Calculating Perpetual Bond After-Tax Cost of Capital

The question asks for the after-tax cost of capital for a perpetual bond. This involves calculating the cost of debt considering the tax shield provided by interest payments.

Formula for After-Tax Cost of Debt (Perpetual)

The formula used to calculate the after-tax cost of debt for a perpetual instrument like a bond is:

$ \text{After-Tax Cost of Debt} = \text{Coupon Rate} \times (1 - \text{Tax Rate}) $

Applying the Formula

Given information:

• Coupon Rate = 7% or $0.07$
• Corporate Tax Rate = 30% or $0.30$

Substitute the values into the formula:

$ \text{After-Tax Cost of Debt} = 0.07 \times (1 - 0.30) $

$ \text{After-Tax Cost of Debt} = 0.07 \times (0.70) $

$ \text{After-Tax Cost of Debt} = 0.049 $

Result

To express this as a percentage, multiply by 100:

$ 0.049 \times 100 = 4.90\% $

Therefore, the after-tax cost of capital for the perpetual bond is 4.90%.