before-tax cost of debt and after-tax cost of debt david abbot is buying a new house, and he is taking out a 3030-year mortgage. david will borrow $199 comma 000199,000 from a bank, and to repay the loan he will make 360360 monthly payments (principal and interest) of $1 comma 117.451,117.45 per month over the next 3030 years. david can deduct interest payments on his mortgage from his taxable income, and based on his income, david is in the 3030% tax bracket.

a. what is the before-tax interest rate (per year) on david's loan?
b. what is the after-tax interest rate that david is paying?

Before-tax interest rate = 6.738%

After-tax interest rate = 4.7169%

Explanation:

Before we determine before and after tax interest rate per year, we need to understand the tax consequences arising from raising debt finance. Normally debt finance is considered a cheaper source of finance than other long term sources of finance due to two main reasons, 1st, debt providers require greater security (i.e assets being secured/charged) and 2nd, interest on debt is tax-deductible which means companies raising debt finance will benefit by paying lower taxes due to the interest being paid before taxes, hence, reducing the taxable income and tax liability. Therefore, an entity's after-tax interest rate will always be lower than before-tax interest rate. This will be proved as follows:

The formula used to compute before-tax interest rate/cost of debt is as follows;

kd = (i÷ market value of debt)×100

i = yearly interest

yearly interest= 1117.451×12= $13409.412

kd = ($13409.412÷$199000)×100

kd= 6.738%

The formula for after-tax interest rate is same except for the inclusion of tax consequences, as follows:

kd = {i(1-t) ÷ market value of debt} ×100

As we know the after-tax interest is interest paid on debt less any income tax savings due to deductible interest expense, that's why the (1-t).

kd = {$13409.412(1-0.30)÷199000}×100

kd= $9386.588 ÷$199000×100

kd= 4.7169%

yup the answer is

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30