Calculate die after-tax cost of debt under each of the following conditions:
a. Interest rate of 13%, tax rate of 0%
b. Interest rate of 13%, tax rate of 20%
c. Interest rate of 13%, tax rate of 35%
To calculate the after-tax cost of debt, you will need to use the formula:
After-Tax Cost of Debt = Pre-Tax Cost of Debt x (1 - Tax Rate)
a. Interest rate of 13%, tax rate of 0%:
After-Tax Cost of Debt = 0.13 x (1 - 0) = 0.13 or 13%
b. Interest rate of 13%, tax rate of 20%:
After-Tax Cost of Debt = 0.13 x (1 - 0.20) = 0.13 x 0.80 = 0.104 or 10.4%
c. Interest rate of 13%, tax rate of 35%:
After-Tax Cost of Debt = 0.13 x (1 - 0.35) = 0.13 x 0.65 = 0.0845 or 8.45%
To calculate the after-tax cost of debt, you need to take into account the interest rate and the tax rate. The formula to calculate the after-tax cost of debt is:
After-tax cost of debt = Interest rate * (1 - Tax rate)
Now, let's apply the formula to each condition:
a. Interest rate of 13%, tax rate of 0%
In this condition, since the tax rate is 0%, there is no tax benefit. Therefore, the after-tax cost of debt is the same as the interest rate.
After-tax cost of debt = 13% * (1 - 0%) = 13%
b. Interest rate of 13%, tax rate of 20%
With a tax rate of 20%, there is a tax benefit. The tax benefit is the difference between the interest payment and the tax savings.
Tax benefit = Interest rate * Tax rate = 13% * 20% = 2.6%
After-tax cost of debt = Interest rate * (1 - Tax rate) = 13% * (1 - 20%) = 10.4%
c. Interest rate of 13%, tax rate of 35%
Similar to the previous condition, the tax benefit is the difference between the interest payment and the tax savings.
Tax benefit = Interest rate * Tax rate = 13% * 35% = 4.55%
After-tax cost of debt = Interest rate * (1 - Tax rate) = 13% * (1 - 35%) = 8.45%
Therefore, the after-tax cost of debt under each condition is:
a. 13%
b. 10.4%
c. 8.45%