## Project Justifications

There are many reasons for doing projects. Some of them are more tangible than others. Projects may be a response to a government order, such as a redesign of an unsafe automobile or changing a process that is found to be polluting air or water. Other projects may be justified by the opportunity to create a new business or enter a new field. The potential benefits of a project can be the result of a market demand for a product, a customer request, a government requirement, or meeting or creating new competition or social needs.

Of course, one of the strongest and most compelling project justifications is the concept of a benefit occurring to the organization after making some effort. The most efficient way to measure this is to compare the monetary benefits to the monetary cost of the project. To this end, many justification methods have been developed over the years. It is important to use the appropriate method for project justification. The selection of a justification technique has its own costs and benefits. Some methods produce results that consider many aspects of the project costs and benefits, while others consider only some of these factors. Of course, the more aspects of the project that are considered, the higher will be the cost of the justification itself.

These analysis techniques are forms of cash flow analysis. Cash flow analysis is measuring the cash flowing into and out of an organization over time. Projects that have more cash flowing into the organization than cash flowing out of the organization are good projects. In most projects it is necessary to make an investment in the project (cash outflow) before the benefits can begin (cash inflow).

### The Breakeven Chart

The breakeven chart is useful when comparing two or more alternatives. In the question of justifying a project, doing the project can be compared to not doing the project. Where there is more than one choice, several alternatives can be considered at the same time.

Refer to Figure 1-1. The vertical axis shows dollars, and the horizontal axis shows time. The variable cost of each of the alternatives is plotted over time and is plotted from time zero. In the case of an alternative requiring that money be spent before the benefits of the project can be realized, the variable cost is plotted from a point on the vertical axis representing the total fixed, one-time cost of the project. In the case of an ongoing alternative, the choice of doing nothing, there is no fixed cost. At some point in time, if the project has an overall benefit, the lines will cross. This is the ''breakeven point,'' the point where the benefits of doing the project outweigh the cost of doing the project when compared to not doing the project at all. The point on the horizontal time axis is the point in time when this occurs. This point in time is also called the ''payback period.''

For example, suppose a manufacturing plant has a machine that is used to make left-handed widgets. The machine is getting old. The machine can manufacture widgets

Figure 1-1. Breakeven chart.

Figure 1-1. Breakeven chart.

for $2 per widget. A new machine can be purchased and installed that will manufacture widgets for $1.50 each. If the company makes 25,000 widgets per month, and the new machine costs $200,000, what is the breakeven point of the project? (See Figure 1-2.)

### Problems with Breakeven Charts

I said earlier that the simpler methods of justification are less expensive to use but produce results that do not consider as many factors as other techniques. The breakeven-point method has some shortcomings.

The time that exists after the breakeven point is reached is not considered. This means that projects that have a high early return will be favored over projects that may have higher returns in the long run. For example, buying a cheap machine that wears out quickly and has high maintenance costs is favored over a machine that is built to last longer but costs more to buy.

Because breakeven-point charts are used as a very rough justification method, it is usually assumed that the production rates are constant, allowing the use of linear variable cost lines.

### Average Rate of Return on Investment

One way to add a little more accuracy to our justification technique is to eliminate the problem of shortsightedness that exists in the breakeven-point and payback-period analy-

Figure 1-2. Example of a breakeven chart.

Total cost

$1.50 per widget

$2 00 per widget / ^^^Variable cost of project

$1.50 per widget

Fixed cost of project $200,000

Time in months ses. In these techniques the analysis stops when the payback point or the breakeven point is reached.

The ''average-rate-of-return-on-investment'' method solves this problem by using the same time period to compare alternative projects. Regardless of when the project has its payback point or breakeven point, the time period in this justification method covers the approximate life of the project. It then measures all of the cash flows from the beginning of the investment to the end of the useful life of the project. In this way we consider all of the money that is being spent.

For example, to expand on our example from above, let's say that the sales forecast for widgets changes over time, and that the maintenance cost of the new machine is now recognized. Table 1—1 summarizes the data. We can see from the table that the total cash flow for this project was a positive $935,000. This represents a return on our investment of $200,000, or 468 percent, an average rate over ten years of 46.8 percent.

This method of project justification is not often used these days because the more sophisticated methods of justification have become easier to calculate since the appearance of the personal computer. However, using these methods requires more time and effort to collect data and make forecasts.

### Present Value of Money

Before we talk about the more sophisticated methods of justification, we should look at the present value of money and the net present value of money.

Suppose I borrow $100 from you today and pay you back $100 tomorrow. This is a reasonable transaction among friends. But suppose I borrow $100 from you and don't pay it back to you for two years. Is this still a fair arrangement? You should say ''No!'' because I have had the use of your money for two years and have paid you nothing for the use of your money. If I had not borrowed the money from you, you could have invested the money in something, and you would have had something more than the $100 you started with.

This is the idea behind using the present value of money. Money that I receive in the future is worth less than money I receive now. This is not to say that money I receive in the future is worthless—it's just worth less than money I get today. The further into the future I receive the money, the less valuable it is to me today. In the example, I should have given you back $115 for borrowing $100 from you for two years.

The calculation that I use to figure out what my $100 will be worth two years from now is the compound interest formula:

If you invest $100 at 7 percent interest for one year, you would receive $107.

where PV is the present value of the money, FV is the future value of the same money, and I is the interest rate paid by the investment.

Table 1-1. Cashflow.

Annual Sales Annual

Table 1-1. Cashflow.

Year |
Volume |
Revenue |
Maintenance |
Cost |
Cash Flows |
Cumulative |

0 |
0 |
0 |
0 |
$200,000 |
-$200,000 |
-$200,000 |

1 |
$300,000 |
$150,000 |
0 |
150,000 |
- 50,000 | |

2 |
300,000 |
150,000 |
$5,000 |
145,000 |
95,000 | |

3 |
300,000 |
150,000 |
5,000 |
145,000 |
240,000 | |

4 |
250,000 |
125,000 |
5,000 |
120,000 |
360,000 | |

5 |
250,000 |
125,000 |
10,000 |
115,000 |
475,000 | |

6 |
250,000 |
125,000 |
10,000 |
115,000 |
590,000 | |

7 |
200,000 |
100,000 |
10,000 |
90,000 |
680,000 | |

8 |
200,000 |
100,000 |
15,000 |
85,000 |
765,000 | |

9 |
200,000 |
100,000 |
15,000 |
85,000 |
850,000 | |

10 |
200,000 |
100,000 |
15,000 |
85,000 |
935,000 |

If you leave the money in the bank at the same interest rate, you would get more the next year.

With a little manipulation, the series of calculations can be generalized into the compound interest formula:

The new term in this formula is n, the number of time periods that the interest is applied.

Your $100 invested at 7 percent for two years looks like this:

FV = 100 (1 + .07)2 FV = 100 (1.07)2 FV = 100 (1.1449) FV = 114.49

Now that we have reviewed compound interest calculations, it is time to look at calculating the present value of money that we will get in the future. This is really just the compound interest calculation solved for the present value instead of the future value.

Start with the compound interest formula:

Solve for the present value:

Now let's say that we can do something that will result in a return of $100 two years from now. We would like to know what the equivalent present value of that money is. Remember that money we receive in the future is worth less than money we receive now. Here we are trying to determine the present value of the $100 we will receive two years from now.

You can check this number by calculating the future value of $87.34 invested at 7 percent for two years. The result should be $100.

To bring all this into the context of a project, projects usually start out by investing an amount of money at the beginning of the project and receiving benefits from the project in the future. By using the present value calculations we can now more accurately determine the true value of the project. Projects that have very high returns early in the project's useful life will be considered better projects than projects that have the same returns but later in the project.

''Net present value'' is the sum of all the cash flows of a project adjusted to present values. For example, suppose we have two projects that have the same initial cost of $100,000. The two projects have the same net cash flows as well, but the time that the money comes to us is different. The interest rate for borrowing money is 7 percent. Table 1—2 illustrates the present value cash flow.

Notice that here the two projects have the same total return over the ten-year life of the projects, but project A gets more of the returns sooner, making the net present value of the money higher. Remember, the present value of the money is the value today of money that will be received in the future.

In this justification analysis, we considered much more than in previous methods. Here we recognized all of the costs and revenues that occur over the useful life of the project. If this were a project to buy a machine, for example, we would look at the cash flows over the expected life of the machine. This would allow us to consider the effect of changing sales forecasts and changing maintenance costs. Then we can adjust for the time value of the money that is involved in the project. This method gives us a pretty good idea of which projects should be selected over other projects.

There is one difficulty with this method. There is a problem distinguishing small projects that have small investments and relatively small returns when compared to large projects. The method of justification we have just seen tells us only the net present value of the project. It does not tell us whether we would be better off selecting a number of small projects or a few large ones. What we need is a method of justification that gives us a single value that will be highest for the most favorable project, regardless of size. If we had a method like that, we would be able to rank all of our potential projects by this value and use the ranking order to pick the projects that are the most favorable for financial reasons.

### Internal Rate of Return on Investment

The internal rate of return on investment (IRR) method meets all of the criteria for a justification method that gives a single value. It is, however, the most complicated of them all. For practical reasons, a computer is required to make the calculations.

In the last example we looked at the cash flows of two different projects. Both of the projects had the same total cash flow at the end of their useful life, but one of them was favored because of the adjustment of the value of future monies received. The factor in our calculations that brought about this result was the interest rate that was used. It

Year |
Project A |
7% Interest |
Project B |
7% Interest | ||||

Outflow |
Inflow |
PV |
NPV |
Outflow |
Inflow |
PV |
NPV | |

0 |
-100,000 |
0 |
-100,000 |
-100,000 |
0 |
-100.000 | ||

1 |
60,000 |
56,075 |
- 43,925 |
30,000 |
28.037 |
-71.963 | ||

2 |
50,000 |
43,672 |
-253 |
30,000 |
26.203 |
-45.759 | ||

3 |
40,000 |
32,652 |
32,399 |
30,000 |
24.489 |
-21.271 | ||

4 |
30,000 |
22,887 |
55,285 |
30,000 |
22.887 |
1.616 | ||

5 |
20,000 |
14,260 |
69,545 |
30,000 |
21.390 |
23.006 | ||

6 |
20,000 |
13,327 |
82,872 |
30,000 |
19.990 |
42.996 | ||

7 |
20,000 |
12,455 |
95,327 |
30,000 |
18.682 |
61.679 | ||

8 |
20,000 |
11,640 |
106,967 |
30,000 |
17.460 |
79.139 | ||

9 |
20,000 |
10,879 |
117,846 |
30,000 |
16.318 |
95.457 | ||

10 |
20,000 |
10,167 |
128,013 |
30,000 |
15.250 |
110.707 | ||

Total |
300,000 |
228,013 |
300,000 |
210,707 |

should be clear that if the interest rate were zero, both projects would be the same in terms of desirability.

What we are really talking about here is what we can do with our money. We usually want to use money to finance projects that will return money to us in the future. But all of these projects have risk attached to them. There is the possibility that we will spend all the money on the project, and it will not work. The marketplace might change, and the expected revenues are not what we had predicted. Many other things can go wrong in any business venture.

Since all of the projects we run into in business have some risk associated with them, we might want to consider what a risk-free investment might be. There is such a thing. For example, investing in U.S. Treasury bills is considered a risk-free investment. Generally speaking, however, investing in the projects of a company and taking advantage of business opportunities are going to generate a higher return on our investment than putting the same money into U.S. Treasury bills.

Suppose interest rates were higher. If they were high enough, we could consider putting money into the risk-free investment of U.S. Treasury bills. If they were not high enough, we would invest in projects. At any given interest rate, it would be wise to invest in some projects and not in others. With this in mind, we can come up with another justification system.

In the internal rate of return on investment justification method, we are calculating the interest rate on Treasury bills that would make the proposed project and investing in the Treasury bills ''equal opportunities.''

To make the calculation we compare the net present value of the project at the end of its useful life to the net present value of the risk-free investment. At low interest rates the project with the risk and relatively higher cash flows into the organization will be favored. As interest rates increase, the difference between the two investments will change and become smaller until the interest rate is high enough to make investing in the risk-free investment as favorable as investing in the risky investment.

Notice that when we look at projects this way, the size of the project does not matter. Only the value of the project matters.

These calculations need to be done by a computer, because the calculations cannot be handled algebraically but must be solved in an iterative manner. An example will show this best.

Suppose we take the project from the previous example and look at what the cash flows would be at various interest rates (Table 1—3). If we calculate the present value of each of the cash flows, we will find that at the end of the time period of the project, the net cash flows are either positive or negative. We have the cash flows already calculated at 7 percent interest. Now we will calculate the net present value cash flows for various interest rates.

Table 1-3. |
Cash flow at various interest rates. | ||

Project A |
7% Interest | ||

Year |
Outflow Inflow |
PV |
1.07 |

0 |
$100,000.00 $0.00 |
-$100,000.00 | |

1 |
$60,000.00 |
$56,074.77 | |

2 |
$50,000.00 |
$43,671.94 | |

3 |
$40,000.00 |
$32,651.92 | |

4 |
$30,000.00 |
$22,886.86 | |

5 |
$20,000.00 |
$14,259.72 | |

6 |
$20,000.00 |
$13,326.84 | |

7 |
$20,000.00 |
$12,454.99 | |

8 |
$20,000.00 |
$11,640.18 | |

9 |
$20,000.00 |
$10,878.67 | |

10 |
$20,000.00 |
$10,166.99 | |

Total |
Project A |
$128,012.88 60% Interest |

Year Outflow Inflow PV 1.6

0 |
$100,000.00 |
$0.00 |
-$100,000.00 |

1 |
$60,000.00 |
$37,500.00 | |

2 |
$50,000.00 |
$19,531.25 | |

3 |
$40,000.00 |
$9,765.63 | |

4 |
$30,000.00 |
$4,577.64 | |

5 |
$20,000.00 |
$1,907.35 | |

6 |
$20,000.00 |
$1,192.09 | |

7 |
$20,000.00 |
$745.06 | |

8 |
$20,000.00 |
$465.66 | |

9 |
$20,000.00 |
$291.04 | |

10 |
$20,000.00 |
$181.90 | |

Total |
-$23,842.39 |

(continues)

Table 1-3. |
(Continued). | ||

Project A |
40% Interest | ||

Year |
Outflow |
Inflow |
PV |

0 |
S100.000.00 |
S0.00 |
-S100.000.00 |

1 |
S60.000.00 |
S42.BSl.14 | |

2 |
SS0.000.00 |
S2S.S10.20 | |

3 |
S40.000.00 |
S14.Sll.26 | |

4 |
S30.000.00 |
Sl.B09.2S | |

S |
S20.000.00 |
S3.l1B.69 | |

6 |
S20.000.00 |
S2.6S6.21 | |

l |
S20.000.00 |
S1.B9l.29 | |

B |
S20.000.00 |
S1.3SS.21 | |

9 |
S20.000.00 |
S96B.01 | |

10 |
S20.000.00 |
S691.43 | |

Total |
S2.040.6B | ||

Project A |
50% Interest | ||

Year |
Outflow |
Inflow |
PV |

0 |
S100.000.00 |
S0.00 |
-S100.000.00 |

1 |
S60.000.00 |
S40.000.00 | |

2 |
SS0.000.00 |
S22.222.22 | |

3 |
S40.000.00 |
S11.BS1.BS | |

4 |
S30.000.00 |
SS.92S.93 | |

S |
S20.000.00 |
S2.633.l4 | |

6 |
S20.000.00 |
S1.lSS.B3 | |

l |
S20.000.00 |
S1.1l0.SS | |

B |
S20.000.00 |
SlB0.3l | |

9 |
S20.000.00 |
SS20.2S | |

10 |
S20.000.00 |
S346.B3 | |

Total |
-S12.l92.43 |

Table 1-3. |
(Continued). | |||

Project A |
45% Interest | |||

Year |
Outflow |
Inflow |
PV |
1.45 |

0 |
$100,000.00 |
$0.00 |
-$100,000.00 | |

1 |
$60,000.00 |
$41,379.31 | ||

2 |
$50,000.00 |
$23,781.21 | ||

3 |
$40,000.00 |
$13,120.67 | ||

4 |
$30,000.00 |
$6,786.55 | ||

5 |
$20,000.00 |
$3,120.25 | ||

6 |
$20,000.00 |
$2,151.90 | ||

7 |
$20,000.00 |
$1,484.07 | ||

8 |
$20,000.00 |
$1,023.50 | ||

9 |
$20,000.00 |
$705.86 | ||

10 |
$20,000.00 |
$486.80 | ||

Total |
-$5,959.88 | |||

Project A |
42.5% Interest |

Year Outflow Inflow PV 1.425

0 |
$100,000.00 |
$0.00 |
-$100,000.00 |

1 |
$60,000.00 |
$42,105.26 | |

2 |
$50,000.00 |
$24,622.96 | |

3 |
$40,000.00 |
$13,823.42 | |

4 |
$30,000.00 |
$7,275.48 | |

5 |
$20,000.00 |
$3,403.73 | |

6 |
$20,000.00 |
$2,388.59 | |

7 |
$20,000.00 |
$1,676.20 | |

8 |
$20,000.00 |
$1,176.28 | |

9 |
$20,000.00 |
$825.46 | |

10 |
$20,000.00 |
$579.27 | |

Total |
-$2,123.34 |

We use the equation:

FV = 1/(1 + int)n where FV is the future value of the cash flow, int is the proposed equivalent interest rate in decimal form, and n is the number of the time periods from present to future value.

When we have reached the point when the net cash flows are no longer positive, then, for the time period in question, we have found the equivalent interest rate that would make investing in a risk-free investment equal to investing in the project. Referring to Table 1—3, we can see that this interest rate is between 40 percent and 42.5 percent.

## 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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