# Introduction to Cash Flow Diagrams, NPV & IRR

Cash flow diagrams are a tool for organizing and visualizing information about a specific investment, business opportunity, or engineering project.  Drawing an accurate cash flow diagram helps financial analysts keep track of all the money flows that result from any decision.  However, the goal of net present value analysis is to simplify all of the disparate information in the cash flow diagram into a single number: present value.

“Net” present value refers to the difference between all of the costs resulting from a project and all of the revenues, after each is discounted to present value.  This video shows an example of a college student who is considering investing \$10K they’ve save for college in equipment for a landscaping business.  They make some assumptions about the cost of the equipment, the revenues they will receive from the business, and what they can sell the used equipment for.  Lastly, to complete the analysis, they need to choose a discount rate that reflects their time preference.  This could be the cost of borrowing the initial \$10K investment, or it could be some other value.

This video uses Excel to show how the net present value changes with respect to changes in discount rate.  Notice that Excel includes an “NPV” formula that saves the analyst the trouble of typing.

When an investment has positive net present value, then it is profitable.  However, this doesn’t necessarily say much about whether this investment is more profitable than alternative investments, relative to amount invested.  Another way to assess the quality of an investment opportunity is to calculate the internal rate of return (IRR).

The next video uses the same example, but instead of selecting a discount rate to calculate a net present value, we look for a discount rate that makes all the future revenues equivalent to the initial investment, which we call the IRR.  Investment opportunities with higher IRR are preferable to lower.

## 19 thoughts on “Introduction to Cash Flow Diagrams, NPV & IRR”

1. Hannah Dixon

PV is \$16,510.80
NPV is \$6,510.80

2. Ahmed Ahmed

The total PV is = \$16.51k hence profit of \$6.51k

3. Kristian Santana

The PV is \$16,510.80 and the NPV is \$6,510.80

1. Thomas P Seager

Well done. Several people miss the importance of NET present value.

Also, it’s interesting to think about the labor required to earn this return. How many hours? If the NPV were amortized over those hours, what would be the hourly wage?

1. Andres Amado

I was also intrigued by how the NPV would amortized over the hours spent working before reading your comment. The 2016 summer months conveniently work out to be exactly 13 working weeks. assuming a 40 hour work week the \$6,510.80 would equate to a value of \$12.52 per hour. this does not include the time spent selling the equipment in the fourth month.

4. Ken

I agree with Brandon. After inserting the formula into excel, It produced a value of 20.7% IRR.

5. Roberto Lins

PV = 16.5 K
NPV = 6.5 K

6. James

PV:\$16,510
NPV:\$6,510

7. Anthony Freitas de Oliveira

Present Value = 16,510.80
Net Present Value = 6,510.80
Internal Rate = 25.7%

1. Thomas P Seager

Your IRR is incorrect! Ask a classmate to post their work in more detail.

8. mariaacarvalho

Present value: \$16,510
Net: \$ 6,510

9. Ken

After subtracting the initial investment, it yields a 6.5k Net Present Value.

1. Thomas P Seager

This IS the present value of the discounted future cash flows. To get the NET present value, subtract the initial investment.

10. Trevor

I Agree with Ken, it took me a minute to come up with the correct present value. As Sal Khan pointed out in an his video, it was nice being able to replay certain content to grasp the understanding.

11. Ken

I ended up getting 16.5k as the present value making it a 6.5k profit at the end of the summer.