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# Calculating the Net Present Value of Education

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Diane has just 18 and also completed high school and is wondering about the value of a college education. She is pretty good with numbers, and driven by financial considerations only, so she sits down to calculate whether it is worth the large sum of money. She knows that her first year tuition will be \$12,000, due at the beginning of the year (that is, right away). Based on historical trends she estimates that tuition will raise at 6% per year for the 4 years she is in school. She also estimates that her living expense above and beyond tuition will be \$8,000 per year (assume this occurs at the end of the year) for the first year and will increase \$500 each year thereafter to keep up with inflation. She does not plan to work at all while attending school. Where she to forgo college she would be able to make \$25,000 per year out of high school and expects that to grow 3% annually. With the college degree, she estimates that she will earn \$45,000/year out of college, again with annual 3% increases in salary. Either way, she plans to work until 60 (she begins college right away). The interest/discount rate is 6%. What is the NPV of her college education? (Note: All cash flows except tuition payments occur at the end of the year.

#### Solution Preview

1st year Tuition = \$12,000
2nd year Tuition = \$12,000 X .06 = 720 , 12000 + 720 = \$12720
3rd year Tuition = \$12720 X 0.06 = 763.2 , 12720 + 763.2 = \$13483
4th year Tuition = \$13483 X 0.06 = 809, 13483 + 809 = \$14292

Total tuition = \$12,000 + \$12720 + \$13483 + \$14292 = \$52,495

Living expenses

1st year = \$8000
2nd year = 8000 + 500 = \$8500
3rd year = 8500 + 500 = \$9000
4th year = 9000 + 500 = \$9500

Total living expenses = \$35000

Her total investments for college ...

#### Solution Summary

The expert calculates the net present value of education.

\$2.19