Diane has just turned 18 and also completed high school. She is wondering about

Question

Diane has just turned 18 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 $14,000, due at the beginning of the year (that is, right away). Based on historical trends she estimates that tuition will rise at 7% per year for the 4 years she is in school. She also estimates that her living expense above and beyond tuition will be $7,500 per year (assume this extra expense occurs at the end of each year only when she is in college) 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 $24,000 per year out of high school and expects that to grow 4% annually. With the college degree, she estimates that she will earn $47,000 per year out of college, again with annual 4% increases in salary. Either way, she plans to work until the day she turns 60 (she begins college right away). The interest/discount rate is 5%. What is the NPV of her college education? (Note: All cash flows except tuition payments occur at the end of the year.)

Explanation / Answer

In the given question, cash flow at the beginning of the period i.e. right away = $ 14000 (tuition fees)

Cash outflow at the end of Year 1 (i.e. beginning of Year 2) = tuition fees + additional living expense + opportunity cost of losing cash inflow

Therefore cash flow at the end of Yr 1 = (14000+7%) + 7500 + 24000 = $ 46,480

Cash outflow at the end of Year 2 = tuition fees + additional living expense + opportunity cost of losing cash inflow = 16028.6 + 8000 + 24960 = $ 48,988.60

Cash outflow at the end of Year 3 = tuition fees + additional living expense + opportunity cost of losing cash inflow = 17150.60 + 8500 + 25958 = $ 51,608.60

Cash outflow at the end of Year 4 = additional living expense + opportunity cost of losing cash inflow = 9000 + 26997 = $ 35,997

Had she taken only high school education, her salary at the end of Year 5 would be (24000+4%+4%+4%+4%) = $ 28,076.88 which would increase every year by 4%. Incremental salary at the end of year 5 on taking college education = 47000 - 28077 = $ 18,923, now this incremental salary of $ 18,923 would increase every year by 4% till next [60-(18+4+1)] = 37 years. So we need to calculate present value of 18923 received at the end of year 5 increasing by 4% every year for 37 years.

The formula for the present value of growing annuity = [P / (r-g)] * [1-(1+g / 1+r)n]

Using this, we get present value at year 4 of 18923 growing at 4% for 37 years = $ 5,64,234.55

Present value (at T0) of $ 564234.55 at the end of year 4 = $ 4,64,197

NPV = Present value of inflows - present value of outflows

NPV = 4,64,197 - (present value of 14000 at yr 0, 46480 in yr 1, 48988.6 in yr 2, 51608.6 in yr 3 and 35997 in yr 4) @ 5% discounting rate = $ 2,87,300

Thus the NPV of her college education = $ 2,87,300

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