Do you or Karen Olsen need life insurance?

Karen Olsen is 24-years old, single, and works in investment banking in New York.   On her day off, she roams freshly cut hay fields.   Her financial condition is similar to other recent graduates:  Karen has student loans, credit card debt, a checking account and a 401(k) to which both Karen and her employer contribute.  One of Karen’s college friends, Don, took his first job with a new England life insurance company.    Don pitched Karen about purchasing a $100,000 life insurance policy, and Karen is unsure what to do.  What should Karen do?

The economics of the life-cycle model provide a clear answer.  Karen should not buy life insurance.   The test of the life insurance purchase decision first considers who would lose economically by Karen’s pre-mature death.   Karen has significant human capital potential that dictates her present and future consumption; however, only Karen loses upon her death.  Karen lives alone, and has no children or husband.  Karen’s human capital is funding her standard of living and no one else.   Any serious consideration of a life insurance purchase by a single person should be a non-starter.

The life insurance question becomes much more interesting for dual income households or families.  Karen and Don have another classmate, Alex who has been married to Cathy for a year.  Both work in well-paying technology jobs and have a bunch of fun with their discretionary spending.   Alex and Cathy separately have promising human capital levels albeit different incomes today.  But imagine what consumption can become when a household is funded by two salaries?   There are many financial advantages to being “coupled,” importantly the living standard per person is higher than either individual living separately because many expenses can be shared.   Two adults who live together live better than two individuals living separately.  One estimate is that two adults who live together live as cheaply as 1.6 singles.
 
The Alex/Cathy household have joint human capital and a jointly higher living standard compared to either Alex or Cathy living individually.  If the living standard per person is higher in a two person household, then it stands to reason that the living standard of the survivor will change disproportionately when the other dies.   The focus here is on death, but disruptions to the household living standard because of human capital changes are obviously not limited to the peril of death.  People get laid off, become ill or disabled, or may elect to stop working.   In pre-mature death, human capital is being taken away and a two-income household becomes a one income household.   The marvelous feature of a life insurance policy is the insurance benefit is triggered by death, and any lost human capital can be immediately restored.  If the standard of living of a survivor changes upon the death of another, the insurance benefit can put the survivor back to their living standard just prior to death.   In Cathy’s case, if Alex or a child(ren) is dependent on Cathy’s ability to product an income, then the risk of pre-mature death can be consequential.  How consequential lies in the numbers.

To illustrate, a life-cycle model for the Alex/Cathy household is built following the same principles as a model for an individual.  Suppose Alex and Cathy are both age 26.  Alex earns $90,000 per year and Cathy earns $130,000 per year.  Both expect to work through age 67 (42 more years) and have a life expectancy of age 90 (65 years of remaining longevity).    Assuming growth in annual incomes matches the inflation rate, these initial income amounts can be treated as real income amounts for every year of their working lives. 
 
The household level of annual consumption is the adding up of the income amounts during the working lifetimes (42 years) of both Alex and Cathy and dividing by their expected longevity (65 years).  Alex and Cathy optimally consume $142,154 each year and the standard of living per person is $88,846 ($142,154/1.6).

Life insurance needed today
Life insurance need is determined separately for Alex and Cathy.   The conceptual approach is the same.  Let’s explore Alex’s need for life insurance on Cathy.  If Cathy dies today, then, ideally, Alex needs to maintain his same living standard as if Cathy were alive.  Alex’s own human capital will not create the same standard of living he is now enjoying as can be seen in Table 2.  His individual living standard is $58,154 per year which is about $30,000 less than the living standard he enjoys while living with Cathy and her human capital.

The life insurance prescription offered by the life-cycle approach is to derive the amount of death benefit needed by Alex today should Cathy die today, in order to fund his living standard annually for the balance of his life.  Table 3 gives the calculations assuming we are at the end of Alex’s current age 26.   Alex needs a total amount today of $5,686,164 (64 * $88,846) to maintain his living standard.  His own remaining human capital covers a large chunk of that number plus Alex and Cathy’s savings to date.  The difference between Alex’s resources and the “total amount needed” would be provided by the life insurance death benefit.  So, the prescription is to buy a life insurance policy in the amount of $1,918,308 (yes that can be done if Alex is healthy) for the current year.

One last note.  Cathy is the higher earner.  Therefore, if the question is the amount of life insurance Cathy should buy on Alex, then we can reason that Cathy will need to buy less life insurance on Alex’s life because she has more human capital.  The calculation is detailed in Table 4.  The target survivor living standard is the same but Cathy’s human capital remaining at the end of the year is $5,330,000, reflecting her higher income potential.  If Alex were to die, then Cathy would need a life insurance death benefit of $278,308 to maintain her living standard.

"Karen Olsen" comes to us from this key contributor.