#### “Projects fail at the beginning, not at the end. The fate of the project is decided on day#1 and gets revealed as the project progress.”

**How do we select the right projects for execution?** . Projects must have a solid business case to support it. A set of ratios comes in handy while picking up the right projects for execution. They are;

Net present value (NPV)

Payback period

Benefit cost ratio (BCR)

Internal rate of return (IRR)

The time value for money

**The time value for money**

Money has a time value. A rupee today is more valuable than a rupee year later. Why? There are several reasons. Capital can be employed productively to generate positive returns. In an inflationary period a rupee today represents a greater real purchasing power than a rupee a year later

**Time lines and notations**

When cash flows occur at different points in time, it is easier to deal with them using a time line. A time line shows the timing and the amount of each cash flow in a cash flow stream. Cash flows can be positive or negative. A positive cash flow is called as cash inflow and a negative cash flow is called a s cash outflow.

#### Future value

Suppose you invest Rs.1000 for three years in a savings account that pays 10 percent interest / year. If you let your interest income be reinvested, your investment will grow as follows;

First year | Principal at the beginning | 1,000 |

Interest for the year (1000×0.10) | 100 | |

Principal at the end | 1,100 | |

Second year | Principal at the beginning | 1,100 |

Interest for the year (1100*0.10) | 110 | |

Principal at the end | 1,210 | |

Third year | Principal at the beginning | 1,210 |

Interest for the year (1210*0.10) | 121 | |

Principal at the end | 1,331 |

The process of investing money as well as re-investing the interest earned thereon is called compounding. The future value, or compounded value of an investment after ‘n’ years, when the interest rate is ‘r’ percent is;

**FV n = PV (1+r) ˆ n**

In this equation, (1+r) ^ n is called future value factor

If we apply this formula;

FV n = 1000 (1+. 1)^3 = 1000 x 1.1 x 1.1 x 1.1 = 1331

**Net present value**

The net present value (NPV) of a project is the sum of the present values of all the cash flows , positive as well as negative , that are expected to occur over the life of the project. To illustrate the calculation of net present value, consider a project, which has the following cash flow stream;

Year | Cash flow |

0 | Rs (1,000,000) |

1 | 200,000 |

2 | 200,000 |

3 | 300,000 |

4 | 300,000 |

5 | 350,000 |

The cost of capital, ‘r’ for the firm is 10 percent.

The net present value of the proposal is;

**NPV = (200000/1.10^1) + (200000/1.10^2) + (300000/1.10^3) + (300000/1.10^4) + (350000/1.10^5) – 1000000 = – 5,273**

The net present value represents the net benefit over and above the compensation for time and risk. Hence the decision rule associated with the net present value criterion is, a*ccept the project if the net present value of the project is positive and reject the project if the net present value is negative.*

**The benefit cost ratio**

Benefit cost ratio BCR = PVB / I where

PVB = present value of benefits and I = initial investment

To illustrate the calculation of these measures, let us consider a project, which is being evaluated by a firm that has a cost of capital of 12 percent.

Initial investment | 100000 |

Benefits Year 1 | 25000 |

Benefits Year 2 | 40000 |

Benefits Year 3 | 40000 |

Benefits Year 4 | 50000 |

The benefit cost ratio measures for this project is;

BCR = ((25000/1.12) + 40000/1.12^2) + (40000/1.12^3) + (50000/1/12^4)) / 100000 = 1.145

**Decision rules**

When BCR > 1 accept the project

When BCR < 1 reject the project

IRR – internal rate of return

The internal rate of return (IRR) of a project is the discount rate, which makes its NPV equal to zero. To illustrate the calculation of IRR, consider the cash flows of a project being considered;

Year | 0 | 1 | 2 | 3 | 4 |

Cash flow | (100,000) | 30000 | 30000 | 40000 | 45000 |

The IRR is the value of ‘r’, which satisfies the following equation;

100,000 = 30000/(1+r)^1 + 30000/(1+r)^2 + 40000/(1+r)^3 + 45000/(1+r)^4

The calculation ‘r’ involves a process of trial and error. We try different values of ‘r’ till we find that the right hand side of the above equation is equal to 100,000. In this case, the value lies between 15 and 16 percent.

*The decision rule for IRR is as follows;*

Accept, if the IRR is greater than the cost of capital

Reject, if the IRR is less than the cost of capital

**Payback period**

The payback period is the length of time required to recover the initial cash outlay on the project. For example, if a project involves a cash outlay of RS. 600000 and generates cash inflows of Rs. 100000, 150000, 150000 and 200000 in the first, second, third and fourth years respectively, its pay back period is 4 years because the sum of cash flows during the four years is equal to the initial outlay. According to the payback criterion, the shorter the payback period, the more desirable the project.

**Opportunity cost**

Opportunity cost (opportunity lost) is the NPV of the next best project, you are not doing, because you have decided to invest in a project.

Let us assume that you have 100,000 rupees and you are investing this money in project ‘A’, whose NPV=200,000 and because of this you are unable to do project ‘B’, whose NPV=150,000 or project ‘C’, whose NPV = 120,000, then the opportunity cost is 150,000, which is the NPV of project ‘B’, which is the next best option after ‘A’.

*In personal life, these concepts of NPV, payback period, BCR, IRR and opportunity cost are really helpful, to protect yourself from unwanted expenses like buying a new flat, car or even mobile phone. Before committing to buy, just think about these ratios, and most probably you will restrain from your impulse to buy unwanted stuff.*

*The project management body of knowledge says that ‘Projects fail at the beginning and not at the end’. A project which does not have a good business case is a bubble, which can burst at any time. So, before starting a project, please ensure that the project has a solid business case, and if the business case is not clear, please document it as a risk.*

**The paradigm shift within PMBOK Version 6 **

So far, if a project got over on time, within budget and met it’s scope, then it was considered as successful. As per the PMBOK Version 6 on wards, projects are considered as successful only when they got completed on time, within budget, met their scope and satisfied the purpose for which it was initiated which includes the payback period. That makes the understanding of the business case of the project from day 1 of the project a critical success factor for the project manager.