The goal of financial management is to increase the value of the firm (Ross, Westerfield & Jaffe, 2010). Put in another way, capital budgeting is concerned with the issues of the kind of long lived assets that a firm should invest in. Implicit in the stated goal of financial management of maximizing stockholder value is the need to identify investments that have favourable impact on the stock value. The Payback Period (PP), Profitability Index (PI) and Net Present Value (NPV) are just three of the techniques that financial managers employ to appraise competing capital projects.

This is undoubtedly one of the most popular techniques for investment appraisal (Ross, Westerfield & Jaffe, 2010). Payback Period is simply the time it takes for the firm to recover its initial investment in a project. An example may be necessary.

Assume a project whose initial investment is £ 60,000 which subsequent cash flows of £ 10,000, £20,000, £30,000 and £40,000 in years 1, 2, 3 and 4 respectively. It is possible to work out the PP of this project. Adding the cash flows of years 1 to 3 gives the same value as that of the initial investment of £ 60,000. The firm would have recovered its investment in 3 years. This is also the payback period for the project.

It is not always the case, however, that the payback period will be in whole numbers. For instance, if the cash flow in year 3 in the above example was £ 40,000 instead of £ 30,000. This requires a formula to calculate the payback period.

A major assumption in this method is that cash flows occur evenly during the year.

The decision maker must first come up with a cut-off payback date. All projects that payoff within that set date are accepted if they are independent projects. Projects that payoff earlier than competing ones and within the cut-off date are accepted if they are mutually exclusive.

The intuitive simplicity inherent in this approach makes it very attractive as an investment appraisal technique. It would not be very difficult for most people to understand that a firm should prefer investing in those projects that promise the break-even as quickly as possible. In addition, it is possible to involve as many people in the firm in discussing capital investment decisions using a simple approach as this. Such an involvement may garner the necessary support for the project.

One of problems with payback is that it ignores the timing of cash flows during the payback period. Projects with the same payback period are considered to be the same irrespective of whether one has higher cash flows in the initial years. The problem with this is that project that promises better value for shareholders may be left for a less promising one.

Secondly, the method ignores all cash flows that occur after the payback period. This short term orientation may lead to the rejection of some valuable projects just because they are long term. In practice, firms cannot just disregard cash flows just because they come after the recovery of the initial investment costs.

Lastly, the choice of a payback cut-off is a largely arbitrary as there is no comparable standards to rely on. Managers must rely on their experience which is not always a very good thing.

As may be apparent from the name, this approach uses a ratio of the Net Present Value of incremental cash flows of a project on the one hand and the initial investment on the other (Ross, Westerfield & Jaffe, 2010). Incremental cash flows simply refer to those cash flows occurring after the initial investment. The formula for calculating profitability index is given below.

Company X applies a 10% discount rate on all its projects. Project A requires an initial cash outlay of £ 20,000 with cash inflows of £ 70,000 and £ 10,000 in year 1 and 2 respectively. The PI of this project is calculated by first getting the Net Present Values (NPV) of the cash flows in year 1 and 2 and then dividing by the initial investment.

There are three possible scenarios in using Profitability Index as a decision tool. In the first scenario involves making decisions in independent projects. In such cases, the rule is to accept all projects with a profitability index which is greater than 1 while rejecting those with a PI of less than 1.

The second scenario involves mutually exclusive projects. The decision criteria in such a situation are not as simple like independent projects. Suppose company X in our earlier example had another competing project B with an initial outlay of £ 10,000 with subsequent cash inflows of £ 15,000 and 40,000 in year 1 and 2 respectively.

With a PI of 4.67, this second project may appear more attractive than the first one. This is, however, not the case as PI suffers from the scale problem. It ignores the fact that Project A had a larger initial investment. A way out of this problem is conduct an incremental analysis of the two projects in which all other projects are compared to the bigger one.

Project | Cash Flows(£) | Present Values of Incremental Cash Flows | Profitability Index | NPV (10%) | ||

Project | C_{0} |
C_{1} |
C_{2} |
|||

A-B | -10,000 | 55,000 | -30,000 | 25,206.61 | 2.52 | 15,206.61 |

Since the PI of the incremental cash flows is greater than 1, the rule is to pick the bigger project which is project A in the present case.

One can attribute three main advantages to the use of PI. For one, it reveals the ratio by which an investment should the wealth of shareholders per £ invested (Baker & Powell, 2005, p.238). This is despite the fact that it does not show the extent of that wealth creation. Secondly, the approach also takes care of the time value of money in addition to the fact that it accounts for all the cash flows of a project. Lastly, the approach can serve as a measure of the margin of error. Relative to projects with low PIs, those with high PIs have a greater capacity to absorb estimation errors while still managing to break even.

The major weakness of this approach is the scale problem already discussed when looking at mutually exclusive projects above. This makes it very inappropriate for appraising mutually exclusive projects (Baker & Powell, 2005, p.239).

Arguably the most appropriate relative to the other approaches, NPV employs the concept of the time value of money. It is premised on the understanding that cash flows with higher NPVs have the greatest potential to maximise shareholder wealth. It is a simple process that relies on a discount factor to equate future cash flows to present terms.

Company Q is intending to invest in new equipment with the initial investment expected to be £ 30,000. The machine will be in use for five years with each of those years have cash inflows of £40,000,£50,000,£60,000,£70,000 and £80,000. Company Q uses a 10% discount rate. The Net Present Value is shown below:

Year | Cash Flow | Present Value (@10%) |

0 | -30,000 | -30,000 |

1 | 40,000 | 36,363.64 |

2 | 50,000 | 41,322.31 |

3 | 60,000 | 45,078.89 |

4 | 70,000 | 47,810.94 |

5 | 80,000 | 49,673.71 |

Net Present Value | 190,249.49 |

This project has a Net Present Value of £ 190,249.49.

For independent projects, the decision criterion is to accept those projects with positive Net Present Values (NPVs). All independent projects with negative NPVs should be rejected (Maher, Stickney & Weil, 2008). In the case of mutually exclusive projects, the rule is to rank all projects with positive NPVs and choose the one which the highest NPV while rejecting the rest.

There are two major advantages to NPV. For one, it allows the analyst to compare the cash payments to the cash receipts. This is possible because the cash outflows and inflows are reduced to present terms by way of discounting.

The other advantage of NPV approach is that it accounts for all cash flows of a project. This makes it difficult for the analyst to accept suboptimal projects over relatively better ones.

The only problem with this approach is that it may not be easily understandable to most people. Those without some basic grounding in the concept of time value of money may see the approach as very complex.

The present case is a classic example of mutually exclusive projects in the sense that the acceptance of any one of the four machines leads to the rejection of the other three. The present appraisal will utilise both the Payback Period (PP) and the Net Present Value (NPV) approaches. Worth noting is the fact that the PP approach is only useful for the initial screening of a project. It follows from this that the decision criterion will arise only from the NPV approach with the PP remaining as a complimentary one.

Year | Cash Flow(£) | Cumulative Cash Flow(£) | Discount Factor (@6%) | Present Value(£) |

0 | – 550, 000 | -550,000 | 1 | -550,000 |

1 | 20, 000 | -530,000 | 0. 9433962 | 18,867.92 |

2 | 75, 000 | -455,000 | 0. 8899964 | 66,749.73 |

3 | 125, 000 | -330,000 | 0. 8396193 | 104,952.41 |

4 | 250, 000 | -80,000 | 0. 7920937 | 198,023.43 |

5 | 200, 000 | 120,000 | 0. 7472582 | 149,451.64 |

Total | -11,954.87 |

Year | Cash Flow(£) | Cumulative Cash Flow(£) | Discount Factor (@6%) | Present Value(£) |

0 | -550, 000 | -550,000 | 1 | -550,000 |

1 | 50, 000 | -500,000 | 0. 9433962 | 47,169.82 |

2 | 175, 000 | -325,000 | 0. 8899964 | 155,749.37 |

3 | 200, 000 | -125,000 | 0. 8396193 | 167,923.86 |

4 | 175, 000 | 50,000 | 0. 7920937 | 138,616.40 |

5 | 70, 000 | 120,000 | 0. 7472582 | 52,308.07 |

Total | 11,767.52 |

Year | Cash Flow(£) | Cumulative Cash Flow(£) | Discount Factor (@6%) | Present Value(£) |

0 | -290, 000 | -290,000 | 1 | -290,000 |

1 | 15, 000 | -275,000 | 0. 9433962 | 14,150.94 |

2 | 80, 000 | -195,000 | 0. 8899964 | 71,199.71 |

3 | 120, 000 | -75,000 | 0. 8396193 | 100,754.32 |

4 | 100, 000 | 25,000 | 0. 7920937 | 79,209.37 |

5 | 60, 000 | 85,000 | 0. 7472582 | 44,835.49 |

Total | 20,149.83 |

Year | Cash Flow(£) | Cumulative Cash Flow(£) | Discount Factor (@6%) | Present Value(£) |

0 | – 460, 000 | -460,000 | 1 | -460,000 |

1 | 30, 000 | -430,000 | 0. 9433962 | 28,301.89 |

2 | 95, 000 | -335,000 | 0. 8899964 | 84,549.66 |

3 | 150, 000 | -185,000 | 0. 8396193 | 125,942.90 |

4 | 210, 000 | 25,000 | 0. 7920937 | 166,339.68 |

5 | 300, 000 | 325,000 | 0. 7472582 | 224,177.46 |

Total | 169,311.59 |

In themselves, the above calculations do not mean so much. They must be subjected to the acceptable decision criteria under each of the two approaches. With respect to the Payback Period, Machine 2 would have been accepted if the company was only interested in the quick recovery of the initial investment in the machine. As already noted, the NPV approach is superior to the Payback Period and any conflict between the two should be resolved in favour of the NPV approach. It means that the board should accept Machine 4 as it gives the highest positive Net Present Value. This decision is in line with the overriding goal of maximising shareholder value. It is also important to note that each of these approaches is subject to the advantages and disadvantages that have already been discussed in the earlier parts of this report.

While the quantitative analysis above may act as a guide as to which of the four machines is the most appropriate to adopt, the mode must note that some unquantifiable factors may lead to a totally different decision. First, the analysis above proceeded on the assumption that the company does not face capital constraints. This is, however, not always the case as most companies are subject to capital rationing.

Secondly, the board will all have to consider how the introduction of any of the four machines with fit in with the overall strategy of the company. It may well be the fact that another machine would fit in with that strategy than even Machine 4.

Lastly, the board must also consider how the other stakeholders of the company would react to the introduction of a machine that promises to automate work that was previously done manually. Confrontations with labour unions would be the last thing that the board would want to engage into. Such confrontations have the potential to bring bad publicity which can in turn destroy shareholder value.

Baker, H.K., & Powell, G.E. (2005). *Understanding Financial Management*: *A Practical Guide*. Garsington Road, Oxford: Blackwell Publishing.

Maher, M.W., Stickney, C.P., & Weil, R.L. (2008).*Managerial Accounting: An Introduction to Concepts, Methods and Uses* (10^{th} Edn.).Mason,OH:Thomson.

Ross, S.A., Westerfield, R.W.,& Jaffe, J.(2010). *Corporate Finance* (9^{th} Edn.). Avenue of the Americas, New York: McGraw-Hill/Irwin.

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