## Project Viability

Return on investment (ROI)

The simplest way to ascertain whether the investment in a project is viable is to calculate the return on investment (ROI). If a project investment is £10 000, and gives a return of £2000 per year over 7 years,

The return on the investment, usually given as a percentage, is the average return over the period considered x 100, divided by the original investment, i.e.

average return x 100

return on investment % =

investment £571.4 x 100

£10000

This calculation does not, however, take into account the cash flow of the investment which in a real situation may vary year by year.

### Net present value

As the value of money varies with time due to the interest it could earn if invested in a bank or other institution, the actual cash flow must be taken into account to obtain a realistic measure of the profitability of the investment.

If £100 were invested in a bank earning an interest of 5% The value in 1 year would be £100 x 1.05 = £105

The value in 2 years would be £100 x 1.05 x 1.05 = £110.25 The value in 3 years would be £100 x 1.05 x 1.05 x 1.05 = £115.76

It can be seen therefore that, today, to obtain £115.76 in 3 years it would cost £100. In other words, the present value of £115.76 is £100.

Another way of finding the present value (PV) of £115.76 is to divide it by 1.05 x 1.05 x 1.05 or 1.157, for

115.76

115.76

If instead of dividing the £115.76 by 1.157, it is multiplied by the inverse of 1.157, one obtains the same answer, since

1.157

The 0.8638 is called the discount factor or present value factor and can be quickly found from discount factor tables, a sample of which is given in Figure 6.1.

It will be noticed from these tables that 0.8638.5 is the PV factor for a 5% return after 3 years. The PV factor for a 5% return after 2 years is 0.9070 or

In the above example the income (5%) was the same every year. In most projects, however, the projected annual net cash flow (income minus expenditure) will vary year by year and to obtain a realistic assessment of the net present value (NPV) of an investment, the net cash flow must be discounted separately for every year of the projected life.

Table A Present value of £1

Years Hence

35% |
40% |
45% |
50% |

0.741 |
0.714 |
0.690 |
0.667 |

0.549 |
0.510 |
0.476 |
0.444 |

0.406 |
0.364 |
0.328 |
0.296 |

0.301 |
0.260 |
0.226 |
0.198 |

0.223 |
0.186 |
0.136 |
0.132 |

0.165 |
0.133 |
0.108 |
0.088 |

0.122 |
0.095 |
0.074 |
0.059 |

0.091 |
0.068 |
0.051 |
0.039 |

0.067 |
0.048 |
0.035 |
0.026 |

0.050 |
0.035 |
0.024 |
0.017 |

0.037 |
0.025 |
0.017 |
0.012 |

0.027 |
0.018 |
0.012 |
0.008 |

0.020 |
0.013 |
0.008 |
0.005 |

0.015 |
0.009 |
0.006 |
0.003 |

0.011 |
0.005 |
0.004 |
0.002 |

0.008 |
0.005 |
0.003 |
0.002 |

0.006 |
0.003 |
0.002 |
0.001 |

0.005 |
0.002 |
0.001 |
0.001 |

0.003 |
0.002 |
0.001 | |

0.002 |
0.001 |
0.001 | |

0.002 |
0.001 | ||

0.001 |
0.001 | ||

0.001 | |||

0.001 | |||

0.001 |

21 22

40 50

0.672

0.608

0.453

0.372

0.208

0.241

0.097

0.054

0.046

0.021

0.022

0.009

0.011

0.005

0.005

0.004

0.004

0.001

0.003

0.001

0.001 0.001

Figure 6.1 Discount Factors

Year |
Income |
Discount |
Discount |
NPV | |

£ |
rate |
factor |
£ | ||

1 |
10 000 |
5% |
1/1.05 = 0.9523 |
10000 x 0.9523 = |
9 523.8 |

2 |
11 000 |
5% |
1/1.052 = 0.9070 |
10000 x 0.9070 = |
9 070.3 |

3 |
12 000 |
5% |
1/1.053 = 0.8638 |
12000 x 0.8638 = |
10 365.6 |

4 |
12 000 |
5% |
1/1.054 = 0.8227 |
12000 x 0.8227 = |
9 872.4 |

Total |
45 000 |
39 739.1 |

One of the main reasons for finding the NPV is to be able to compare the viability of competing projects or different repayment modes. Again an example will demonstrate the point.

A company decides to invest £12000 for a project which is expected to give a total return of £24000 over the 6 years. The discount rate is 8%.

There are two options of receiving the yearly income.

1 £6000 for years 1 and 2 = £12000 2 £5000 for years 1, 2, 3 and 4 = £20000

£4000 for years 2 and 3 = £8000 £2000 for years 5 and 6 = £4000 £2000 for years 5 and 6 = £4000

Total £24000 £24000

The DCF method will quickly establish which is the most profitable option to take as will be shown in the following table.

Year |
Discount factor |
Cash flow A |
NPV A |
Cash flow B |
NPVB |

£ |
£ |
£ |
£ | ||

1 |
1/1.08 = 0.9259 |
6 000 |
5555.40 |
5000 |
4629.50 |

2 |
1/1.082 = 0.8573 |
6 000 |
5143.80 |
5000 |
4286.50 |

3 |
1/1.083 = 0.7938 |
4000 |
3175.20 |
5000 |
3969.00 |

4 |
1/1.084 = 0.7350 |
4000 |
2 940.00 |
5000 |
3 675.00 |

5 |
1/1.085 = 0.6806 |
2 000 |
1 361.20 |
2000 |
1 361.20 |

6 |
1/1.086 = 0.6302 |
2 000 |
1 260.40 |
2000 |
1 260.40 |

Total |
24000 |
19 437.00 |
24000 |
19181.50 |

Clearly A gives the better return and after deducting the original investment of £12 000, the net discounted return for A = £7437.00 and for B = £7181.50.

The mathematical formula for calculating the NPV is as follows:

If NPV = Net Present Value r = the interest rate n = number of years the project yields a return B1, B2, B3, etc. = the annual net benefits for years 1, 2 and 3 etc. NPV for year 1 = B1/(1 + r)

for year 3 = B1/(1 + r) + B2/(1 + r)2 + B3/(1 + r)3 and so on If the annual net benefit is the same for each year for n years, the formula becomes

As explained previously, the discount rate can vary year by year, so that the rate relevant to the year for which it applies must be used when reading off the discount factor table.

Two other financial calculations need to be carried out to enable a realistic decision to be taken as to the viability of the project.

### Payback

Payback is the period of time it takes to recover the capital outlay of the project, having taken into account all the operating and overhead costs during this period. Usually this is based on the undiscounted cash flow. A knowledge of the payback is particularly important when the capital must be recouped as quickly as possible as would be the case in short-term projects or projects whose end products have a limited appeal due to changes in fashion, competitive pressures or alternative products. Payback is easily calculated by summating all the net incomes until the total equals the original investment, e.g. if the original investment is £600 000, and the net income is £75000 per year for the next ten years, the payback is £600000/£75000 = 8 years.

Internal rate of return (IRR)

It has already been shown that the higher the discount rate (usually the cost of borrowing) of a project, the lower the net present value (NPV). There must therefore come a point at which the discount rate is such that the NPV becomes zero. At this point the project ceases to be viable and the discount rate at this point is the internal rate of return (IRR). In other words it is the discount rate at which the NPV is 0.

While it is possible to calculate the IRR by trial and error, the easiest method is to draw a graph as shown in Figure 6.2.

The horizontal axis is calibrated to give the discount rates from 0 to any chosen value, say 20%. The vertical axis represents the NPVs which are + above the horizontal axis and - below.

By choosing two discount rates (one low and one high) two NPVs can be calculated for the same envisaged net cash flow. These NPVs (preferably one +ve and one -ve) are then plotted on the graph and joined by a straight line. Where this line cuts the horizontal axis, i.e. where the NPV is zero, the IRR can be read off.

Time

Figure 6.3 Cost/Benefit profile

The basic formulae for the financial calculations are given below.

Investment appraisal definitions

NPV (net present value) Net income Payback period

Profit

Average return/annum

= summation of PVs - original investment = incoming moneys - outgoing moneys = no. of years it takes for net income to equal original investment = total net income - original investment total net income

no. of years average return x 100 investment net income x 100

IRR (internal rate of return)

no. of years x investment = % discount rate for NPV = 0

## Project Management Made Easy

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

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