The Cost of Capital (K) represents the weighted average costs of debt and equity, in proportion to the levels specified by the company's debt/equity ratio (based on market rather than book values).
The "cost" refers to the fact that suppliers of capital demand a return on their investment, and that return represents a cost to the recipient (i.e., the firm).
The Cost of Debt is less than the Cost of Equity to the borrower for these reasons:
The returns demanded by debtholders and stockholders are both important because the Shareholder Value Method discounts after-tax, pre-interest cash flows—cash flows on which both debtholders and shareholders have claims. The cost of capital, therefore, incorporates the claims of both these groups in proportion to their relative capital contribution. The cash flows discounted by the cost of capital yields corporate value. The market value of debt is subtracted from the corporate value to obtain shareholder value (the value of the equity).
By establishing a cost of capital, you are estimating a minimum acceptable rate of return. Returns above that rate create value for shareholders.
Most firms are comprised of different business units, each with a different exposure to macro-economic events. Not only should these units be analyzed as businesses, but each may well have a different cost of capital.