# Rajiv and Laurie Amin are recent college graduates looking t

Rajiv and Laurie Amin are recent college graduates looking to purchase a new home. They are purchasing a $200,000 home by paying $20,000 down and borrowing the other $180,000 with a 30-year loan secured by the home. The Amins have the option of (1) paying no discount points on the loan and paying interest at 8 percent or (2) paying one discount point on the loan and paying interest of 7.5 percent. Both loans require the Amins to make interest-only payments for the first five years.

Unless otherwise stated, the Amins itemize deductions irrespective of the amount of interest expense. The Amins are in the 25 percent marginal ordinary income tax bracket.

a. Assuming the Amins do not itemize deductions, what is the break-even point for paying the point to get a lower interest rate?

b. Assuming the Amins do itemize deductions, what is the break-even point for paying the point to get a lower interest rate?

c. Assume the original facts, except that the amount of the loan is $300,000. What is the break-even point for the Amins for paying the point to get a lower interest rate?

d. Assume the original facts, except that the $180,000 loan is a refinance instead of an original loan. What is the break-even point for paying the point to get a lower interest rate?

e. Assume the original facts, except that the amount of the loan is $300,000 and the loan is a refinance and not an original loan. What is the break-even point for paying the point to get a lower interest rate?

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#### Solution Preview

Please see the attached file.

a. 2 years.

Cost of paying 1 point= loan principal x 1%

=$180,000 x 1%

=$1,800

Because the Amins do not itemize deductions, they will receive no tax benefit from the deduction for the points paid. Consequently, the after-tax cost of the point is the same as the before-tax cost of the point?$1,800. The Amins need to determine how long it will take them to recoup this cost due to a lower interest rate. To do this, they should divide the after-tax cost of paying the point by the yearly after-tax interest savings from the point. The after-tax cost of paying the point is $1,800. The after-tax savings due to a lower interest rate is $900 calculated as follows:

Before-tax savings due to a lower interest rate= $180,000 loan x (8%-7.5%)

= $900

Because the Amins are not itemizing deductions, additional interest payments do not generate any tax savings, therefore the after-tax savings from the lower interest rate is the same as the before-tax savings of $900.

The break-even period, then, is 2 years ($1,800 after-tax cost of the point/$900 after-tax annual savings from the lower interest rate).

b. 2 years.

Loan summary: $180,000; 8% rate ...

#### Solution Summary

The solution provides detailed calculations and explanations for the problem.