The cost of capital of a company that uses 45 percent debt that has an after-tax cost of debt of 10 percent and 55 percent equity that has a cost of 15 percent is:.

12.75 %

Explanation:

Cost of Capital is calculated on a Weighted Average basis. This is because there is a Pooling of Funds when it comes to financing projects. So Cost of Capital is the Return that is Required by providers of Long Term source of finance.

Cost of Capital = E/V × Ke + D/V × Kd

Where,

E/V = Market Weight of Equity

      = 0.55

Ke = Cost of Equity

    = 15%

D/E = Market Weight of Debt

      = 0.45

Kd = Cost of Debt

     = 10%

Therefore,

Cost of Capital = 0.55 × 15% +  0.45 × 10%

                         = 12.75 %

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