The project requires an upfront investment of $150 million to be paid today.

The analysts, the CFO, decides that reasonable discount rate is 5% per annum.

So the net present value of these cash flows of 50, 50,

100 are now easily determined as $50 million discounted at 5% for

one year, plus $50 million discounted at 5% for two years,

plus $100 million discounted at 5% for three years, and

subtracting the $150 million of initial investment outlet, which doesn't

have to be discounted to the present because it is already a present value.

Adding up the present values of $47, $45 million and $86 million,

and then subtracting the $150 million gives us a net present value for

this particular project of $29.4 million.

Positive.

So the decision go, don't go into the project, is easily made.

Go is the word.

Just to illustrate that graphically.

What I've done in this graph is to indicate with buzz, the future cash flows.

There's the initial investment outlay of $150 million,

the cash outflow, that's the blue bar on the left.

Then, in year one and year two, there's a $50 million positive future cash flow.

And in year three,

there's a $100 million positive cash flow at the end of year three.

If I discount each of those cash flows at 5% per annum, I get the red bars.

So the $150 million remains $150 million.

It already is a present value investment outlay.

But, you can see that the gap between the blue bars and the red bars is

increasing with time, as the further in the future the cash flows occur,

the lower their present value will be.

Adding the red bars together, we arrive at the green bar at time period zero,

the net present value which is about $25 million, as we've seen just a moment ago.

A positive number, hence the project adds shareholder wealth,

the project should be invested in.

Let's push the envelope a little.

Because we know that investment projects for the cooperation are not risk-free.

So 5% seems an entirely unrealistic discount rate.

It turns out that the CFO is aware of this and

decides to increase the discount rate to 20%.

To capture the increased riskiness of these future cash flows.

If I again compute the net present value of $50,

$50, $100 million over the next three years and

subtract the $150 million initial outlay,

I now arrive at negative $15.7 million of net present value.

So, all of a sudden, we see that the net present value has turned negative.

So, the go, don't go decision now turns negative.

This project is destroying shareholder wealth.

You should not be investing upfront $150 million to be entitled to those

cash flows.

Clearly, the increased riskiness of the future cash flows

had a major impact on its net present value.

Turning it from a go decision into a don't go decision.

Again, illustrating this with the bar chart,

we can see that the gap between the blue cash flow bars and

their present value, the red cash flow bars,

is now a lot larger because of the higher discount rate.

The more risk, the higher the discount rate.

The lower the present value, the lower the positive red bars are going

to contribute to the net present value, which is this negative

net present value for this example at a discount rate of 20%.

So clearly, there must be a discount rate somewhere between 5% and

20%, where we've crossed the line.

Where a positive net present value turned into a negative net present value.

At that point, it no longer pays off.

The corporation should not be investing its $150 million in this project.

So, what would be the trigger discount rate at which we break even?

Well, you can solve this equation.

And it will tell you, then, exactly where the crucial break even discount rate is.

I've already indicated it's somewhere between 5 and 20%.

So let's just do the analysis we've done for 5% and

20% individually for a whole sequence of discount rates.

Slowly increasing from 5% to 20% and see what happens with the net present value.