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 semiannual 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 semiannual payout for rules two and three?
·
Why does an analysis based on only the first six
semiannual 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 semiannual
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 semiannual 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 semiannual 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 30^{th} month.
Fund Balances 36 Months
Into Retirement


Rule One

Rule Two

Rule TwoRule 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 midcap fund and a largecap 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
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