Your success in business thus far has put you in a position to purchase a home for $500,000
located close to the university you attend. You plan to pay a 20% down payment of $100,000
and borrow the remaining $400,000. You need to decide on a mortgage, and realize you can
apply the skills you have acquired in the last several chapters to evaluate your choices. To find
the available options, go to www.bankrate.com. Select “Mortgages,” then “Mortgage Rates.”
For location, choose the nearest large city; for mortgage type, choose purchase (not refinance).
Consider 30-year fixed rate mortgages with 20% down, and assume your credit score is the
highest possible.
Consider all the options by selecting loans with “All points.” Update rates and sort by “Rate” to
find the loan with the lowest rate (not APR). Record the rate, points, fees, “APR,” and monthly
payment for this loan.
Next consider only loans with “0 points” and find the loan with the lowest fees. Again, record
the rate, points, fees, “APR,” and monthly payment for this loan.
First, use the annuity formula or PMT function in Excel to verify the monthly payment for each
loan. (Note that to convert the “Rate” to a monthly interest rate you must divide by 12. Your
result may differ slightly due to rounding.)
Next, calculate the actual amount you will receive from each loan after both fees and points.
(Note that fees are a fixed dollar amount; points are also paid up front and are calculated as a %
of the loan amount.) Using this net amount as the amount you will receive (rather than
$400,000), show that the quoted “APR” of the loan is the effective IRR of the loan once all fees
are included (you may use the Rate function in Excel, or calculate the NPV at the quoted
“APR”).
Compare the loans, assuming you will keep them for 30 years, as follows:
- What is the IRR associated with paying the higher fees for the lower rate loan? (Again, the RATE function can be used.)
- Plot the NPV profile of the decision to pay points for the lower rate loan. Do the NPV rule and the IRR rule coincide?
Create a data table showing the NPV of paying points for different horizons (1 to 30 years) and different discount rates (0% to the IRR in (3) above). What can you conclude about whether it is a good idea to pay points?
Suppose the bank gives you the option to increase either loan amount so that for either loan, you will receive $400,000 today after all fees and points are paid. How would this affect your decision to pay points?
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