Question

After-tax cost of debt Personal Finance Problem Bella Wans interested in buying a new motorcycle. She has decided to borrow the money to pay the $20,000 purchase price of the bike. She is in the 24% income tax bracket. She can either borrow the money at an interest rate of 2% from the motorcycle dealer or she could take out a second mortgage on her home. That mortgage would come with an interest rate of 8% Interest payments on the mortgage would be tax deductible for Bella, but interest payments on the loan from the motorcycle dealer could not be deducted on Bella's federal tax return

a. Calculate the after-tax cost of borrowing from the motorcycle dealership.
b. Calculate the after-tax cost of borrowing through a second mortgage on Bella's home
c. Which source of borrowing is less costly for Betta?
d. Should Belle consider any other factors when deciding which loan to take out?

Answer 1

The after-tax cost of the motorcycle dealership loan is $400 annually, which is less than the after-tax cost of the second mortgage ($1,216 annually) when considering a 24% tax bracket. Therefore, borrowing from the dealership is less costly for Bella. She should also consider other factors like risks associated with the use of the home as collateral, loan terms, and payment flexibility.

Step-by-step explanation:

To answer the student's question regarding the after-tax cost of debt for different financing options for purchasing a motorcycle, we need to first calculate the after-tax interest cost of both the loan from the motorcycle dealership and the second mortgage.

a. The after-tax cost of borrowing from the motorcycle dealership is calculated by simply taking the interest rate since it is not tax deductible. The annual cost is 2% of $20,000 which is $400.

b. The after-tax cost of borrowing through a second mortgage on Bella's home is calculated by considering the tax deductibility of the interest. The annual interest at 8% of $20,000 is $1,600. Since Bella is in the 24% tax bracket, the tax savings from the interest deduction is 24% of $1,600, which is $384. Thus, the after-tax interest would be $1,600 - $384 = $1,216.

c. The less costly source of borrowing for Bella is the motorcycle dealership loan since $400 is less than $1,216.

d. Bella should consider other factors like potential risks, such as the risk of her home should she default on a second mortgage, the term length of both loans, and flexibility of payment options.