## Tuesday, October 4, 2016

### Calculating Required Retirement Savings Rates: Part 2

In Part 1 of this series I outlined how to estimate the savings rate required to ensure a financially secure retirement. The required savings rate estimate depends a lot on various projections and assumptions that I outlined in Part 1. In this post I'll discuss how to estimate your expenses in retirement. In subsequent posts in the series I'll discuss how to estimate your Social Security retirement benefits, how to estimate the expected rate of return on your investments, and how much you should expect to be able to safely withdraw from your retirement savings each year.

Remember that we are doing these calculations in real dollars, and we're assuming that your income increases at the same rate as inflation from when you start saving at age 25 until you retire at age 65. So if your current annual income is \$50,000, and we assume that your retirement expenses will be 80% of this, your annual retirement expenses will be \$40,000 in real dollars.

Here's quick refresher on the difference between real dollars and nominal dollars. In Part 1 I explained that at an annual average inflation rate of 2%, you multiply real dollars by about 2.2 to get the equivalent number of nominal dollars in 40 years. So your annual income in nominal dollars just before you retire in 40 years would be about \$110,000 (2.2 x \$50,000), and your estimated annual expenses in in nominal dollars in your first year of retirement would be about \$88,000 (2.2 x \$40,000, or 80% x \$110,000) . In other words, you would see a gross year to date income of \$110,000 on your last pay stub before you retired in 40 years, but this amount of nominal dollars would only have the purchasing power that \$50,000 has today.

So is 80% of your income a reasonable estimate for living expenses in retirement? It's a fairly common number used by financial planners. You can verify this by doing a Google search something like this: retirement living expense 80%. Reading some of the articles that come up in a search like this will give you some insight into how people come up with estimates for expenses in retirement.

Why might your expenses be less in retirement than while working? One obvious reason is that you won't be saving for retirement once you retire. If we use the 14% savings rate we calculated in Part 1, you can subtract that, getting to 86% of income (100% - 14%). You may also have lower commuting costs, clothing costs, and other costs related to working, which could get you down to the 80% number.

But this percentage can vary a lot, depending on costs that you have now that you won't have in retirement, or vice versa. If you have a mortgage that you plan to pay off before retiring, that will significantly reduce your expenses in retirement. If you plan to travel a lot or expect higher health care costs in retirement, that could significantly increase your retirement living expenses. So the best way to estimate your retirement living expenses is to work through the differences in your own living expenses before retirement and expected living expenses after retirement. If you find this too difficult, then you can just plug a range of numbers into the calculations to get a range of savings rates based on different assumptions. Let's do that.

Let's say that you own your home and are spending 30% of your gross income on mortgage payments. This 30% figure does not include property taxes, insurance, and maintenance, since these expenses will continue after the mortgage is paid off. If you plan to pay off the mortgage before retiring, then your retirement spending will be reduced by 30% of gross income due to the elimination of the mortgage payment expense.

We assume that you are able to to save enough for retirement, on top of the incremental expenses of home ownership (a challenge in itself). We'll calculate your required retirement savings rate assuming no other changes in retirement living expenses compared to pre-retirement living expenses, other than elimination of the mortgage expense and the expense of saving for retirement, while keeping all other assumptions the same.

Since we haven't calculated the required savings rate yet, we don't know how much to reduce estimated retirement spending due to the elimination of the retirement saving expense, but with a spreadsheet set up to do the calculations, it's quite easy to use trial and error to quickly figure out the required savings rate. The required savings rate comes out to about 9%, with retirement living expenses at about 61% of pre-retirement living expenses (100% minus 30% mortgage expense minus 9% retirement savings expense). Let's run through the calculations like we did in Part 1 to check this.

Assuming a real annual income of \$50,000, our estimated real annual retirement living expense is \$30,500 (61% x \$50,000). In Part 1 we assumed that Social Security benefits would cover \$14,000 of our annual retirement living expenses. We aren't changing any assumptions that affect estimated social security benefits, so we can subtract this same assumed annual Social Security benefit from our estimated annual living expenses to calculate our annual residual living expenses (RLE) of \$16,500 (\$30,500 - \$14,000).

As in Part 1, we are assuming that we can safely withdraw an inflation-adjusted 4% annually from our retirement savings to cover our annual RLE. In Part 1 we determined that this implies that we must accumulate 25 times our annual RLE before retiring. Thus we calculate that we must accumulate \$412,500 (25 x \$16,500) in real dollars before retirement.

As in Part 1, we plug into the spreadsheet PMT function our assumed real rate of return of 4% on the investments that will generate our retirement savings, the 40 years between ages 25 and 65 that we will be saving, our current savings of \$0, and the required amount of \$412,500 that we must save:

=PMT(4%, 40, 0, -412500)

This PMT formula returns the required annual savings amount of \$4,341, which is 8.7% of our assumed \$50,000 annual income (4,341 / 50,000), and we can round this to approximately 9%, the required savings rate. So being able to buy a house and pay off the mortgage before retirement could lower the required savings rate from about 14% to about 9%, given our other assumptions.

As a final example, let's calculate the required savings rate assuming that retirement living expenses will be 100% of pre-retirement living expenses, with all other assumptions the same. This basically means that you will be spending enough more on travel, medical care, and other retirement living expenses to offset any reductions, such as eliminating the retirement saving expense. For this scenario I calculate a required savings rate of about 19% of gross income. Let's check this.

With post retirement living expenses at 100% of pre-retirement expenses, your RLE is \$36,000 (\$50,000 minus \$14,000 in annual Social Security benefits). Multiplying by 25 (based on our 4% safe withdrawal rate assumption) gives \$900,000 in required savings at retirement. Plug this into the PMT function:

=PMT(4%, 40, 0, -900000)

The result is \$9,471 in required annual savings, which is 18.94% of gross income (9,471 / 50,000), which we can round to 19%.

So with various assumptions about post-retirement spending as a percent of pre-retirement spending, we've come up with required savings rates anywhere from about 9% to about 19%. For a gross annual income of \$50,000, this corresponds to real savings at retirement of anywhere from \$412,500 to \$900,000. Remembering that these are real dollars, we multiply by 2.2 to get nominal dollars in 40 years at 2% inflation, so you'd actually need to see values of your retirement accounts between \$907,500 (\$412,500 x 2.2) and \$1,980,000 (\$900,000 x 2.2).

Keep in mind that the savings rate calculations so far have been based on certain assumptions about Social Security retirement benefits, the real rate of return you can expect on your investments, and a safe withdrawal rate from your retirement savings. In Part 3 of this series I'll discuss how to come up with an estimate of your Social Security retirement benefit, since this is a key factor in determining your residual living expenses in retirement. In Part 4 I'll discuss how to evaluate reasonable estimates for the real rate of return on your investments, since this has significant impact on how much savings you'll end up with given a certain savings rate. In Part 5 I'll discuss the 4% safe withdrawal rate assumption. At least that's my plan.