Question

Bella Wans is interested in buying a new motorcycle. She has decided to borrow the money to pay the ​$25000 purchase price of the bike. She is in the 28​% 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 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​ Bella? d.  Should Bella consider any other factors when deciding which loan to take​ out?

a. The​ after-tax cost of borrowing from the motorcycle dealership is

nothing​%.

​(Round to the nearest whole​ percentage.)

b. The​ after-tax cost of borrowing through a second mortgage is

nothing​%.

​ (Round to two decimal​ places.)

c.  Which source of borrowing is less costly for​ Bella?  ​(Select the best answer​ below.)

A.Bella should borrow by taking the

second mortgagesecond mortgage.

B.Both loans have the same rate of

2828​%,

so Bella should choose the loan she likes best.

C.Both loans have the same rate of

2828​%,

so Bella should not take either loan.

D.Bella should borrow by taking the

dealership loandealership loan.

d.  Is there any other consideration that Bella ought to think about when deciding which loan to take out to pay for the​ motorcycle?  ​(Select the best answer​ below.)

A.

Using the motorcycle dealership loan does put Bella at risk of losing her home and motorcycle if she is unable to make the loan payments.

B.

Using the second home mortgage does put Bella at risk of losing her motorcycle if she is unable to make the mortgage payments.

C.

Using the motorcycle dealership loan does put Bella at risk of losing her home if she is unable to make the loan payments.

D.

Using the second home mortgage does put Bella at risk of losing her home if she is unable to make the mortgage payments.

Answer 1

A) After tax cost of borrowing from motorcycle dealership is the interest rate offered by the dealer ie 6% as the interest payments on the loan is not tax deductible hence no benefit of taxation on the cost of borrowing.

B) After tax cost of borrowing through a second mortgage = interest rate * ( 1 - tax rate)

= 8 ( 1 - 0.28)

= 5.76%

The interest payments on mortgage is tax deductible hence the same has been deducted from the payments.

C) Bella should borrow by taking the second mortgage as the after tax cost of borrowing is less for second mortgage than taking loan.

D)  Using the second home mortgage does put Bella at risk of losing her home if she is unable to make the mortgage payments. Because there is already a mortgage on the house and the non payment will increase the risk of losing the home.