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Now we know the basics of the discounted cash flow valuation method.

Â Let's put it to the test and extend the example to a project.

Â What analysts do is value firms' equity.

Â What CFOs in corporations do is value investment projects for the firm.

Â But there's no fundamental difference.

Â We apply the same methodology.

Â Both CFOs and

Â analysts will assess whether the present value of future cash flows of the firm or

Â the project are, in fact, worth an initial investment outlay.

Â That could be, if it is the firm's value, the current share price,

Â the price you need to pay to acquire a share in the firm.

Â For the CFO, it would be the capital investment required to start the project.

Â So the entitlements of investing in the firm or investing in the project

Â are given, as we've seen before, a set of cash flows that happen after one year,

Â two-year until the lifetime expires of the project or the firm n years.

Â And we need to discount each of those cash flows back appropriately

Â to a present value, which will tell us what the project or firm, are worth today.

Â So to make that decision, and

Â bring in the initial investment outlay, we go about that as follows.

Â So both analysts and CFOs use, what we call, a net present value analysis.

Â When net present value, NPV, is defined as the difference

Â between the present value of the benefits and the present value of the costs.

Â So we first compute the present value of the cash flow entitlements that

Â the firm or the project delivers, and then we subtract from that the present value

Â of the initial investment, the initial outlay.

Â So for our entitlement of N cash flows discounted to the present,

Â we subtract, in this simplified example,

Â an initial investment at time period zero, the present.

Â The decision rule is straightforward.

Â Whenever the net present value is positive, that project of

Â the firm would show that it increases shareholder wealth.

Â Buying a share in the firm,

Â investing in that project would be a good decision.

Â On the other hand, if the net present value turns out negative,

Â then we should be rejecting the project.

Â We should not be investing in shares of the firm

Â as they would reduce shareholder wealth.

Â What happens if net present value is in fact zero?

Â Well then, at least it doesn't destroy shareholder wealth, but

Â it also doesn't add

Â shareholder wealth.

Â Let's put some numbers in.

Â Consider a project with a three year life span, n equals 3.

Â And we have a set of positive expected cash flow generated by this project of,

Â in the first year 50 million, in the second year 50 million and

Â in the third year $100 million entitlements.

Â 3:09

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

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

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

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

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

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

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

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

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

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

Â this particular project of $29.4 million.

Â Positive.

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

Â Go is the word.

Â Just to illustrate that graphically.

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

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

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

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

Â And in year three,

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

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

Â So the $150 million remains $150 million.

Â It already is a present value investment outlay.

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

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

Â the lower their present value will be.

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

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

Â A positive number, hence the project adds shareholder wealth,

Â the project should be invested in.

Â Let's push the envelope a little.

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

Â So 5% seems an entirely unrealistic discount rate.

Â It turns out that the CFO is aware of this and

Â decides to increase the discount rate to 20%.

Â To capture the increased riskiness of these future cash flows.

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

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

Â subtract the $150 million initial outlay,

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

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

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

Â This project is destroying shareholder wealth.

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

Â cash flows.

Â Clearly, the increased riskiness of the future cash flows

Â had a major impact on its net present value.

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

Â Again, illustrating this with the bar chart,

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

Â their present value, the red cash flow bars,

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

Â The more risk, the higher the discount rate.

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

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

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

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

Â 20%, where we've crossed the line.

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

Â At that point, it no longer pays off.

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

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

Â Well, you can solve this equation.

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

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

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

Â 20% individually for a whole sequence of discount rates.

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

Â