Sunday, December 15, 2013

The Cost of Child Care

How much does infant care cost in Eugene?

For the "big three" centers, the average price for infant day care is roughly $12,900 per year.

Oregon is the third most expensive state for infant care.

So much for the price.  What is the financial cost?

Let's consider two families.  Both pay for two years of infant care.  They could be doing something else with that money.  Let's measuring the "opportunity cost" in dollars.

If they saved their monthly payments those would earn interest.  So we should use the Sum of Annuity Due formula from Activity 11 of my Math 25 Workbook.
Total = [Principal × (1 + rate)(payments + 1) − Principal × (1 + rate)] ÷ rate
They have 24 payments (2 years is 24 months).  The first family instead does something with their money worth 5% annual interest.  The second family is better at investing and uses 11% annual interest.

(Note: 5% and 11% are reasonable lower and upper bounds for traditional investment portfolios.  In fact, 11% is my family's five-year average rate of return.  That is much less than the overall stock market, at 17.6%, but of course not all of our money is at risk in stocks!)

The two-year costs for each family are:
At 5% annual interest:  [ $1,075 × (1 + 0.05/12)25 − $1,075 × (1 + 0.05/12) ] ÷ (0.05/12) ≈ $27,188

At 11% annual interest:  [ $1,075 × (1 + 0.11/12)25 − $1,075 × (1 + 0.11/12) ] ÷ (0.11/12) ≈ $28,975

But the opportunity cost does not end when their children enter preschool.  The families are no longer making a choice spending money on infant care instead of saving it (or spending it on other things).  But their expense does grow through the lost interest it could have been earning them.

We use compound interest formula.
Total = Principal × (1 + rate)payments
Let us think about college.  These children will be college-aged in 16 more years.
At 5% annual interest:  $27,188 × 1.0516$59,000

At 11% annual interest:  $28,975 × 1.1116 $154,000

So the money they spent on infant care could cover the expense of private college, depending upon how wisely it was saved and invested.

I wonder how many families paying for infant care in Eugene realize that the expense is equivalent to paying for college for their kid?  Or doing that much other stuff with the money?

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