Homework Set 3 due November 5

A high school graduate has to decide between working or going to college.If the person works, he or she will work for the next 50 years.If the person goes to college, he or she will be in college for 5 years, and then work for 45 years.In this model, the rate of discount that equates the lifetime present value of not going to college and going to college is 6.249% when the cost of each year of college is $26,000, each year of non-college work pays $36,000, and each year of post-college work pays $65,000.For each of the parts below, explain how the rate of discount that equalizes the two options (the internal rate of return) would be determined, what the internal rate of return is, and who would make a different schooling decision based on the change.(Hint: Use Excel to show that the internal rate of return to schooling is 6.351115% in the above case, and solve for the rates of discount that equalize the present discounted value for both of the options in each of the parts below. Calculating the internal rate of return for each case is straightforward in Excel by using the IRR function.) An Excel spreadsheet will be provided to students and reviewed in class before the homework is due.

(1) Each year of college still costs $26,000 and each year of post-college work still pays $65,000, but each year of non-college work now pays $35,000.

(2) Each year of college still costs $26,000 and each year of non-college work still pays $36,000, but each year of post-college work now pays $70,000.

(3) Each year of non-college work and post-college work still pays $36,000 and $65,000 respectively, but now each year of college costs $28,000.

(4) Each year of college again costs $26,000.The first year of non-college work pays $36,000 but then increases by 3 percent each year thereafter.The first year of post-college work pays $65,000 but then increases by 4 percent each year thereafter. (You will need to know how to determine pay for non-college and post-college work in later years using the spreadsheet.)

Note: In the human capital model of the decision to go to college, an individual compares the "rate of return" from going to college and their own personal discount rate. The "rate of return" is the internal rate of return calculated in the spreadsheet based on specific assumptions about the pay levels for non-college work and post-college work and the cost of college. The personal discount rate, however, varies from person to person. If a person has a personal discount rate less than the rate of return, they will decide to go to college. If the person has a personal discount rate more than the rate of return, they will decide not to go to college. Comparing two cases (as in either (2) or (3) above), if the rate of return is different, some people will decide to go to college in one of the cases but not the other, depending on their personal discount rates. These are the people who make a different schooling decision.

In considering these alternative examples, be sure to discuss how the discount rate that equalizes the two Present Values changes, and who would make a different decision based on the change (that is, people who originally would not have gone to college deciding to go to college, or people who originally decided to go to college changing their mind and now deciding not to go to college).

Year PDV College 100.000000% $36,000 107.734766% $36,000 $33,415 $26,000 SO $26,000 $62,000) 125.045370% $36,000 $28,790 ($26,000 ($20,792 PDV College 134.717336% $36,000 $26,723 $26,000 $26,000 $19,300) PDVNo College $489,341 145.137407% $36,000 $24,804 $65,000 $29,000 156.363445% $36,000 SO $65,000 $65,000 $41,570 $29,000 IRR, internal rate of retu 168.457792% $0 Assumptions 10 195.525249% $36,000 $18,412 SO $65,000 $33,244 $29,000 Cost of College $26,000 11 226.941850% $36,000 SO $65,000 $65,000 $28,642 $29,000 College Income $36,000 $0 $65,000 $65,000 $26,585 $29,000 263.406407% $36,000 $13,667 SO $65,000 $65,000 $29,000 283.780276% $36,000 SO $65,000 $29,000 305.730016% 329.377516% $36,000 $10,930 SO $65,000 $65,000 $19,734 $29,000 354.854096% $36,000 $10,145 SO $65,000 $65,000 $29,000 19 $36,000 SO $65,000 $29,000 411.871334% $36,000 SO $65,000 $29,000 443.728617% $8,113 $0 $29,000 22 478.049986% $36,000 SO $65,000 $65,000 $29,000 23 515.026033% $36,000 $6,990 SO $65,000 $65,000 $29,000 24 554.862090% $36,000 $6,488 SO $65,000 $65,000 $11,715 $29,000 25 26 644.016208% $36,000 $5,59 SO $65,000 $65,000 $10,093 $29,000 27 693.829353% $0 $65,000 $65,000 $9,368 $29,000 28 747.495429% $36,000 $4,816 SO $65,000 $65,000 $29,000 29 805.312450% $36,000 SO $65,000 $8,071 $29,000 30 867.601482% $4,149 $65,000 $29,000 31 934.708424% $36,000 $3,851 $O $65,000 $65,000 $6,954 $29,000 32 $36,000 SO $65,000 $65,000 $6,455 $29,000 33 1084.895482% $36,000 $3,318 SO $65,000 $65,000 $5,991 $29,000 34 $0 $29,000 35 1259.214293% $36,000 $2,859 SO $65,000 $65,000 $29,000 36 1356.611569% $2,654 SO $65,000 $29,000 37 1461.542297% $36,000 $2,463 SO $65,000 $65,000 $29,000 38 1574.589171% $2,286 SO $65,000 $65,000 $29,000 39 $0 40 1827.590972% $1,970 SO $65,000 $3,557 $29,000 41 $36,000 $1,828 SO $65,000 42 2121.244591% $36,000 SO $65,000 $65,000 $29,000 43 2285.317892% $36,000 $1,575 SO $65,000 $65,000 $2,844 $29,000 44 2462.081879% $1,462 $0 $65,000 $65,000 $29,000 45 SO $65,000 $65,000 $29,000 46 2857.684212% $36,000 SO $65,000 $65,000 $29,000 47 3078.719393% $1,169 SO $65,000 $65,000 $2,111 $29,000 48 3316.8511289 $0 49 3573.401794% $36,000 So $65,000 $29,000 50 $935 So $65,000