Explain what is wrong with the following$$ argument: $"$If a firm issues debt that is risk$$ free, because there is no possibility of$$ default, the risk of the$$ firm's equity does not change.$$ Therefore, risk$-$free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of capital of$$ equity."

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Part $1$

$($Select the best$$ choice.$)$

A$.$

The argument is wrong because any leverage raises the equity cost of capital.$$ Risk$-$free leverage raises it the most because it does not share any of the risk.

B$.$

The argument is correct because debt has a lower cost of capital than equity and a firm can reduce its overall weighted average cost of capital by increasing the amount of debt financing.

C$.$

The argument is correct.

D$.$

The argument is wrong because any leverage raises the equity cost of capital.$$ Risk$-$free leverage raises it the least because it does not share any of the risk.