**Week 4: Personal Finance**

*“Putting It All Together with NPV and IRR”*

*(Source URL)*

**Summaries**

- Week 4 > Module 3 - Part 3: Putting It All Together with NPV and IRR > Introduction to Net Present Value and Internal Rate of Return
- Week 4 > Module 3 - Part 3: Putting It All Together with NPV and IRR > Work Interruptions - A More Realistic View
- Week 4 > Module 3 - Part 3: Putting It All Together with NPV and IRR > Putting It All Together

__Week 4 > Module 3 – Part 3: Putting It All Together with NPV and IRR > Introduction to Net Present Value and Internal Rate of Return__

__Week 4 > Module 3 – Part 3: Putting It All Together with NPV and IRR > Introduction to Net Present Value and Internal Rate of Return__

- So how do we make dollars received in the future comparable to dollars received today? We use a discount rate.
- A big question is, what discount rate to use? The discount rate should be the minimum return that you would accept to make the investment.
- Over time, stocks yield around 6%. And in today’s environment, treasury bonds are yielding around 2%. So what is the minimum return that you would accept to make an investment in human capital? In today’s environment, discount rates are typically around 4%. And we’re going to use a 4% discount rate for this course.
- With this discount rate, overall, does it look like human capital investments are good investments? Recall from previous work that on average, returns to human capital range from around 5% to 15%. So on average, it seems as if human capital investment, in today’s environment, is worth it.
- Armed with the discount rate, we are ready to pull all costs and all benefits of human capital investments together.
- The first is net present value, and the second is the internal rate of return.
- The internal rate of return is the discount rate that would make the net present value equal 0.
- How do we interpret, and how do we use, the internal rate of return? First of all, use- the internal rate of return is a rate of return like the rate of return on a stock or a bond.
- It allows you to compare the rate of return for your human capital investment with any alternative that you might have.
- If the internal rate of return is greater than the discount rate, then your human capital investment is worth it.
- If the internal rate of return is less than the discount rate, forget it.
- If the internal rate of return is equal to the discount rate, I think I’ll leave you with this question and let you answer it.
- As we’ve discussed previously, we’re going to assume the discount rate is 4%. Now let’s take a look at how we’re going to calculate net present value and internal rate of return.
- In order to do this, we have to have both the costs of her college and the returns to her college.
- It is this row, column F, that we’re going to use to calculate both the internal rate of return and the net present value.
- The discount rate is in cell B11. We have that here.
- What about getting an internal rate of return, so we can compare, let’s say, to the return on stocks or the return on bonds? We again use the same sort of information, but we don’t use a discount rate.
- Rather, we’re going to see what discount rate would make the net present value equal to 0.
- That is, what is her rate of return to her college investment? And here what we do is we use the function IRR, and we use the information from cells 19 through 66.
- Doing this, we find out that the internal rate of return to her investment in college, if she works all the time, is 15%. An extremely good rate of return.

__Week 4 > Module 3 – Part 3: Putting It All Together with NPV and IRR > Work Interruptions – A More Realistic View__

__Week 4 > Module 3 – Part 3: Putting It All Together with NPV and IRR > Work Interruptions – A More Realistic View__

- As you can see, the female high school graduates spend the smallest proportion of their careers employed, a little less than 70%. And male college graduates spend the largest proportion of their time employed, 88%. None of those numbers are 100%, so our assumption to date have not been very realistic.
- Life happens, and when you’re estimating your returns to education, you need to incorporate the fact that you will sometimes be unemployed, and sometimes be out of the labor force.
- So what would Natalia’s return to her investment in a college education be, if we make more realistic assumptions regarding labor force participation? This spreadsheet will show you that.
- Here’s the rate of increase in the money costs of college, and in the opportunity costs of college.
- Question is, how does this affect her net present value and internal rate of return? So let’s calculate the net present value.
- That is all of the cost data and all of the returns data in cells I25 through I72.
- Returning, we find out that her net present value, when she has a more realistic life trajectory, is only about $400,000, rather than almost $660,000.
- What about internal rate of return? Well, recall that our internal rate of return formula requires only the data on all of the costs and all the returns to the investment.
- All in column I. Some of you have asked what this 0.1 is, and this is the default guess as to the rate of return.
- If you thought the return was going to be 20%, you would put 0.2 there.
- We see that the internal rate of return also declines, from 15% to 13%. But still, much higher rate of return than you would expect for stocks over the long run, of say about 6%. Her college education, even with time out of the labor force, and unemployment, still is a very good investment.
- How does a more realistic life affect Natalia’s return to her college education? Well, the net present value of her college education is approximately half what it was if she worked all the time.
- Natalia’s internal rate of return to her college education goes from 15%, when she works all the time, to 13% when life happens.

__Week 4 > Module 3 – Part 3: Putting It All Together with NPV and IRR > Putting It All Together__

__Week 4 > Module 3 – Part 3: Putting It All Together with NPV and IRR > Putting It All Together__

- In order to make future dollars comparable to present dollars we discount them, and we do this using the discount rate.
- We developed two measures that give you an overall evaluation of the worth of any investment in education and training.
- The first of these is net present value, and the net present value gives you a dollar value for your investments in education and training.
- The second is the internal rate of return, which tells you what rate of return your human capital investment is earning.
- Net present value and internal rate of return are central concepts to economics and finance, and we will be using these concepts as we analyze other types of investments, such as real estate investments, bond investments, and stock investments.

**Return to Summaries**

**Return to Summaries**

*(image source)*