Early retirement: Our young (compared to us) neighbors have just announced that

Question

Early retirement: Our young (compared to us) neighbors have just announced that they are going to retire at age 53! Their goal was to have $1 million in investments and they just reached that milestone. I asked them how much they planned on living on. They plan on taking out $75,000 a year. Eventually, in about 14 years, they will supplement that with social security. Their financial advisor says their $1 million nest egg will last them until they are 80 years old not including any Social Security income. The advisor is assuming an annual rate of return of 6%.

A.Check that the advisor is correct.

B.Then explain what happens if the annual rate of return is only 4%.  

C.Will our neighbors be underfunded or overfunded? By how much and how many years will they be over/underfunded compared to their 80-year target. Ignore taxes and inflation.

Explanation / Answer

(a) Nest Egg Size = $ 1 million, Annual Withdrawal = $ 75000, Retirement Age = 53 years and Target Age = 80 years, Withdrawal Tenure = 80 - 53 = 27 years

The nest egg will be enough to last 27 years in conformation with the advisor's advice if the present value of the annual withdrawals at 6 % per annum is equal or almost equal to the nest egg of $ 1million

PV of Annual Withdrawals = 75000 x (1/0.06) x [1-{1/(1.06)^(27)}] = $ 990790.06 ~ $ 1000000

Hence, the advisor was correct.

(b) Annual Return Rate = 4 %

PV of Annual Withdrawals = 75000 x (1/0.04) x [1-{1/(1.04)^(27)}] = $ 1224718.93

As the PV of Annual Withdrawals is more than the nest egg, the advisor would be incorrect in his/her advice.

(c) The neighbours were underfunded as their nest egg falls short of the cumulative present value of their annual withdrawals.

Amount of Underfunding = 1224718.93 - 1000000 = $ 224718.93

Let the number of years for which the nest egg lasts at the annual withdrawal value of $ 1 million be T

Therefore, 1000000 = 75000 x (1/0.04) x [1-{1/(1.04)^(T)}]

Using EXCEL's Goal Seek Function to solve the above equation, we get:

T = 19.43 years ~ 19 years as years cannot have fractional values.

Underfunding in years = 27 - 19 = 8 years approximately.

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