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Suppose I attend college with 10k tuition fee per year meanwhile I have a part time job for 5k annually. After 3 years, I get a job for 45 years and earn 40k each year. What is my net present value in term of interate rate x?

I did try to form a formula like this, is it correct?

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To calculate the net present value of studying, you need to consider:

  1. the cash flow over your working life if you study;
  2. the cash flow over your working life if you do not study.

You have the information to infer 1. But the information you provide does not enable you to infer 2, so you cannot calculate the net present value.

The key information that is missing is how much you would have been able to earn in each of the 48 years if you did not study. Suppose for example that you would have earned 25k per annum in each year. Then the effect of studying would be that in each of the first 3 years, you would be worse off by 25k + 10k - 5k = 30k, and in each of the next 45 years you would be better off by 40k - 25k = 15k. The net present value from studying, given a discount rate $x$, is:

$$NPV = \displaystyle\sum_{n=1}^3\bigg(\frac{-30}{(1+x)^n}\bigg) + \displaystyle\sum_{n=4}^{48}\bigg(\frac{15}{(1+x)^n}\bigg)$$

This assumes that all cash flows are at the end of the relevant year and would need adjusting if any are at the beginning of or during a year.

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  • $\begingroup$ Thank you, now I know one more criterion for life decisions $\endgroup$ – Learner132 Feb 3 '19 at 13:53
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I did try to form a formula like this, is it correct?

No. You need to include the NPV of all years. Right now you are only considering two of those years (and it is not clear which year you refer to in the 2nd term).

Also, it is unclear from the problem whether tuition is paid in the beginning of each year or at the end thereof.

The discounting factor in the 2nd term is wrong. The discounting factor for a cash flow at the end of year $n$ is $$1/(1+x)^n$$.

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  • $\begingroup$ For the 1st term, if I paid at the beginning then t=2 and if at the end of t=3? $\endgroup$ – Learner132 Feb 3 '19 at 7:53
  • $\begingroup$ @Learner132 If both tuition and (part time) salary are paid at the end of year n (n=1, 2, 3), then t=n. Otherwise, t=n-1. But you still need to add the terms corresponding to the other two years of college+part_time_job and the other 44 corresponding to the job that pays 40k/year. $\endgroup$ – Iñaki Viggers Feb 3 '19 at 12:56

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