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%?
a) calculate the present value of the investment. Since this requires a rate of discount (r), which you do not provide, just show the formula. The PV of the investment is 10000*(1 + (1+r) + (1+r)^2 + (1+r)^3 + (1+r)^4))
for b) increase a) by 10%
To determine the present value of the increment to earnings, we need to calculate the future value of the increment and then discount it back to the present value using an appropriate discount rate.
a) To make the investment show a positive return, the present value of the increment to earnings from getting a college degree must be larger than the cost of obtaining the degree. Here's how to calculate it:
1. Calculate the total earnings from a high school graduate over 5 years: $25,000 * 5 = $125,000
2. Calculate the total earnings from a college graduate over 5 years: ($25,000 + increment) * 5 = $125,000 + (5 * increment)
3. Subtract the cost of obtaining the degree ($10,000) from the total earnings of a college graduate over 5 years: $125,000 + (5 * increment) - $10,000
4. Set the result of step 3 greater than zero to find the minimum value for the increment:
$125,000 + (5 * increment) - $10,000 > 0
Solving the inequality:
$125,000 + (5 * increment) - $10,000 > 0
5 * increment > $10,000 - $125,000
5 * increment > -$115,000
increment > -$115,000 / 5
increment > -$23,000
Therefore, the present value of the increment to earnings must be greater than -$23,000 for the investment to show a positive return.
b) To calculate the present value of the increment to earnings needed for a 10% return, we need to discount the future earnings back to the present using the 10% discount rate. Here's how to calculate it:
1. Calculate the future value of the increment to earnings using the formula for compound interest:
Future Value = present value * (1 + interest rate)^n
In this case, the interest rate is 10% or 0.10, and n is 5 years.
Future Value = present value * (1 + 0.10)^5
2. Divide both sides of the equation by (1 + 0.10)^5 to isolate the present value:
present value = Future Value / (1 + 0.10)^5
3. Substitute the values into the equation:
present value = ($125,000 + (5 * increment)) / (1.10^5)
Therefore, the present value of the increment to earnings must be equal to or greater than the result of the equation ($125,000 + (5 * increment)) / (1.10^5) for the investment to show a return of 10%.