The cost of capital is the rate of return that providers of finance expect to generate on the capital that they have provided. A company has two broad options for external financing: to contract debts or issue equity capital. The costs are expressed in the form of interest payments and distribution of dividends respectively.
The cost of capital is calculated as the average between the cost of debt and the cost of equity. The WACC is used to discount the Free Cashflow to derive the NPV, and as the FCF is an after-tax term, the WACC should also be taking an after-tax perspective. Interest payments are deductible from profit before tax, which implies that the cost of debt (the interest) enjoys a tax credit (tax shields). Therefore, the net cost of debt to the business is actually lower than what the company pays to bondholders as interest.
Estimating the WACC is a difficult exercise. In many companies, a single value will be applied across the board to all projects whatever their risks, but the correct approach would be to use a project WACC, i.e. apply a mark-up or a discount to the company WACC to reflect the additional or lower risk compared to the overall business. Monte Carlo simulation can be used to estimate the value of the mark-up or the discount. In addition, project risk might vary over time, so that the WACC might be higher in the first phase, but return to a lower value in a second phase. As the WACC is applied in a compound manner in the NPV calculation, business valuation will be most sensitive to the WACC value. Sensitivity analysis of various WACC values on the NPV is recommended when calculating an NPV. If sensitivity analysis (instead of a time-dependent WACC) is too crude an approach, do call on the help of a financial expert.