“A .01% increase in taxes would prevent all this. That’s $150 a year on a $150,000 house.”

.01% increase in taxes…

Seems really low, doesn’t it? It’s not. Here is how it translates into taxes:

My house is worth roughly $150,000 on the tax rolls. We paid $3,500 in property taxes last year. If they were to increase another $150, it would represent a 4.3% increase as I show in my math:

The reason for the difference is that the .01% increase is PER $100 of value.

Politicians framed this issue in such a way to make it seem like the tax increase isn’t that much when in fact it’s MUCH more than they make it seem.

The guy got rather testy with me when I told him that I would not be willing to fork over another $150 per year. My reasoning is that although it’s “only” $150, it’s a tax increase. Once taxes go up (especially property taxes), they seldom if ever come back down again. Once this particular budget shortfall is cured by a tax increase, they’ll find another place to use the tax increase. Not only that, the $150 is based on property value, which will most likely increase in the future.

• 12 years left on a 15-year mortgage.

• Current mortgage rate is 4.75%.

• Current monthly payment $1,369

• Current balance on the mortgage around $150,000 (this is the amount to be refinanced).

This couple is looking to refinance into:

• 15-year mortgage.

• $150,000 loan.

• $3,000 in closing costs (to be paid upfront).

This couple is in the 25% income tax bracket.

So…based on those numbers, would it be a good idea to refinance?

Well, as Larry points out, there are a lot of things to consider before jumping into a refinance.

1. In this example, the spread between the two interest rates is less than a 100 basis points (less than one percent). Naturally, the bigger the spread, the more advantageous it is to refinance.

2. There is more to the calculation than simply looking at the difference in payments since the payment includes principal, which is your own money. So, we have to look at the difference in the interest portion of the payment.

3. As Larry also points out, interest payments are tax deductible (if you itemize your deductions). Larry uses the 25% income tax bracket for his example. Based on that, the couple is paying $.75 for each $1.00 of interest. Basically, what this means is that this makes the refinance less advantageous (you’ll see this in the spreadsheet).

4. This couple is already three years into their loan. They are looking to refnance into a new 15-year mortgage. That means they have paid 3 years of interest on the old loan and will be paying 15 years of interest on the new loan for a total of 18 years of interest.

5. The closing costs are paid upfront.

After running the example, I came to the conclusion that refinancing this loan will cost an additional $702 in after-tax interest. I arrived at this number by adding up the three year’s of interest paid on the original loan plus the 15 year’s of interest on the new loan. Were they to continue with the old loan, they would have paid a total of $70,417 in interest ($52,812 after-tax in a 25% income tax bracket).

What Larry leaves out, in my opinion, is a discussion of the opportunity cost between the two loans. By choosing to refinance, this couple would be freeing up cashflow that could be put to work elsewhere (unless they are using the cashflow to shore up their budget). The payment difference of $296 per month could be invested elsewhere for the next 12 years. Using a monthly total return on the S&P 500 Index of .75% (including a management fee), that $296 per month payment difference could grow to more than $112,000 in 15 years. If they invested the $3,000 plus the entire $1,369 monthly payment for 3 years after the end of the original mortgage, they would have over $60,000 at the end of 15 years. Another thing worth mentioning is that all of the $296 per month could be put into a Roth IRA where only a portion of the $1,369 payments could be put in a Roth because they would exceed the Roth limits.

Based on those numbers, the refinance looks like a no-brainer. But, I left out three things: 1. Investing in the stock market is not a sure thing and 2. I didn’t make adjustments for taxes, which favored the refinance. 3. In order for the scenario to work, the payment difference MUST be invested and not spent.

With that said, I am making available the spreadsheet I used for this post, which you can download here: Mortgage Amortization Comparison (Two 15-year Mortgages). I didn’t spend a lot of time making it user-friendly but if you understand the basics of Excel, you can get in there and change up the variables yourself.

Hello,

I have a question. If a person owed money to someone in 1998, but did not repay that amount until 2010, how can he calculate what amount to return now (in 2010) considering that much inflation has taken place since 1998? Should he use the yearly CPI inflation rate for his country? Will appreciate your help. Thanks.

The amount to be paid back and the term of the loan should have been spelled out when the money was initially borrowed. Although the CPI can be used, it should be the beginning point. The person who loaned the money was out that money for the last 12 years. Paying back money with only an adjustment for the CPI is basically paying them back the original amount. To compensate them for the usage of the money, the borrower would need to include some percentage above the rate of inflation (the CPI in this case). I would say a good starting point is 2% over the CPI.

Basically, what that means is if this person borrowed $1,000 back in 1998, they should pay back around $1,726.93 at CPI +2% (or $1,351.59 just using the CPI for the last 12 years).

What Are Financial Goals?

There are many different kinds of financial goals:

• Get out of debt

• Create an emergency fund

• Pay cash for a new (or used) car

• Downpayment on a house

• College fund

• Retirement

The Goal-Setting Process

I’m not a goal-setting expert but I was able to come up with six steps in the goal-setting process:

1. Determine your goal and the amount of money needed to meet the goal.

2. Set a due date for meeting the goal.

3. Decided what investment vehicle that will be used to meet the goal.

4. Calculate the lump sum or periodic payment that will be needed to meet the goal.

5. Track your progress.

6. Reach your goal.

Example

Let’s look at what the process looks like for someone saving up for a downpayment on a house. Let’s say in 5 years you desire a 20% downpayment on a $200,000 house ($40,000).

1. $40,000

2. 5 years (60 months)

3. Since the goal is relatively short-term, the savings will be kept in an interest-bearing savings account. For this exercise, we’ll use an annual interest rate of 1.28%.

4. To determine the lump sum or monthly payment necessary to meet this goal, you can use any number of online calculators, a regular calculator, or you can download this simple Excel Spreadsheet I put together for this post. Because interest rates on savings accounts are so low, the lump sum needed to meet a $40,000 goal in 5 years is really high at $37,500. If you’re going to reach the goal with monthly savings, you’ll need to save $645 per month.

5. For short-term goals, you’ll want to track your performance on a regular basis (monthly or quarterly) and make adjustments as necessary.

6. If all goes to plan, this goal should be met in five years (sooner if interest rates are higher or you can add more to your savings).

If you’ve never set and reached a financial goal, I urge you to give it a try.

Thoughts?

Came across this post and had a question….how do you calculate your PRR for the time period when the Annualized PRR is a negative number??

When you enter a negative number into the Excel IRR function you get an error because you can’t raise a negative number to a power (i.e. -8.43% ^ (180/365) = #NUM error).

Thanks for your help…great blog!

Okay, this is easy enough to address. The actual formula for calculating a periodic return is…

In this case, it would like this:

The readers problem was that he tried to perform the calculation using -8.43% rather than its decimal equivalent.

Hope this helps.

Related:

Reader Question Regarding Personal Rate of Return

How to Annualize a Rate of Return

Reader Question: How Do You Calculate Compound Growth (or Interest)?

Sure, you could go to an online calculator but it’s also good to know the formula. To make this particular calculation, you need this formula:

Where…

Principal = $200,000
Rate = .05 ÷ 12 or .0041667
N = Number of payments (360)

Now I’ll walk you through the calculation:

I ran the calculation in Excel, and it game me a payment of $1,073.64. The one penny difference is due to rounding.

The cool thing about this formula is that it works on any kind of loan as long as you make the proper adjustments. You would do yourself well to learn this formula or at least know how to use a financial calculator the next time you purchase a car.

Hi, I was wondering if you could help me out and explain why each month the amount of my car payment applied to interest goes up and down as opposed to gradually going down? Does the time of the month you make your payment affect this? Or something else?

L

After a couple of email exchanges, I got the following information:

Amount financed: $16,788
Interest rate: 12%
Term: 6 years (72 months)

I plugged those into a spreadsheet to find that his monthly payment should be around $328.21. He told me his actual payment is $331.99 per month. Most likely, there’s some program included in his monthly note. He also sent me a record of his payments:

As you can see, his first payment had a ton of interest. That’s most likely due to the fact that they probably put off the first car payment for 45 days (at least that’s what I came up with). My theory is that interest on this loan is charged on a daily basis. In this case, they divided 12% by 365 and then multiply that figure by the outstanding balance and add that amount to the balance. Like this:

Then, on the date the payment is made, the current balance is reduced by the amount of the payment and the interest charge is calculated on that balance. The interest portion of the payment is simply the sum of the daily interest charges since the last payment. So, if he goes longer between payments, there will be more interest for that particular month. I came pretty close to getting the same numbers as this reader sent me.

He then asked me if there was a way to reduce the interest charges by sending in his payments early. That will reduce his interest charges slightly but to REALLY make a difference, he needs to pay more towards his principal each month. That would give him the most benefit. And, since his interest rate is 12%, it would be very wise of him to do so. According to my numbers, he will end up paying over $6,900 in interest on this loan. He only financed $16,788.

The only good thing I can say is at least he bought a Honda. I just hate seeing people with these kinds of loans.

3/26/2010 – $188.50
4/8/2010 – $377.02
4/16/2010 – Balance of $593.54

The XIRR formula requires both negative and positive numbers in order for it to work. So, the best thing to do is to enter contributions as negative numbers since they are “outflows” to you. Like this:

Then, the ending balance would be a positive number. I explained this to the reader and this morning he sent me back an email telling me that he did it but got a return of 314%, which didn’t seem correct because his company was telling him the answer was 8.53%.

Both answers are correct. This is because the XIRR formula is annualized. To get the personal rate of return for the this time period, we have to adjust the annualized number. It’s easy enough to do. You just use this formula:

PRR (Personal Rate of Return) = [(1 + 3.148)^{# of days/365}] – 1

To get the number of days you simply subtract 3/26/2010 from 4/16/2010 to get 21 days.

PRR (Personal Rate of Return) = [4.148^21/365] – 1

PRR (Personal Rate of Return) = [4.148^.0575] – 1

PRR (Personal Rate of Return) = [1.08524] – 1

PRR (Personal Rate of Return) = .08524 or 8.52% (different due to rounding)

In other words, his personal rate of return over that 21-dayperiod was 8.53% but if you annualize the number, it’s 314%.

Anyway, I hope this was helpful. The XIRR formula can be confusing.

First off, you use the RATE function when you want to calculate what rate of return would be required to meet a certain goal, based on a few assumptions. Let’s use the information from yesterday’s post:

Retirement Goal: $1,000,000
Years until retirement: 20 (240 months)
Current retirement account balance: $100,000
Monthly contribution amount: $500

You can set it up like this in Excel:

Then, to solve for the rate, you simply put your click on cell E1 and then choose Insert > Function from the menu. You should then see this:

If you don’t see the RATE function listed in the center menu, then you might need to select “All” from the drop down menu above and then scroll down in the main menu until you see RATE.

Once you click on RATE and then “Okay”, you’ll see a menu that looks like this:

Then, you simply fill in the information, referencing the appropriate cells like this:

Here’s a quick explanation of each input:

Nper – the number of periods involved in this example. It’s 20 years but we’re making monthly contributions, so it’s more accurate to use 240 months. So we reference cell C1 and multiply it by 12.

Pmt – the monthly contribution amount expressed as a negative number. Think of it like a cash flow amount. The $500 is flowing out each month. So, we reference cell D1 and multiply it by -1 to get a negative number.

Pv – the present value of the retirement account—again expressed as a negative number. We reference cell A1 and multiply it by -1.

Fv – the future value of the retirement account. This value is expressed as a positive number. We reference cell B1.

Type – input 1 if the payment is made at the beginning of the month or 0 or leave it blank if the payment is made at the end of the month. I chose the beginning of the month and therefore inserted 1.

Guess – (you’ll have to scroll down to see this input as it is located under Type) This function requires a rate guess in order work properly. The default is 10 percent. I left this blank.

After you enter all the necessary information, click “OK.” You should see .78%, although you might see 1%. In that case, simply go into cell format and change the number settings to two decimal places.

Also, the formula will give you a monthly return. To convert it to an annual number, simply convert the percentage to a decimal and raise that number to the 12th power. Like this:

Hopefully, if I have done a good job, you now know how to use Excel’s RATE function. If you have any questions, please feel free to leave a comment.

Have a question:

What reasonable standards should investors use to measure how well or poorly that they are doing?

I’m sure that an answer would include “it depends” but if so, depends on what?

We are about 10% under our 12.31.07 balances and we are pleased but how pleased should we be? There is always someone who well fare better or worse but I’m at a loss as to which reasonable “standards” that I should use to know how I’m doing?

That’s a very good question.

Unfortunately, the appropriate answer is: it depends.

From a general standpoint, your portfolio’s performance should be judged against the appropriate benchmark or benchmarks.

For instance, if you have a portfolio of 50% large-cap stocks and 50% bonds, you would not base your performance on solely on the S&P 500 Index. Rather, you’d base it on a 50/50 split between the S&P 500 Index and the appropriate bond index.

If your portfolio is comprised of large-cap, mid-cap, small-cap, bonds, and real-estate investment trusts, then you need to base the performance on benchmarks for all of those asset classes.

The reason for this is that it’s easy to say, “Wow! We did awesome last year. Our portfolio was up 8%!” The reality could be that a benchmark portfolio might have been up 12%, making your 8% return not so stellar.

Of course, another way to judge your performance is to do what BG suggested in the comments of that post and that is to base your performance on whether or not you’re meeting your future goals. It doesn’t matter how your portfolio is doing if it’s not helping you meet your future goals.

For example…

Let’s say you have a retirement goal of $1,000,000 (purely hypothetical, ignoring inflation). Your retirement is 20 years away and you have $100,000 saved up so far. You are contributing $500 per month into an S&P 500-based fund. You don’t expect your contribution amount to change (again, hypothetical).

Using the RATE function in Excel, I figured that the required rate of return to meet that goal is .78% per month (9.79% annualized). Given that the monthly geometric average total return on the S&P going all the way back to 1926 is .77% (9.64% annualized), you most likely will fall short of your goal by around $25,000.

This leaves you a few choices:

1. You can accept the lower amount at retirement.

2. You can take on more risk by moving into small cap stocks, which have a higher expected return but also are a lot more volatile (more on that in a future post).

3. You can increase your contributions. Based on my numbers, increasing the contribution amount to $540 per month, put’s the expected account value at a little over $1 million.

I realize that we are talking about math based on linear growth, which never happens in the real world. But, it can still be beneficial to have some sort of basis in reality. If your goal is $1 million and you’re investing a certain amount per month, it would be wise to know if you have a shot at meeting your goal.

Thoughts?