Project Evaluation: Net Present Value Calculation

What piece of information from the time value of money calculations do you think will be the deciding factor?

Suppose you buy a website for EUR 100,000 that will generate after-tax cash inflows of 30,000 per year in Year 2 through Year 5. Then the project is over, with no residual value. So it looks like this on a timeline: | Year | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | Cash Flow | -100,000 | 0 | 30,000 | 30,000 | 30,000 | 30,000 |

Absolutely! You have to get all of these value in the same time period in order to evaluate them, and that requires discounting. So a discount rate is chosen; something like the cost of capital for the project. What sort of discount rate would make this project still look good?

No, the periodicity does make a difference, but a small one. With projects, you'll typically just use annual compounding.

To summarize this discussion: [[summary]]

No, the PV is known as 100,000, but the attractiveness of the project still depends on something else.

Does this look like a good project?

Not so fast; that's 100K out and 120K in. The answer is that it depends.

Not necessarily. It's true that you're turning a 100K investment into 120K of cash inflows, but it depends.

Good answer! Yes, 100K out and 120K in looks good, but waiting for the cash inflows looks bad. So it depends.

Of course. A high rate will mean a lot of discounting, so those future cash flows are worth less, making the project not look so good. But a low rate will mean less discounting, and allow these cash flows to still be attractive.

No, a low rate. Remember that discounting involves bringing future cash flows back to the present by dividing by a factor with 1+r in it. So a _high_ r will mean a lot of discounting, and that will suggest that those future cash flows are worth less, making the project not look so good. But a low rate will mean less discounting, and allow these cash flows to still be attractive.

Here are those cash flows discounted at a low rate of 2%: | Year | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | Cash Flow | -100,000 | 0 | 30,000 | 30,000 | 30,000 | 30,000 | | PVs | -100,000 | 0 | 28,835.06 | 28,269.67 | 27,715.36 | 27,171.92 | The sum of these present values is 11,992. How would you interpret the meaning of this number?

Right.

No, it's positive, so the inflows sort of "beat" the outflow, and it should therefore add wealth.

This number is the __net present value (NPV)__ of the project, given the estimated cash flows and that 2% discount rate. The formula for NPV in general form is: $$\displaystyle NPV={\sum_{t=1}^{n}}{\frac{CF_t}{(1+r)^t}-{Outlay}}$$ where _CF_ is the expected cash flow for time periods 1 to _t_ and _r_ is the required rate of return.

How would you summarize the process of performing this calculation?

Perfect!

No, just the opposite: discount each cash flow to the present, and then add up those present values. You can't meaningfully add together values from different time periods.

And what would you conclude if this project was offered to a firm with a 6% discount rate?

There's really no way to support that statement. Consider the power of discounting in this case.

Correct. In this case, the NPV is -1,931, found by discounting the pieces and adding them up once more. | Year | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | Cash Flow | -100,000 | 0 | 30,000 | 30,000 | 30,000 | 30,000 | | PVs | -100,000 | 0 | 26,699.89 | 25,188,58 | 23,762.81 | 22,417.75 | The higher the discount rate, the lower the NPV. This makes logical sense as well. If the cost of borrowing is high (maybe due to higher risk), then that should lessen the chance of undertaking investment. NPV is a great tool since it harnesses the power of TVM and brings everything to the present, giving you a simple decision: pick up things with positive value, and avoid things with negative value. That's the decision rule for NPV. Accept when NPV>0, and reject if NPV<0. Applications of this idea are everywhere in life once you start looking for them; a powerful tool, indeed!

There is; just discount as before, dividing each cash flow by $$1.06^n$$.

The PV

The discount rate

The compounding periodicity

It depends

Yes

No

A low rate

A high rate

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The project should add wealth

The project should destroy wealth

Discount every cash flow to the present, and then add them up

Sum all of the cash flows, and then discount the sum to the present

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It's still a good deal

It shouldn't be accepted

There's no way to estimate that

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