Financial Modeling Service | Picking the Best Home Loan or Refi
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Picking the Best Home Loan or Refi

By Jeff Greenspan, Managing Director, Financial Modeling Services

For most people, your home loan is the biggest loan you will ever take, so it makes sense to structure your loan in a way that saves you money if possible. To get the most out of this discussion, you will need to have some basic financial knowledge, so please review my Finance 101 document or video before continuing.

Too many finance gurus, who should in my opinion know better, fail to use Net Present Value (NPV) to identify the best home loan for you. They do this for two reasons: 1) it’s a bit complicated to explain; and 2) less complicated techniques often get the right answer. However, when you are talking about amounts exceeding $100k, optimal is better than just OK! So let’s GET STARTED!

Think about a mortgage as a series of cash flow. Each month you pay principal plus interest, and maybe escrow amounts and private mortgage insurance. At some point you either pay off the mortgage in full or you sell your house and pay off the mortgage in full. In additional to the typical information used to calculate the cost of a loan (loan amount, interest rate, and amortization period), we need to know two other pieces of information to figure out the NPV of a loan to you: your discount rate and how long you expect to continue owning the home. For our example, we’ll assume that Harriet Homeowner is buying a $300,000 house, putting 20% down, and plans to live there for the rest of her life (30+ years). She’s been told by Barry Banker that she can get a 30-year loan at 4.5% or a 15-year loan at 3.75%, and that the closing costs are $6000 regardless of which loan she picks. Harriet’s personal discount rate is 7%. To determine which loan is better for Harriet, we calculate the NPV of each of these two loans, as follows:

1. Determine the outgoing1 cash flows.

Time 0 - Start EOM 1 ... EOM 180 EOM 360 Total $$$ Spent
30-year Loan -$6000 -$1216.04 -$1216.04 -$1216.04 -$1216.04 $443,774.40
15-year Loan -$6000 -$1745.33 -$1745.33 -$1745.33 0 $320,159.40

At first glance, it looks like selecting the 15-year loan will save Harriet more than $123k! Unfortunately, that calculation doesn’t take into account the time value of money.

2. Discount the series of cash flows at the discount rate to determine the NPV. When we calculate the NPV of each of these two loans, we come up with a far different result.

Loan Harriet's NPV
30-year Loan -$188,780.72
15-year Loan -$200,178.79

Let’s review. First, these numbers are negative because the cash flows out. The 30-year loan costs Harriet about $189k, and the 15-year loan costs her about $200k. The 30-year loan saves Harriet $11,398.07! Second, it’s critically important to understand that a $240k loan costs less than $240k in each case because of 1) the time value of money: the value of the equal monthly payment in the 180th month is less than the same payment in month one because of inflation; and 2) the interest rate is less than Harriet’s discount rate. If Harriet had a discount rate of 3%, the shorter loan would be the better value by almost $35.7k and the true cost (NPV) of the loan would be greater than $240k.

The story doesn’t end here. Harriet was smart enough to ask Barry Banker if she could “buy down” the interest rate. With this option, which is available for almost every loan, Harriet pays an extra fee up front for a lower interest rate. Barry tells Harriet that she can decrease her 30-year rate from 4.5% to 4% by paying 1.5 “points,” where a point is equal to 1% of the $240k loan amount, or she could pay 2.5 points and get a rate of 3.75%. Harriet is now looking at 4 possible loans:

Basic 30 Year Buy Down 1 Buy Down 2 Basic 15 Year
Amount $240,000 $240,000 $240,000 $240,000
Rate 4.5% 4% 3.75% 3.75%
Monthly Payment $1216.04 $1145.80 $1111.48 $1745.33
Closing Costs $6000 $9600 $12,000 $6000
Term 360 months 360 months 360 months 180 months
Loan NPV -$188,780.72 -$181,821.92 -$179,063.46 -$200,178.79

Which loan should Harriet select? The one with the highest NPV2 , which is named “Buy Down 2” in the table above.

Selecting the best loan becomes more difficult when you don’t know how long you will own a property. If you are following my guide ABCs to Amassing Long-Term Wealth, you won’t have this concern! But perhaps you know that you will definitely not own this property for 30 years. Let’s see how the NPV changes over time for these four loans.

NPV over Time Basic 30 Year Buy Down 1 Buy Down 2 Basic 15 Year
48 months -$225,771.41 -$225,393.85 -$225,815.36 -$221,497.86
60 months -$221,740.49 -$220,590.13 -$220,630.21 -$217,184.22
72 months -$218,061.63 -$216,213.17 -$215,909.74 -$213,478.38
84 months -$214,709.14 -$212,231.17 -$211,618.96 -$210,329.27
96 months -$211,659.09 -$208,614.57 -$207,725.37 -$207,689.59

It turns out that the “Basic 15 year” loan has the highest NPV for the first 8 years (96 months) of the loan, after which “Buy Down 2” becomes the best value. Harriet Homeowner now has the information she needs to make an optimal decision!

The process for determining whether to refinance your existing loan is basically the same. If you know your time frame and discount rate, you can compare the NPV of your existing mortgage to a set of alternatives, and you should always pick the option with the highest NPV. Our company, Financial Modeling Service, will do the analysis for you for a flat $50 fee, and we guarantee that you will save at least that much in NPV when selecting a loan or the analysis is free.

Remember to read our exciting DISCLAIMER!

Resources:

For finding which loans to consider, I like https://www.bankrate.com/ and https://www.mtgprofessor.com/home.aspx. You should also consider online lenders: see nerdwallet’s article on the 11 Best Online Mortgage Lenders of December 2020.

IMHO, the best free mortgage calculator can be found at the Mortgage Professor’s site. However, because it is not based on NPV, it uses a number of alternative constructs (like the opportunity cost of savings) to try to arrive at the best answer. You will be better served using NPV to analyze loans.

1 Ignoring the incoming cash flow of +$240,000 does not change the analysis in any way: the comparative values between the loans are exactly the same.

2 A smaller negative number is greater than a larger negative number: -$179K > -$181k > -$188k > -$200k.