Consider an 18-year old who is about to undertake an investment in college. Supp
ID: 3210114 • Letter: C
Question
Consider an 18-year old who is about to undertake an investment in college. Suppose a college education begins now and continues for three more years into the future. Suppose this year’s tuition is $20,000 and tuition is expected to increase 7% per year while enrolled. The returns to schooling are in the form of a yearly $25,000 earnings premium (paid at year end) for this person from age 22 through age 67.
A. Calculate the net present value of this investment assuming an interest rate (discount rate) of 2.5%. Be sure to show the formula you use to calculate the net present value. (I have to be able to figure out how you calculated your answer.) Is there a financial payoff from this schooling? Demonstrate and explain.
B. Now suppose there is a 25% probability of failing/dropping out of college during the first year of school; having completed the first year suppose there is a 10% probability of failing/dropping out of college during the second year of school; having completed the second year suppose there is a 2% probability of failing/dropping out of college during the third year of school; having completed the third year suppose there is a 1% probability of failing/dropping out of college during the fourth year of school. If the student leaves college, then (s)he receives only a $1,500 earnings premium from dropout through age 67. Still presuming an interest rate of 2.5%, now what is the expected net present value of this investment? Be sure to show the formula you use to calculate the expected net present value. (I have to be able to figure out how you calculated your answer.) Is there an expected financial payoff from college education?
Explanation / Answer
a) Formula: NPV = R x {[1 – (1+i)-n] / i} – Initial Investment
R is the net cash inflow expected to be received in each period = $25,000
i is the discount rate per period = 2.5%
n are the number of periods during which the project is expected to operate and generate cash inflows = 67 – 22 = 45
Initial Investment = Present Value of all tuition fees paid
In order to calculate the NPV, we first need to determine the present value of all yearly tuition fees paid.
Fees paid in Year 1 = $20,000
Fees paid in Year 2 = $20,000*1.07 = $21,400
Fees paid in Year 3 = $20,000*(1.07)2 = $22,898
Fees paid in Year 4 = $20,000*(1.07)3 = $24,500.86
PV of fees paid in Year 1 = $20,000
PV of fees paid in Year 2 = $21,400 / (1.025)1 = $20,368.83
PV of fees paid in Year 3 = $22,898 / (1.025)2 = $21,263.07
PV of fees paid in Year 4 = $24,500.86 / (1.025)3 = $22,196.57
PV of total fees paid = $20,000 + $20,368.83 + $21,263.07 + $22,196.57 = $83,828.47
NPV = $25,000 x {[1 – (1+0.025)-45] / 0.025} – $83,828.47
= ($25,000 x 26.83302386) - $83,828.47
= $670,825.60 - $83,828.47
= $586,997.13
So, the NPV of the investment would be $586,997.13
Financial Payoff:
Year 1: Cash Outflow of $20,000
Year 2: Cash Outflow of $21,400
Year 3: Cash Outflow of $22,898
Year 4: Cash Outflow of $24,500.86
Year 5 to Year 49: Cash Inflow of $25,000 each year
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