# Why NPV is so Important

# Why CeeVex is the best software available to calculate it

# Why IRR is meaningless

## How do NPV calculations work in practice?

### Step 1 - add up all the money that is going to be spent in each year of the Project

# Step 2 - Add up all the money that will flow into the Project every Year

# Step 3 - Calculate the Total Cash Flows In and Out of the Project during Each Year of the Life of the Project

# Step 4 - Calculate the Discounted Cash Flows

# Step 5 - Add all the Cash Flows up to get the NPV

# What is NPV in Accountants Speak?

The total of the cash flows in and out discounted by the cost of using the money invested in the project or business - known as the discount rate

# What is IRR in Accountants Speak?

The discount rate that would need to be applied for the cash flow in to be equal to the cash flow out of the project or business

What this means is that the total cash flow into the project is made to equal the cash flow out of the project by adjusting the discount rate so that they are equal

# Which one is the Most Important?

# - NPV because IRR is completely meaningless - see more below

## How NPV works in Practice

Our Graphic above illustrates how the NPV is calculated but let's look at the actual numbers in a bit more detail.

Lets assume that the project periods are being allocated as years - this is commonly the case because everyone is familiar with interest rates based on the annual rate

First of all the cash flow out is calculated

- The cost of everything that is spent in year 1 is added up and divided by a factor of 1 + the discount rate e.g. with a 5% discount rate the divisor = 1.05
- The cost of everything that is spent in year 2 is added up and divided by 1.05 x 1.05 because there is two years discounting to take into account
- The cost of everything that is spent in year 3 is added up and divided by 1.05 x 1.05 x 1.05 because there is three years discounting to take into account
- The cost of everything that is spent in year 4 is added up and divided by 1.05 x 1.05 x 1.05 x1.05 because there is4 years discounting to take into account
- And so on

The sort of discount factors that apply are shown in the following table for a 5% discount rate on $10.

I am using the Excel shorthand for the power of numbers e.g. 1.05 x 1.05 x 1.05 = 1.05^3

The important thing to note is that the calculations assume that the payments are made at the start of the 1 year periods - if the payments were being made at the end then the divisor in year 1 would be 1 and not 1.05. When payments are made throughout a period the calculation is distorted and this needs to be born in mind when setting up the calculation spreadsheet.

Year | Discount Factor at 5% | Calculation |

1 |
9.52381 |
1/1.05 |

2 |
9.070295 |
1/1.05^2 |

3 |
8.638376 |
1/1.05^3 |

4 |
8.227025 |
1/1.05^4 |

5 |
7.835262 |
1/1.05^5 |

NPV | 43.29477 |

You can see exactly how the $10 payment each month is discounted so that the 5 x $10 payments only add $43.29 to the NPV of the project.

**The NPV of the cash flow in is then calculated in exactly the same way**

The two are added together to obtain the net NPV - note that it can be negative or positive.

The net cash flows can be calculated each year as shown in our graphic and then discounted.

Or the total positive and negative cash flows for the project, discounted for each year, can be set off against each other to get the NPV.

The higher the positive NPV - the more attractive the project is.

When projects are purely cost generators the best project will be that which produces the smallest negative NPV

## Considerations Regarding the Use of NPV

The big advantage of using NPV comes from the fact that it is absolutely ideal for the Comparison of Options - and that is why CeeVex uses it during the Optionology Stage of a Project.

One disadvantage of using NPV is that it is very sensitive to the discount rates used.

One discount rate might produce a positive NPV and another rate a negative NPV.

However when making comparisons between Options this can be dealt with by using high, likely and low discount rates on each Option. One of the factors used in the Choice of Option would then be the Sensitivity to Discount Rates.

This can be set up and tested very easily in Ceevex. The software is set up so that by simply clicking on "Print All" a pdf files is produced that can be saved onto your computer and then printed out whenever you need copies. So you can set up your three Options with High, Medium and Low Discount rates and save / print out 3 x pdf files with the data and NPV's for all three discount rates as well as the Options - giving 9 different project NPV's

This is very important because we are all familiar with variable rate loans where the annual costs can increase dramatically when interest rates increase.

If the options carry very different levels of risk and so attract different discount rates then the method falls down and this needs to be allowed for by adding the cost of specific insurance premiums into the cash flows to allow discount rate differentials to be reduced or even eliminated.

So if a risk is identified it is a simple matter to enter an insurance premium at an appropriate rate - these can be as high as 10% of the total risk - depending of course on how likely the probability of the risk event occuring.

NPV is far too crude a tool to use in forecasting the precise financial advantage to be gained from a project. These are so heavily influenced by accounting policies, taxation and differential rates of inflation that far more sophisticated analysees are needed to forecast the effect on the financial health of the project promoter - this is provided by our RoiVex software www.roivex.com

A lot of confusion has been around for a long time regarding whether NPV and IRR requires the reinvestment of cash flows - this is not true.

It is true that the two methods will sometimes rank projects in a different order.

This is because NPV assumes re-investment of cash receipts at the discount rate whereas IRR assumes reinvestment at the Internal Rate - see more on this below.

## More on IRR

#### I believe that the whole IRR concept is flawed - for instance - Why should cash flow out = cash flow in?

#### And why should this entirely artificial equation be made to be true by varying the discount rate!

When we have done this we are the supposed to use the following rules:-

- The best project has the highest IRR
- The best project will be acceptable if its IRR > a hurdle rate

The assumption that cash flows will be reinvested at the IRR rate is an assumption about the opportunity cost of project cash flows.

But this opportunity cost should equate with the capital market rate of return for the risk level involved.

NPV does this and IRR does not.

The IRR decision rules above can be changed to get over this but it gets very complicated and an even more opaque process

The other problem with IRR revolves around the mathematics. The IRR calculated is the solution to a polynomial equation that can have no roots, one root or several roots if the cash flow curve is a polynomal.

Hence the there is either no answer (when the cash flow is all positive or all negative), one answer or several answers - when confusion is total and absolute.

# IRR is a misguided concept and You should forget about it entirely!

## Project Evaluation

The NPV method is not appropriate for the overall evaluation of the intrinsic value that any particular project will provide.

When the Best Option for development has been selected the Details of the Project need to be refined and the Project Valuation tool RoiVex should be used to forecast the Profit and Loss Figures over the First 10 years of the Project Life.

This is an accountancy tool that will provide the information that funding Banks or Investors will require to see.

## Residual Value

After 10 Years the Project will still have a substantial Residual Value if it is making a profit. This can be valued by using conventional techniques. So that a profit of 1m in Year 10 will provide a Capital Value of 10m at a Yield of 10% (on a Non Discounted basis)

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Best Regards