Wednesday, October 30, 2013

### Present Value and Cash Flows

Several critics of the *Economic
Value of a Law Degree* have made mathematical errors or misunderstood the
contents of the study. One example
relates to a fundamental financial concept, net present value. The net present value is the value today of
cash flows or payments that will be given or received in the future.

The psychological and financial costs to the recipient of delay in payment are already incorporated into present value—present value is the equivalent of an immediate lump sum payment with no delay.

The difference between present value and nominal future value can be large. For example, the value of a single $1,000,000 payment forty years from now is just over $97,200 today (assuming a 6 percent nominal discount rate). In other words, receiving $1,000,000 in forty years is financially and psychologically the same as receiving $97,200 today.

In *The Economic Value of
a Law Degree, *Frank McIntyre and I describe the law degree earnings
premium—the difference in earnings between law degree holders and similar
bachelor’s degree holders—on both an annual basis and, for the lifetime value,
in present value terms. In other words,
we show what a lifetime of higher earnings is worth *immediately*, as of the start of law school, not spread out over the
course of a lifetime.

The pre-tax, pre-tuition present value of a lifetime of higher earnings is approximately $1,000,000 at the mean and $600,000 at the median. This includes the opportunity costs of lower earnings while in school, and the cost of interest payments on student loans.

The law graduate will not get to keep the full present value. Approximately 30 percent will go to the government as income and payroll tax revenue, and some of the remainder will go to the law school to pay for the cost of the legal education.

One critic, Steven Harper, took an estimate of the after-tax, after tuition net present value at the median ($330,000) and erroneously claimed that this amount of money would be spread out over a 40-year career. Dividing by 40 years and again by 12 months, Harper claimed that the law graduate would receive “at most a lifetime average of $687 a month.” (Or $8,175 per year).

In other words, Harper conflated present value with future values and miscalculated the private return on a legal education. If cash flows were level during the 40 years after law school, it would take more than $25,000 per year in after tax, after debt-service payment, nominal dollars to equal a present value of $330,000 as of the start of law school. In 2012 inflation-adjusted dollars, it would require about $16,000 per year. Harper is off by a factor of about 2 or 3.

In practice, cash flows will not be level—they will be lower in the initial years and rise through middle age. The present value calculation already incorporates the cost of lower cash flows in the initial years. To the extent that cash flows in the initial yeasrs are a concern, some students may use debt repayment options with lower payments in the initial years. The costs of these programs are already incorporated into our present value calculations.

http://leiterlawschool.typepad.com/leiter/2013/10/present-value-and-cash-flows.html