Question

why is it cheaper to raise capital through debt instead of equity

Answer 1

In addition to the above. Debt is cheaper than equity because providers of debt are exposed to less risks than providers of equity (shareholders). This is because (1) interest needs to be paid out regardless of net income, while dividends can only be paid when the firm has been profitable, and, (2) in case of bankrupcy, debt providers have priority over shareholders. :)