The first step in conducting an economic evaluation analysis is to understand the concept of “*cash flow*.” “*Cash flow*” represents the *net inflow or outflow of money* during a given period of time that can be month, quarter, or year. Cash flow can be reported as before-tax cash flow (BTCF) and after-tax cash flow (ATCF).

Operating Profit or EBITDA = Gross Revenue or Savings – Operating Expenses

Before tax Cash Flow = Operating Profit or EBITDA – Capital Expenditure

After tax Cash Flow = Before tax Cash Flow – Income Tax Expenditure

Which is formatted as:

Gross Revenue or Savings

– Operating Expenses

_____________________________

Operating Profit or EBITDA

– Capital Expenditure

_____________________________

Before tax Cash Flow

– Income Tax Expenditure

_____________________________

After tax Cash Flow

EBITDA : Earnings before interest, taxes, depreciation, and amortization

### Example 1-9:

Assume an investment project for which you need to invest 20 and 15 million dollars in year 0 and year 1 (you can think of it as 20 million dollars now and 15 million dollars next year) to build a facility. In year 2, the plant will start producing and you can make revenue by selling the products. Each year, starting from year 2, operating costs and tax have to be paid. Project net cash flow can be calculated as:

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | |
---|---|---|---|---|---|---|---|---|---|

Revenue | 18 | 20 | 22 | 24 | 26 | 28 | 30 | ||

Operating Cost | -4 | -4 | -4 | -5 | -6 | -8 | -10 | ||

Capital Cost | -20 | -15 | |||||||

Tax Cost | -3 | -4 | -5 | -6 | -7 | -8 | -9 | ||

Project Cash Flow | -20 | -15 | 11 | 12 | 13 | 13 | 13 | 12 | 11 |

Each column stands for a time period (that can be year, quarter, month, …) and each cell shows the inflow or outflow of money. Investment cash flow in any year represents the net difference between inflows of money from all sources, minus investment outflows of money from all sources. The cash flow for this project for all years is calculated in the last row.

As you can see, all the costs (Capital Cost, Operating Cost, Tax, ...) are entered with the negative sign in the table, and then summation of each column gives the net cash flow in that year. The negative cash flow incurred in years 0 and 1 will be paid off by positive cash flows in years 2 through 8.

### Discounted Cash Flow (DCF)

If future cash flow is discounted, we can have cash flow in terms of present value, which is called discounted cash flow (DCF). As explained before, DCF considers the time value of money and applies it to the inflow and outflow of money occurred in the future. DCF is a tool that enables us to compare the future cash flow with the present value of money.

Different investment projects have different cash flows that happen in different time intervals in the future and DCF can give an assessment to decide which project is more profitable. DCF brings the future amounts to a same base that is easily understandable for decision makers. For example, assume you have two options: investing your money in Project A that gives you 1000 dollars every year from 2025 to 2035 or investing in Project B that gives you 1500 dollars every year from 2030 to 2040. Which project will you choose? DCF is a tool that can help you finding the answer. DCF can also be used to estimate the value of a company based on its future performance.

#### Example 1-10:

Please calculate the discounted cash flow from Example 1-9 assuming:

1) Discount rate = 10%

2) Discount rate = 12%

3) Discount rate = 15%

Assuming discount rate = 10%:

$$\begin{array}{l}\text{Cashflowinyear0:}-20\left[1/{\left(1\text{}+\text{}0.1\right)}^{0}\right]=-20\\ \text{Cashflowinyear1:}-15\left[1/{\left(1\text{}+\text{}0.1\right)}^{1}\right]=-13.6\\ \text{Cashflowinyear2:}11\left[1/{\left(1\text{}+\text{}0.1\right)}^{2}\right]=9.1\\ \text{Cashflowinyear3:}12\left[1/{\left(1\text{}+\text{}0.1\right)}^{3}\right]=9.0\\ \text{Cashflowinyear4:}13\left[1/{\left(1\text{}+\text{}0.1\right)}^{4}\right]=8.9\\ \text{Cashflowinyear5:}13\left[1/{\left(1\text{}+\text{}0.1\right)}^{5}\right]=8.1\\ \text{Cashflowinyear6:}13\left[1/{\left(1\text{}+\text{}0.1\right)}^{6}\right]=7.3\\ \text{Cashflowinyear7:}12\left[1/{\left(1\text{}+\text{}0.1\right)}^{7}\right]=6.2\\ \text{Cashflowinyear8:}11\left[1/{\left(1\text{}+\text{}0.1\right)}^{8}\right]=5.1\end{array}$$We can repeat the same procedure for discount rate = 12% and 15%. Table 1-2 shows the results.

Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|

Project Cash Flow | -20 | -15 | 11 | 12 | 13 | 13 | 13 | 12 | 11 |

DCF (discount rate = 10%) | -20 | -13.6 | 9.1 | 9.0 | 8.9 | 8.1 | 7.3 | 6.2 | 5.1 |

DCF (discount rate = 12%) | -20 | -13.4 | 8.8 | 8.5 | 8.3 | 7.4 | 6.6 | 5.4 | 4.4 |

DCF (discount rate = 15%) | -20 | -13 | 8.3 | 7.9 | 7.4 | 6.5 | 5.6 | 4.5 | 3.6 |

### Net Present Value (NPV)

Now, all the DCFs in Table 1-3 have the same base, which is present value, consequently it’s possible to add them together and create a new criterion for project evaluation. The criterion which represents this summation is called net present value (NPV). *NPV is the cumulative present worth of positive and negative investment cash flow using a specified rate to handle the time value of money.*

#### Example 1-11:

Please calculate the NPV for the cash flow in Example 1-9 assuming:

1) Discount rate = 10%

2) Discount rate = 12%

3) Discount rate = 15%

Discount rate = 10%:

$$NPV=\left(-20\right)+\left(-13.6\right)+9.1+9.0+8.9+8.1+7.3+6.2+5.1=20.1\text{milliondollars}$$Assuming discount rate = 12%:

$$NPV=\left(-20\right)+\left(-13.4\right)+8.8+8.5+8.3+7.4+6.6+5.4+4.4=16\text{milliondollars}$$Assuming discount rate = 15%:

$$NPV=\left(-20\right)+\left(-13\right)+8.3+7.9+7.4+6.5+5.6+4.5+3.6=10.8\text{milliondollars}$$As you can see, the discount rate has a substantial effect on the project NPV, higher discount rates give lower NPV of the cash flow. The other important factor is the time. The closer the money is to present time, the higher present value it has, which affects the NPV.

#### Example 1-12:

Assume you have two alternative projects to invest your 600 dollars. The cash flow in Project A and Project B are shown in Table 1-4. Which project do you choose if the discount rate is 10%?

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Project A Cash Flow | -600 | 500 | 300 | 200 |

Project B Cash Flow | -600 | 200 | 300 | 500 |

Please note that two projects have similar numbers for cash flow but they happen in different times. DCFs are displayed in following table.

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

DCF for Project A | -600 | 454.5 | 247.9 | 150.3 |

DCF for Project B | -600 | 181.8 | 247.9 | 375.7 |

This example shows how time affects the NPV of an investment project. As displayed in Table 1-5 and NPV calculations, Project A which has higher positive cash flows in closer time has higher NPV and it is a better alternative for investment than Project B.

### Minimum Rate of Return

*The terms “minimum rate of return," “hurdle rate," “discount rate," “minimum discount rate," and “opportunity cost of capital” are interchangeable with the term “cost of capital” as used in this course and in common practice. These terms should not be confused with the “financial cost of capital,” which is the cost of raising money by borrowing or issuing a bond, debenture, common stock or related debt/equity offerings. When the usual situation of capital rationing exists, the “opportunity cost of capital” generally is larger than the “financial cost of capital."*