Calculate the net present value of the difference between the average salary of
ID: 2458819 • Letter: C
Question
Calculate the net present value of the difference between the average salary of a high school graduate and the average salary of a collge graduate between 22 and 65 years old. How does this compare to the tuition cost over four years? Make sure to discount salaries before taking a sum. A proper solution should have clear assumptions and do proper discounting of the salary over time. Calculate the net present value of the difference between the average salary of a high school graduate and the average salary of a collge graduate between 22 and 65 years old. How does this compare to the tuition cost over four years? Make sure to discount salaries before taking a sum. A proper solution should have clear assumptions and do proper discounting of the salary over time.Explanation / Answer
Assume that, when an 18 year old graduates from high school, he has two options: enter the work force or continue his education. If he enters the workforce, then he begins to earn an annual salary at the age of 18. If, however, he decides to invest in higher education, he will forfeit four years of annual salary and will have the cost of tuition and fees until the age of 22. The magnitude of this cost will depend on the level of institution he decides to attend.
Let Cth be the person's compensation in the year t given that he holds only a high school diploma. The person's expected lifetime compensation is E(Ch ). In each year t, compensation is the total of annual wage , Wth , plus employer-paid benefits that are a fraction , Bth , of the person's salary.
Cth = Wth (1+ Bth ) .
Assuming that the person's wage grow at a constant rate , gh , compensation for the year t+k is.
Ct+kh = Cth (1+ gh )k
The compensation the person expects to receive in a given future year is a function of the future compensation and the likelihood of the person being employed. The likelihood of being employed is the product of the labor force participation rate for the high school graduate , Lth , one minus the unemployment rate Uth , and one minus the absence rate, Ath . There is also a labor force participation rate by age , Pt , regardless of educational attainment. To ensure participation rates are not double counted , let Fth , be the average between Pt and Lth . The eqaution for expected income of high school graduate is
E(Ch ) = Et=20032052 Cth Fth (1- Ath) (1- Uth ) (Here Et=20032052 is summation symbol)
The present value will be calculated using a risk free interest rate r, since, the risk is already included in the form of particitpation, absence and unemployment rates. Present value is calculated by :-
PVth,2003 = E(Ch )/ (1+r)t
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