Final answer:
The effective annual after-tax cost of capital accounts for both compounding interest and tax deductions on interest paid. For a loan with 5.25% interest compounded daily and a 21% tax rate, the after-tax cost of capital would be 4.266%. Simple interest examples further clarify how interest accrues and the effect of taxes on the total interest paid.
Step-by-step explanation:
The effective annual after-tax cost of capital is an important metric for businesses to understand the true cost of borrowing after considering the effects of compounding interest and taxes. When an association offers a loan with a 5.25% compounded daily interest rate, this compounding can significantly increase the effective rate over the course of a year.
However, businesses can also deduct interest expenses when calculating taxable income, which can lower the effective annual rate paid. To calculate the after-tax cost of capital, the formula to use is (1 − tax rate) × interest rate, where the tax rate is given as 21%. This calculation adjusts the interest to reflect the tax shield provided by the interest expense deduction.
For example, if the effective annual rate (compounded daily) is found to be 5.4% using the appropriate formula for daily compounding, the after-tax cost of capital would be (1 - 0.21) × 0.054 = 0.04266, or 4.266%. This is a more accurate reflection of the true cost of the loan for the business.
To further illustrate related concepts, consider two examples involving simple interest rates: A $5,000 loan with a 6% simple interest rate over three years would accrue a total of $900 in interest (($5,000 × 0.06 × 3) × (1 - 0.21)), and a loan of $10,000 that generates $500 in simple interest over five years would have an annual interest rate of 1% ($500 / $10,000 / 5).