Suppose that the average earnings for high school graduates is $25,000, the tuition, fees, and books for typical

year of college total $10,000 and that a college degree takes 5 years.
a) How large must the present value of the increment to earnings from getting a college degree be to make this
investment show a positive return?
b) How much must the present value of the increment to earnings be for this investment to show a return of
10%?

To calculate the present value of the increment to earnings, we can use the concept of net present value (NPV). NPV is the present value of cash inflows minus the present value of cash outflows. In this case, the cash inflow is the increment to earnings from getting a college degree, and the cash outflow is the cost of college education.

To calculate the NPV, we need to discount the cash flows to their present value using an appropriate discount rate. The discount rate can represent the rate of return desired or the opportunity cost of investing the money elsewhere.

a) To make the investment show a positive return, the present value of the increment to earnings should be greater than the present value of the cost of college education.

Let's calculate the NPV assuming a discount rate of 0% (no discounting applied):

Increment to earnings: $25,000 - $10,000 = $15,000 per year
Present value of increment to earnings (PVIE):

PVIE = Increment to earnings * Number of years
= $15,000 * 5
= $75,000

Since the cost of college education is $10,000 per year, the present value of the cost (PVC) would be:

PVC = Cost of college education * Number of years
= $10,000 * 5
= $50,000

The NPV is calculated as:

NPV = PVIE - PVC
= $75,000 - $50,000
= $25,000

Therefore, the present value of the increment to earnings should be at least $25,000 for the investment to show a positive return.

b) To calculate the present value of the increment to earnings that would result in a 10% return, we need to use the discount rate of 10%:

Present value of the increment to earnings (PVIE) = Increment to earnings * (1 - (1 + r)^(-n)) / r

Where r is the discount rate (0.10 in this case) and n is the number of years (5 years).

PVIE = $15,000 * (1 - (1 + 0.10)^(-5)) / 0.10

PVIE ≈ $54,555.70

Therefore, the present value of the increment to earnings should be approximately $54,555.70 for the investment to show a return of 10%.

Note: The above calculations assume a simple discounting method and do not account for factors such as inflation or other potential variables that may affect the calculation in real-life scenarios.