Chapter17: Valuation and Capital Budgeting for the Levered Firm
17.3 Weighted Average Cost of Capital Method
Finally, we can value a project using the weighted average cost of capital (WACC) method. Although this method was discussed in earlier chapters, it is worth while to review it here. The WACC approach begins with the insight that projects of levered firms are simultaneously financed with both debt and equity. The cost of capital is a weighted average of the cost of debt and cost of equity. The cost of equity is RS. Ignoring taxes, the cost of debt is simply the borrowing rate, RB. However, with corporate taxes, the appropriate cost of debt is (1 - tC)RB, the after-tax cost of debt.
The formula for determining the weighted average cost of capital, RWACC, is
The weight for equity, S/(S + B), and the weight for debt, B/(S + B), are target ratios. Target ratios are generally expressed in terms of market values, not accounting values. (Recall that another phrase for accounting value is book value.)
The formula calls for discounting the unlevered cash flow of the project (UCF) at the weighted average cost of capital, RWACC. The net present value of the project can be written algebraically as
If the project is a perpetuity, the net present value is
We previously stated that the target debt-to-value ratio of our project is 1/4 and the corporate tax rate is 0.28, implying that the weighted average cost of capital is
Note that RWACC, 0.186, is lower than the cost of equity capital for an all-equity firm, 0.20. This must always be the case, because debt financing provides a tax subsidy that lowers the average cost of capital.
We previously determined the UCF of the project to be £100,800, implying that the present value of the project is
This initial investment is £520,000, so the NPV of the project is:
Note that all three approaches yield the same value.