Question

# Consider an 18-year old who is about to start a three-year course of study. The total...

Consider an 18-year old who is about to start a three-year course of study. The total cost of the course is \$18,000, payable in advance. The returns take the form of annual \$5,000 earnings premiums (paid at year-end) that the individual receives from age 21 through to age 25. Calculate the net present value of this investment assuming the discount rate of 5%. Should the project go ahead? Please, explain all the calculations! :)

NPV = Present value of the earnings premium - The total cost of the course

First earnings premium is when the individual is 21 and the last premium is when the individual is 25. There are 25 - 21 + 1 = 5 earnings premium.

The first earnings premium (when 21) is 3 years away, the second premium (when 22) is 4 years away and so on..

The last earnings premium (when 25) is 7 years away.

NPV = 5000/(1 + 0.05)^3 + 5000/(1 + 0.05)^4 + 5000/(1 + 0.05)^5 + 5000/(1 + 0.05)^6 + 5000/(1 + 0.05)^7 - 18,000

NPV = 4,319.1879926574 + 4,113.5123739594 + 3,917.6308323423 + 3,731.0769831831 + 3,553.4066506506 - 18,000

NPV = \$1,634.81483279

Yes, the project should be taken because it has a positive NPV.