For these comparisons, I create a case study for a forty-year-old married couple with two children who are now constructing a lifetime financial plan. Jerry and Beth have determined that it is time to get serious about retirement and life insurance planning. Jerry is employed and Beth is a homemaker. These gender roles could be switched, but since life insurance is less expensive for women because of their heightened longevity, having the male be the worker is the more conservative case to consider. Jerry is seeking an additional amount of life insurance death benefit equal to $500,000. This, along with his other life insurance, will be adequate to support his family in the event of his death prior to age sixty-five.
Jerry presently has $60,000 saved in a 401(k) plan with his employer, which is invested with an equity glide path strategy representative of a typical target date fund: 80 percent stocks to age forty-five, 65 percent stocks from forty-five to fifty-four, 50 percent stocks from fifty-five to sixty-four, 40 percent stocks from sixty-five to seventy-four, and 30 percent stocks thereafter. He would like to plan for retirement at sixty-five. I will investigate a portion of his assets to be saved in the future that is equivalent to 401(k) employee contribution limits in 2019 with assumed inflation adjustments: $19,000 can be saved each year until age fifty, and then $25,000 thereafter until age sixty-five to account for the allowed catch-up contributions at those ages.
These contribution limits are inflation-adjusted such that real savings are kept the same, but the nominal amounts increase. Because life insurance premiums are fixed without inflation adjustments, the percentage of the savings directed to insurance decreases over time in real terms. Jerry expects to be in a combined 25 percent marginal tax bracket (22 percent for federal taxes and 3 percent for state taxes) in both his preretirement and postretirement years.
For investment returns, I follow the approach explained in Exhibit 3.11 from Chapter 3. Stock returns are simulated with a randomized risk premium above the fixed 3 percent bond yield. That risk premium has a 6 percent average value with a 20 percent volatility. Inflation is fixed at 2 percent annually. This implies a 1 percent real interest rate. Interest rate risk is eliminated from the analysis, as there is no possibility for fluctuating interest rates to create capital gains or losses for the underlying bond portfolio. The risky asset is based on large-capitalization stocks in the United States. Overall, this represents a 9 percent arithmetic average for stocks (7 percent in real terms). The compounded real growth rate for stocks is 5 percent. The investment portfolio is modeled using 10,000 Monte Carlo simulations for investment returns based on these capital market expectations. I assume investors earn these returns net of any investment or advisory fees. As investments are held in tax-deferred accounts, there is no further tax drag to worry about. Investors earn the gross returns and portfolio distributions are taxed as income.
Life insurance is priced using the 3 percent interest rate and the Social Security Administration 1980 cohort life tables for mortality. Pricing for the term and whole life policies was provided in Exhibits 7.1 and 7.2. Income annuities are priced in the same manner using the Society of Actuaries mortality data as explained in Chapter 4, assuming an annual 2 percent cost-of-living adjustment for payments to match the assumed inflation rate. In Chapter 4, the income annuity was priced for females. It offered a 4.56 percent payout rate.
In this case study, we use income annuities for males and couples, and we must also account for the fact that the annuity will not be purchased for twenty-five years. The corresponding payout rates for males and couples with annuities purchased today are 4.83 percent and 3.93 percent, respectively. However, with the longevity improvements assumed by the Society of Actuaries over the next twenty-five years, the male and joint income annuity payout rates at that time are 4.47 percent and 3.75 percent, respectively. These latter numbers are what I use. It makes sense to use different mortality tables to price the life insurance and annuities on account of the different populations that use these financial products. Annuity owners will tend to live longer.
To better understand the impacts of investment volatility on the upside and downside, Monte Carlo simulations are used to create a distribution of outcomes. The exhibits report the 10th percentile, median, and 90th percentile from this distribution. We can interpret the 10th percentile outcome as a bad luck case with poor investment returns. It is possible that retirement outcomes could be even worse, but generally Jerry and Beth could expect better retirement outcomes than seen at the 10th percentile. The median reflects more typical outcomes. It is the midpoint of the distribution, with a 50 percent chance for worse outcomes and a 50 percent chance for better outcomes. These are reasonable outcomes for Jerry and Beth to expect. The 90th percentile is a good luck outcome in which investments perform very well, supporting greater spending and larger account balances.
Note that these results are presented in terms of nominal dollars to avoid reader confusion about why inflation-adjusted dollars are less than nominal dollars. This decision does not impact any comparisons for the relative outcomes between scenarios. However, readers should understand that the purchasing power of a given amount of income or wealth will be less in the future. For today’s forty-year-olds, the real purchasing power of money will be about 60 percent of what it is today at age sixty-five, and about 30 percent of today at age 100, assuming 2 percent inflation.