## Sunday, January 3, 2016

### 401(k) Disbursement Strategies: A Simplified Example

Question One:  A person has \$300,000 in a 401(k) plan.  The funds are in a single index covering the entire U.S. stock market.  She is just starting her retirement and is considering two different disbursement rules.

Rule One:  Disburse \$6,000 every 6 months.

Rule Two:  Disburse the minimum of 0.04/2 x the initial account balance or \$6,000 every 6 months.   Should \$6,000 exceed the disbursement the difference would be made up from an emergency cash account outside the 401(k) plan.  Under rule two, the retiree will never sell more than 200 shares in one disbursement period.

A financial crisis starts as soon as she retires.   The price history of the stock fund over the first six semi-annual payments is described below.

 Month Price of Stock Fund 0 \$30 6 \$25 12 \$20 18 \$15 24 \$20 30 \$30

Questions:

·      What is the balance of the 401(k) plan at month 30 under the three scenarios?

·      How much extra cash does the person need to fund the \$6,000 semi-annual payout for rules two and three?

·      Why does an analysis based on only the first six semi-annual payments understate the advantages of rule two over rule one?

Analysis:

Analysis of Rule One:

The fund initially has 10,000 shares (\$300,000/\$30).

The number of shares sold to fund the \$6,000 semi-annual disbursement varies based on the price of the shares.   The number of shares sold is simply \$6,000/Share Price.

The financial calculations for disbursements from rule one are laid out in the table below

 Financial Calculations For Rule One Month SPRICE SSOLD DISB ECASH Month Price of Stock Fund Shares Sold Disbursement From 401(k) Disbursement From Cash Account 0 \$30 200.0 \$6,000 \$0 6 \$25 240.0 \$6,000 \$0 12 \$20 300.0 \$6,000 \$0 18 \$15 400.0 \$6,000 \$0 24 \$20 300.0 \$6,000 \$0 30 \$30 200.0 \$6,000 \$0 Total 1640.0 \$36,000 \$0

Observations for Rule One:

·      Under rule one, the fund needs to sell 1640 shares over the first six semi-annual payments.

·      No extra cash payment is made.

Analysis of Rule Two:

Again we start with a fund that has \$300,000 invested in a stock index with an initial share price of \$30.   Initially we have 10,000 shares.

Under rule two, we sell 200 shares every six months and make up any short fall from a separate cash account.  (Rule two creates an upper bound on shares sold at 200 shares every disbursement period.)

Disbursement calculations for rule two are summarized below.

 Financial Calculations For Rule Two Month SPRICE SSOLD DISB ECASH Month Price of Stock Fund Shares Sold Disbursement From 401(k) Disbursement From Cash Account 0 \$30 200.0 \$6,000 \$0 6 \$25 200.0 \$5,000 \$1,000 12 \$20 200.0 \$4,000 \$2,000 18 \$15 200.0 \$3,000 \$3,000 24 \$20 200.0 \$4,000 \$2,000 30 \$30 200.0 \$6,000 \$0 Total 1200.0 \$28,000 \$8,000

Observations for Rule Two:

·      Under rule two the fund sells 1200 share on the first six semi-annual payments.

·      The retiree needs to take \$8,000 out of her emergency cash fund to make up for the shortfall due to stock price decline.

Comparing End of Fund Values:

Is the person better off under rule one or rule two?

The table below summarizes the changes in wealth under the two rules on the 30th month.

 Fund Balances 36 Months Into Retirement Rule One Rule Two Rule Two-Rule One Remaining Share in 401(k) Plan 8360 8800 440 Value of 401(k) Plan \$250,800 \$264,000 \$13,200

Observations:

·      The balancer under rule two at 30 months after retirement is \$13,200 higher than the balance under rule one.  The savings from the 401(k) plan from limiting disbursements during the downturn exceeds the \$8,000 disbursement from the emergency cash fund.

Concluding Comments:

The comparison of fund balances at 30 months understates the potential gains from a rule that limits disbursements during market down turns.   The gap in outstanding fund balances between the two disbursement rules studied here will grow overtime if the market continues to rebound.

Author’s Note:  This post assumes all money in one fund.   A previous post found potential gains from dividing the equity allocation into a mid-cap fund and a large-cap fund rather than putting all money in a total stock market fund.

The link to this post is below.

You may want to look at my finance books on Kindle:

Solving Financial Problems in Excel

The Nine Essays on Debt and Your Retirement