Question

In: Finance

You are a homebuilder with excess houses in inventory and the local economy heading towards a...

You are a homebuilder with excess houses in inventory and the local economy heading towards a recession. In order to stimulate home sales, you offer the following promotion: 1.5% annual interest for the first 3 years of your new mortgage!

You have contracted with a local bank to offer 30-year, fully amortizing mortgages for your buyers at a rate of 3.95% per year with a .8 Loan-to-Value (LTV) ratio.

You have agreed to pay the bank the Present Value of the difference in monthly payments between their rate of 3.95%/year and your “teaser” rate of 1.5%/year.

Your promotion is working, and soon you have a home under contract to sell for $300,000. Using a Discount Rate of 5%/year, what is the amount which you willpay the bank at closing to compensate them for the 3-year teaser interest rate?

Use Excel. Use $$$ please

Solutions

Expert Solution

With 1.5% annual interest, the monthly payment is calculated using PMT function in Excel as below :

rate = 1.5% / 12 (converting annual rate into monthly rate)

nper = 30 * 12 (30 year mortgage with 12 monthly payments each year)

pv = 300000 * 0.8 (loan amount = price of home * loan to value ratio)

PMT is calculated to be $828.29

With 3.95% annual interest, the monthly payment is calculated using PMT function in Excel as below :

rate = 3.95% / 12 (converting annual rate into monthly rate)

nper = 30 * 12 (30 year mortgage with 12 monthly payments each year)

pv = 300000 * 0.8 (loan amount = price of home * loan to value ratio)

PMT is calculated to be $1,138.39

The lower interest rate is applicable for 3 years, or 36 months. The present value of the difference in monthly payments is calculated by multiplying the difference in monthly payments with the present value factor.

Present value factor = 1 / (1 + (discount rate / 12))month

Present value of differences in monthly payments is $10,363.42


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