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How Long To Hold?
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THE SCENARIO
In the past, we've covered the concept of paying money up-front when getting a loan in order to get a lower interest rate. This week, I was evaluating just such a situation, and determined that I could make a 17.65% return on my money if I bought the rate down as much as the lender will allow. However, I only achieved that return if I kept the loan until it was entirely paid off, and oftentimes loans are paid off through sale or refinance before their entire (usually 30-year) term elapses.
The question: If I want to make at least 10% on my up-front rate-buydown money, how long will I have to keep the loan*? Ignore amortization, and concentrate only on month-to-month cash flow with no future payoff.
* The loan they offered me has a balance of $83,500 at 6.875% for 30 years, fully amortizing (we'll call it the "base" loan), but if I pay $5,035, I can reduce the interest rate to 5.5% (we'll call it the "bought-down" loan).
THE SOLUTION
This one has several parts, but they're all pretty straightforward.
- Find out the payment on the 'base' loan.
- Find out the payment on the 'bought-down' loan.
- Find out the monthly savings by buying down the rate.
- Find out how long I'd have to keep the bought-down loan to make 10% on my $5,035.
First things first, make sure the calculator is using 12 Payments per Year.
Step 1: The Base Loan
N: 360 (This is a 30-year loan, which is 30 x 12 = 360 months)
I/YR: 6.875 (The 'base' loan rate is 6.875%)
PV: 83,500 (The original borrowed amount is $83,500)
PMT: (This is what I'm trying to find)
FV: 0 (The loan amortizes fully)
The payment on the 'base' loan is $548.54.
Step 2: The Bought-Down Loan
N: 360 (This is a 30-year loan, which is 30 x 12 = 360 months)
I/YR: 5.5 (The rate can be bought down to 5.5%)
PV: 83,500 (The original borrowed amount is $83,500)
PMT: (This is what I'm trying to find)
FV: 0 (The loan amortizes fully)
The payment on the 'bought-down' loan is $474.10.
Step 3: Monthly Savings
The payment on the 'base' loan is $548.54, and on the 'bought-down' loan is $474.10. The monthly savings from buying down the loan is $548.54 - $474.10 =
$74.44.
Step 4: How Long To Keep It?
N: (This is what I'm trying to find)
I/YR: 10 (My target return is 10%)
PV: -5,035 (It cost me $5,035 to buy down the rate)
PMT: 74.44 (This is my monthly savings from buying down the rate)
FV: 0 (At the end, no money changes hands)
To make 10% on my buydown money, I'd have to keep the loan for 99.94 months (around 8 years and 4 months).
Given that the buydown doesn't break even until $5,035 ÷ $74.44 = 67.74 months into the loan, this result isn't very surprising.
What would you do? Would you buy down the rate, locking in a lower monthly payment? Or would you keep the higher rate, and keep your eye out for a profitable sale opportunity in the nearer term? What factors would lead you to do one versus the other? Let us know in the comments!
