Question

After-tax cost of debt Bella Wans is interested in buying a new motorcycle. She has decided to borrow money to pay the $25,000 purchase price of the bike. She is in the 25% federal income tax bracket. She can either borrow the money at an interest rate of 5% from the motorcycle dealer, or she could take out a second mortgage on her home. That mortgage would come with an interest rate of 6%. 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?

Answer 1

a.

After-tax Cost of debt is the interest rate on the debt multiplied by (100% minus the incremental income tax rate).

In the given case loan amount is $25000.

Federal income tax bracket is 25%

Interest rate from motorcycle dealer is 5%

As per the above formula the after-tax cost of borrowing from the motorcycle dealership will be 5%×(100%-25%)=3.75%.

b.

Second mortgage on Bella's home

Loan amount is $25000

Federal income tax bracket is 25%

Interest rate from mortgage is 6% which is tax deductible for Bella.

So total interest payment is (6% $25000)=$1500

As income tax savings equals (6%of 25%)=1.5%,hence,income tax savings is (1.5%of $25000)=$375

So net cost is $(1500-375)=$1125 per year on the $25000 loan.

So after-tax cost of borrowing through a second mortgage on Bella's home is $(1125/25000)×100=4.5%.

C.

It can be seen from above that borrowing from motorcycle dealer will be less costly for Bella.

d.

There is no other consideration that Bella ought to think about when deciding which loan to take out to pay for the motorcycle.