Bella is interested in buying a new motorcycle. She has decided to borrow money

Question

Bella is interested in buying a new motorcycle. She has decided to borrow money to pay the $20,000 purchase price of the bike. She is in the 28% federal income tax bracket. She can either borrow the money at an interest rate of 6% from the motorcycle dealer, or she could take out a mortgage on her home. That mortgage would come with an interest rate of 9%. 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 Bella?

d. Is there any other consideration that Bella ought to think about when deciding which loan to take out to pay for the motorcycle?

Explanation / Answer

a. After tax cost of borrowing on motorcycle will be equal to the interest rate on loan from motorcycle dealer as it's interest payment does not get any benefit of tax deduction.

Thus, after-tax cost of borrowing from the motorcycle dealership = 6%

b. after-tax cost of borrowing through a second mortgage on Bella's home = Interest rate * (100% - Tax rate)

= 9% * (100%-28%) = 9% * 0.72 = 6.48%

c. Loan from Motorcycle dealer is cheaper at 6%.

d. Yes. Bella should also consider her future income and tax deductions before making the choice. Today she is in 28% bracket, but if she gets a good increment, she could land in the higher tax brackets making the home loan option attractive. If her tax rate goes up to 35%, the after tax cost would become 9% * 0.65 = 5.85% which is lower than the dealer loan.

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