Category Archives: House

Home improvement and related

Refinance Analysis

So time to get my math/finance on.

I got a letter telling me what great interest rates are available to me via the FHA loans. I didn’t want to reward people sending junk mail, but on the other hand who doesn’t want to save on their biggest expense? So I looked into it.

I got a good faith estimate that showed me I could save money each month. Sounds nice, right? Well, two problems. 1) I would have to start paying mortgage insurance, which may not be tax deductible after 2010. Principle is not tax deductible, but interest currently is, and this gives me a nice tax break at the end of the year. I will ignore this for now. 2) I would have to roll all my closing costs into the mortage, which means I would greatly increase my debt immediately after the refi. I had already had one refi on my primary mortgage, and I did not like how my mortgage balance was increasing over time.

So how could I know if I was better off with one verse the other? In short, I can not, especially given how tax laws may change over time. One simple analysis would be to add up all the payments of the two. Not suprisingly, the refi would cost me more over time because I would have to make 30*12=360 payments on the new mortage, but I had already made twenty some of those payments on my first mortage.

However, I would gladly pay tomorrow for a hamburger today… that is the time-value of money. In fact, thats what the mortgage is all about, I borrow a whole lot of money so I can “own” a house, and in exchange I agree to make a bunch of payments to a mortgagee. Not surprisingly, the mortagee makes more money than they lend, to compensate them for not having that money around. The amount they make is measured in interest rate. The mortagee’s payout and subsequent payments to the mortgagee comprise a cash flow.

Note that I can compare the mortage options and generate a different cash flow for each. This is where I can thank Ohio State for showing me how to do a cash flow analysis. With a cash flow analysis, you can compute the internal rate of return on an investment. Better yet, your computer can do it for you! I have done a quick example that you can download here or see below:

First I entered the date of my next mortage payment, then I used formulas to compute the next payment, and I copied that formula for the next 30-some years. I filled in my primary mortgage principle+interest and copied that in each cell forward in time until my primary mortgage maturity date. Note I did not include escrow (taxes+insurance) in the calculation because these costs are irrelevant to the comparison, and also because my good faith estimate had estimates for these…. they happened to be close, but there is no point comparing these. I next added an entry for my secondary mortage payment, prinicple+interest. Note that I did not refinance this at the same time as my first, and it matures earlier than my first. The next cell just totals this for a complete mortage payment. After that is my proposed (cheaper) mortgage payment, principle+interest+mortgage insurance. Finally, I do a difference between the two and, sure enough, it looks like the new payment saves me over $10 a month! However, if you scroll way down into the future that changes a lot. I am still making full mortgage payments years after I would have had my house paid off. In fact, in this example, I would end up spending an extra $589.26 by refinancing! Even though it costs me more, I could do other things with that money until I finally fell behind and lost money.

One tool I could use in this analysis is imagine that I had a savings account. Every month I took that $10 I saved by refinancing and deposited it into my savings account. How much interest would that account need to return to make up that $589.26 difference? This is a concrete example of understanding rate of return. If I use the XIRR function to calculate that rate based on just those cash flows, it tells me the rate is 0.99% (on the top of the spreadsheet, off to the right). Right now, there are a lot of savings accounts that offer a higher rate of return than 0.99%. Other comparisons can be made with investments in stock or inflation.

Of course, when my appraisal comes back saying my house is worth a fraction of what I bought it for, this is all moot :).