Have you ever wondered if a college education is financially worthwhile? The U.S. Census Bureau collects data on income and education that throws some light on this question. A recent census publication (Current Population Reports, Series P-70, No. 11) reports the average annual wage income in 1984 of persons aged 35–44 by the level of schooling achieved. The average wage income of high school graduates was $13,000 per year. The average wage income of persons with bachelor’s degrees was $24,000 per year. The average wage income of persons with master’s degrees was $28,000 per year. The average wage income of persons with Ph.D.’s was $40,000 per year. These income differences probably overstate the return to education itself, because it is likely that those people who get more education tend to be more able than those who get less.
Some of the income difference is, therefore, a return to ability rather than to education. But just to get a rough idea of returns to education, let us see what would be the return if the reported wage differences are all due to education.
(a) Suppose that you have just graduated from high school at age 18. You want to estimate the present value of your lifetime earnings if you do not go to college but take a job immediately. To do this, you have to make some assumptions. Assume that you would work for 47 years, until you are 65 and then retire. Assume also that you would make $13,000 a year for the rest of your life. (If you were going to do this more carefully, you would want to take into account that people’s wages vary with their age, but let’s keep things simple for this problem.) Assume that the interest rate is 5%. Find the present value of your lifetime earnings. (Hint: First find out the present value of $13,000 a year forever. Subtract from this the present value of $13,000 a year forever, starting 47 years from now.)
(b) Again, supposing you have just graduated from high school at age 18, and you want to estimate the present value of your life time earnings if you go to college for 4 years and do not earn any wages until you graduate from college. Assume that after graduating from college, you would work for 43 years at $24,000 per year. What would be the present value of your lifetime earnings?
(c) Now calculate the present value of your lifetime earnings if you get a master’s degree. Assume that if you get a master’s, you have no earnings for 6 years and then you work for 41 years at $28,000 per year. What would be the present value of your lifetime income?
(d) Finally calculate the present value of your lifetime earnings if you get a Ph.D. Assume that if you get a Ph.D., you will have no earnings for 8 years and then you work for 39 years at $40,000 per year. What would be the present value of your lifetime income?
(e) Consider the case of someone who married right after finishing high school and stopped her education at that point. Suppose that she is now 45 years old. Her children are nearly adults, and she is thinking about going back to work or going to college. Assuming she would earn the average wage for her educational level and would retire at age 65, what would be the present value of her lifetime earnings if she does not go to college?
(f) What would be the present value of her lifetime earnings if she goes to college for 4 years and then takes a job until she is 65?
(g) If college tuition is $5,000 per year, is it financially worthwhile for her to go to college? Explain.