Diane has just turned 19 and also completed high school. She is wondering about

Question

Diane has just turned 19 and also completed high school. She 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 involved. She knows that her first year tuition will be $13,000, due at the beginning of the year (that is, right away). Based on historical trends she estimates that tuition will rise at 5% 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. Were she to forgo college she would be able to make $23,000 per year out of high school and expects that to grow 3% annually. With the college degree, she estimates that she will earn $47,000 per year out of college, again with annual 3% increases in salary. Either way, she plans to work until 64 (she begins college right away). The interest/discount rate is 8%. What is the NPV of her college education?

Explanation / Answer

Hi,

Please find the correct answer as follows:

Tution fee:

Year 0 = $13000

Year 1 = 13000*1.05

=$13650

Year 2 = 13650*1.05

=$14332.50

Year 3 = 14332.50*1.05

=$15049.13

Living Expense:

Year 1 = $8000

Year 2 = $8500

Year 3 = $9000

Year 4 = $9500

Present Value of college expenditure:

Hence, the present value of college expenditure is $78695.24

Present Value of salary:

Present value of salary earned = $805389.14

NPV = $(805389.14-78695.24)

=$726693.90

Year Expenditure Present Value 0 13000 13000 1 21650.00 20046.30 2 22832.50 19575.19 3 24049.13 19090.97 4 9500.00 6982.78 Present Value 78695.24

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