firm finance the project half from debt

cost of debt = k_d = interest (1-Tax rate) = 3%(1-21%) = 2.37%

levered cost of Equtiy =

= 10% + 500/1000(10% - 2.37%)

= 10% + 3.815% = 13.815%

Weighted average cost of capital = (Cost of equity x Weight of Equity) + (Cost of Debt x Weight of debt)

= (13.815% x 0.5) + (2.37% x 0.5)

= 8.0925%

PV of cash inflows at the end of next year = 100/8.0925% = $1235.71

PV of cash inflows today = $1235.71PVAF_{(8.0925%, 2 year)} = $1041.51

NPV of the project = PV of cash inflows - PV of cash outflows = 1041.51 - 1000 = $41.51

So, if the firm finance 50% from debt NPV of the project becomes negative $173.55 to Positive $41.51.