Risks commonly considered to understand project financing are:

From Table 14–15, Project A will last for exactly five years with the cash inflows shown. The payback period will be exactly four years. If the cash inflow in Year 4 were $6,000 instead of $5,000, then the payback period would be three years and 10 months.

The problem with the payback method is that $5,000 received in Year 4 is not worth $5,000 today. This unsophisticated approach mandates that the payback method be used as a supplemental tool to accompany other methods.

14.23 THE TIME VALUE OF MONEY

Everyone knows that a dollar today is worth more than a dollar a year from now. The reason for this is because of the time value of money. To illustrate the time value of money, let us look at the following equation:

FV � PV(1 � k)n

where FV � Future value of an investment PV � Present value

k � Investment interest rate (or cost of capital) n � Number of years

Using this formula, we can see that an investment of $1,000 today (i.e., PV) invested at 10% (i.e., k) for one year (i.e., n) will give us a future value of $1,100. If the investment is for two years, then the future value would be worth $1,210.

Now, let us look at the formula from a different perspective. If an investment yields $1,000 a year from now, then how much is it worth today if the cost of money is 10%? To solve the problem, we must discount future values to the present for comparison purposes. This is referred to as “discounted cash flows.”

The previous equation can be written as:

PV � � (1

F �

V k)n

�

Using the data given:

PV � � (1

$ �

1,0 0 0 . 0 1)1

� � $909

The Time Value of Money 615

TABLE 14–15. CAPITAL EXPENDITURE DATA FOR PROJECT A

Initial Investment Expected Cash Inflows

Year 1 Year 2 Year 3 Year 4 Year 5 $10,000 $1,000 $2,000 $2,000 $5,000 $2,000

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Therefore, $1,000 a year from now is worth only $909 today. If the interest rate, k, is known to be 10%, then you should not invest more than $909 to get the $1,000 return a year from now. However, if you could purchase this investment for $875, your interest rate would be more than 10%.

Discounting cash flows to the present for comparison purposes is a viable way to assess the value of an investment. As an example, you have a choice between two investments. Investment A will generate $100,000 two years from now and investment B will generate $110,000 three years from now. If the cost of capital is 15%, which investment is better?

Using the formula for discounted cash flow, we find that:

PVA � $75,614 PVB � $72,327

This implies that a return of $100,000 in two years is worth more to the firm than a $110,000 return three years from now.

14.24 NET PRESENT VALUE (NPV)

The net present value (NPV) method is a sophisticated capital budgeting technique that equates the discounted cash flows against the initial invest- ment. Mathematically,

NPV � � n

t�1 ��(1F�Vtk)t�� � II

where FV is the future value of the cash inflows, II represents the initial investment, and k is the discount rate equal to the firm’s cost of capital.

Table 14–16 calculates the NPV for the data provided previously in Table 14–15 using a discount rate of 10%.

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TABLE 14–16. NPV CALCULATION FOR PROJECT A

Cash Year Inflows Present Value

1 $1,000 $11,909 2 $2,000 $11,653 3 $2,000 $11,503 4 $5,000 $13,415 5 $2,000 $11,242

Present value of cash inflows $18,722

Less investment $10,000

Net Present Value �1,278�

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This indicates that the cash inflows discounted to the present will not recover the initial investment. This, in fact, is a bad investment to consider. Previously, we stated that the cash flow stream yielded a payback period of four years. However, using discounted cash flow, the actual payback is greater than five years, assuming that there will be cash inflow in years 6 and 7.

If in Table 14–16 the initial investment was $5,000, then the net present value would be $3,722. The decision-making criteria using NPV are as follows:

● If the NPV is greater than or equal to zero dollars, accept the project. ● If the NPV is less than zero dollars, reject the project.

A positive value of NPV indicates that the firm will earn a return equal to or greater than its cost of capital.

14.25 INTERNAL RATE OF RETURN (IRR)

The internal rate of return (IRR) is perhaps the most sophisticated capital budgeting technique and also more difficult to calculate than NPV. The internal rate of return is the discount rate where the present value of the

cash inflows exactly equals the initial investment. In other words, IRR is the discount rate when NPV � 0. Mathematically

� n

t�1 ��(1 �FVIRt R)t�� � II � 0

The solution to problems involving IRR is basically a trial-and-error solution. Table 14–17 shows that with the cash inflows provided, and with a $5,000 initial investment, an IRR of 10% yielded a value of $3,722 for NPV. Therefore, as a second guess, we should try a value greater than 10% for IRR to generate a zero value for NPV. Table 14–17 shows the final calculation.

The table implies that the cash inflows are equivalent to a 31% return on investment. Therefore, if the cost of capital were 10%, this would be an excellent investment. Also, this project is “probably” superior to other projects with a lower value for IRR.

Internal Rate of Return (IRR) 617

TABLE 14–17. IRR CALCULATION FOR PROJECT A CASH INFLOWS

IRR NPV

10% $3,722 20% 1,593 25% 807 30% 152 31% 34 32% �78�

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14.26 COMPARING IRR, NPV, AND PAYBACK

For most projects, both IRR and NPV will generate the same accept- reject decision. However, there are differences that can exist in the under- lying assumptions that can cause the projects to be ranked differently. The

major problem is the differences in the magnitude and timing of the cash inflows. NPV assumes that the cash inflows are reinvested at the cost of capital, whereas IRR assumes reinvestment at the project’s IRR. NPV tends to be a more conservative approach.

The timing of the cash flows is also important. Early year cash inflows tend to be at a lower cost of capital and are more predictable than later year cash inflows. Because of the downstream uncertainty, companies prefer larger cash inflows in the early years rather than the later years.

Magnitude and timing are extremely important in the selection of capital projects. Consider Table 14–18.

If the company has sufficient funds for one and only one project, the natural assump- tion would be to select Project D with a 35% IRR. Unfortunately, companies shy away from long-term payback periods because of the relative uncertainties of the cash inflows after Year 1. One chemical/plastics manufacturer will not consider any capital projects unless the payback period is less than one year and has an IRR in excess of 50%!

14.27 RISK ANALYSIS

Suppose you have a choice between two projects, both of which require the same initial investment, have identical net present values, and require the same yearly cash inflows to break even. If the cash inflow of the first investment has a probability of occurrence of 95% and that of the second investment is 70%, then risk analysis would indicate that the first

investment is better. Risk analysis refers to the chance that the selection of this project will prove to be

unacceptable. In capital budgeting, risk analysis is almost entirely based upon how well we can predict cash inflows since the initial investment is usually known with some degree of certainty. The inflows, of course, are based upon sales projections, taxes, cost of raw materials, labor rates, and general economic conditions.

Sensitivity analysis is a simple way of assessing risk. A common approach is to esti- mate NPV based upon an optimistic (best case) approach, most likely (expected) approach,

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TABLE 14–18. CAPITAL PROJECTS

Payback Period Project IRR with DCF

A 10% 1 year B 15% 2 years C 25% 3 years D 35% 5 years

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and pessimistic (worst case) approach. This can be illustrated using Table 14–19. Both Projects A and B require the same initial investment of $10,000, with a cost of capital of 10%, and with expected five-year annual cash inflows of $5,000/year. The range for Project A’s NPV is substantially less than that of Project B, thus implying that Project A is less risky. A risk lover might select Project B because of the potential reward of $27,908, whereas a risk avoider would select Project A, which offers perhaps no chance for loss.

14.28 CAPITAL RATIONING

Capital rationing is the process of selecting the best group of projects such that the highest overall net present value will result without exceeding the total budget available. An assumption with capital rationing is that the pro- jects under consideration are mutually exclusive. There are two approaches often considered for capital rationing.

The internal rate of return approach plots the IRRs in descending order against the cumulative dollar investment. The resulting figure is often called an investment opportu- nity schedule. As an example, suppose a company has $300,000 committed for projects and must select from the projects identified in Table 14–20. Furthermore, assume that the cost of capital is 10%.

Capital Rationing 619

TABLE 14–19. SENSITIVITY ANALYSIS

Project A Project B Initial Investment $10,000 $10,000

Annual Cash Inflows Optimistic $18,000 $10,000 Most likely 5,000 5,000 Pessimistic 3,000 1,000 Range $15,000 $19,000

Net Present Values Optimistic $20,326 $27,908 Most likely 8,954 8,954 Pessimistic 1,342 �6,209� Range $18,984 $34,117

TABLE 14–20. PROJECTS UNDER CONSIDERATION

Discounted Cash Project Investment IRR Flows at 10%

A $150,000 20% $116,000 B 120,000 18% 183,000 C 110,000 16% 147,000 D 130,000 15% 171,000 E 90,000 12% 103,000 F 180,000 11% 206,000 G 80,000 18% 66,000

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Figure 14–19 shows the investment opportunity schedule. Project G should not be considered because the IRR is less than the firm’s cost of capital, but we should select Projects, A, B, and C, which will consume $280,000 out of a total budget of $300,000. This allows us to have the three largest IRRs.

The problem with the IRR approach is that it does not guarantee that the projects with the largest IRRs will maximize the total dollar returns. The reason is that not all of the funds have been consumed.

A better approach is the net present value method. In this method, the projects are again ranked according to their IRRs, but the combination of projects selected will be based upon the highest net present value. As an example, the selection of Projects A, B, and C from Table 14–20 requires an initial investment of $280,000 with resulting dis- counted cash flows of $446,000. The net present value of Projects A, B, and C is, there- fore, $166,000. This assumes that unused portions of the original budget of $300,000 do not gain or lose money. However, if we now select Projects A, B, and D, we will invest $300,000 with a net present value of $170,000 ($470,000 less $300,000). Selection of Projects A, B, and D will, therefore, maximize net present value.

14.29 PROJECT FINANCING2

Project financing involves the establishment of a legally independent project company, usually for large-scale investments (LSI) and long term where the providers of funds are repaid out of cash flow and earnings, and where the assets of the unit (and only the unit)

620 PRICING AND ESTIMATING

2%

0 $1000

4%

6%

$200 $300 $400 $500 $600 $700 $800

8%

10%

12%

14%

16%

18%

20%

IR R

$280K

A

COST OF CAPITAL

BUDGET CONSTRAINT

B

C D

E F

G

TOTAL INVESTMENT (IN THOUSANDS)

FIGURE 14–19. Investment Opportunity Schedule (IOS) for Table 14–20.

2. Project financing is a relatively new topic and is now being taught in graduate programs in business. At Harvard University, it is taught as a course entitled Large Scale Investment by Professor Benjamin C. Esty. Many excellent examples appear in Professor Esty’s text, Modern Project Finance (Hoboken, NJ: Wiley, 2004).

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are used as collateral for the loans. Debt repayment would come from the project company only rather than from any other entity. A risk with project financing is that the capital assets may have a limited life. The potential limited life constraint often makes it difficult to get lenders to agree to long-term financial arrangements.

Another critical issue with project financing especially for high-technology projects is that the projects are generally long term. It may be nearly eight to ten years before service will begin, and in terms of technology, eight years can be an eternity. Project financing is often considered a “bet on the future.” And if the project were to fail, the company could be worth nothing after liquidation.

There are several risks that must be considered to understand project financing. The risks commonly considered are

Financial Risks ● Use of project versus corporate financing ● Use of corporate bonds, stock, zero coupon bonds, and bank notes ● Use of secured versus unsecured debt ● The best sequence or timing for raising capital ● Bond rating changes ● Determination of the refinancing risk, if necessary

Development Risks ● Reality of the assumptions ● Reality of the technology ● Reality of development of the technology ● Risks of obsolescence

Political Risks ● Sovereignty risks ● Political instability ● Terrorism and war ● Labor availability ● Trade restrictions ● Macroeconomics such as inflation, currency conversion, and transferability of

funding and technology

Organizational Risks ● Members of the board of directors ● Incentives for the officers ● Incentives for the board members ● Bonuses as a percentage of base compensation ● Process for the resolution of disputes

Execution Risks ● Timing when execution will begin ● Life expectancy of execution ● Ability to service debt during execution

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14.30 STUDYING TIPS FOR THE PMI® PROJECT MANAGEMENT CERTIFICATION EXAM

This section is applicable as a review of the principles to support the knowledge areas and domain groups in the PMBOK® Guide. This chapter addresses:

● Integration Management ● Scope Management ● Time Management ● Cost Management ● Initiating ● Planning

Understanding the following principles is beneficial if the reader is using this text to study for the PMP® Certification Exam:

● What is meant by cost-estimating relationships (CER) ● Three basic types of estimates ● Relative accuracy of each type of estimate and the approximate time to prepare the

estimate ● Information that is needed to prepare the estimates (i.e., labor, material, overhead

rates, etc.) ● Importance of backup data for costs ● Estimating pitfalls ● Concept of rolling wave planning ● What is meant by life cycle costing ● Different ways of evaluating a project’s financial feasibility or benefits (i.e., ROI,

payback period, net present value, internal rate of return, depreciation, scoring models)

The following multiple-choice questions will be helpful in reviewing the principles of this chapter:

1. Which of the following is a valid way of evaluating the financial feasibility of a project? A. Return on investment B. Net present value C. Internal rate of return D. All of the above

2. The three common classification systems for estimates includes all of the following except: A. Parametric estimates B. Quick-and-dirty estimates C. Analogy estimates D. Engineering estimates

3. The most accurate estimates are: A. Parametric estimates B. Quick-and-dirty estimates

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C. Analogy estimates D. Engineering estimates

4. Which of the following is considered to be a bottom-up estimate rather than a top-down estimate? A. Parametric estimates B. Analogy estimates C. Engineering estimates D. None of the above

5. Which of the following would be considered as a cost-estimating relationship (CER)? A. Mathematical equations based upon regression analysis B. Learning curves C. Cost–cost or cost–quantity relationships D. All of the above

6. If a worker earns $30 per hour in salary but the project is charged $75 per hour for each hour the individual works, then the overhead rate is: A. 100% B. 150% C. 250% D. None of the above

7. Information supplied to a customer to support the financial data provided in a proposal is commonly called: A. Backup data B. Engineering support data C. Labor justification estimates D. Legal rights estimates

8. Estimating pitfalls can result from: A. Poorly defined statement of work B. Failure to account for risks in the estimates C. Using the wrong estimating techniques D. All of the above

9. The source of many estimating risks is: A. Poorly defined requirements B. An inexperienced project manager C. Lack of management support during estimating D. All of the above

10. A project where the scope evolves as the work takes place is called either progressive plan- ning or: A. Synchronous planning B. Continuous planning C. Rolling wave planning D. Continuous reestimation planning

11. The calculation of the total cost of a product, from R&D to operational support and disposal, is called: A. Birth-to-death costing B. Life-cycle costing C. Summary costing D. Depreciation costing

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ANSWERS

1. D

2. B

3. D

4. C

5. D

6. B

7. A

8. D

9. D

10. C

11. B

PROBLEMS

14–1 How does a project manager price out a job in which the specifications are not prepared until the job is half over?

14–2 Beta Corporation is in the process of completing a contract to produce 150 units for a given customer. The contract consisted of R&D, testing and qualification, and full production. The industrial engineering department had determined that the following number of hours were required to produce certain units:

Unit Hours Required Per Unit 1 100 2 90 4 80 8 70

16 65 32 60 64 55

128 50

a. Plot the data points on regular graph paper with the Y-axis as hours and the X-axis as number of units produced.

b. Plot the data points on log–log paper and determine the slope of the line. c. Compare parts a and b. What are your conclusions? d. How much time should it take to manufacture the 150th unit? e. How much time should it take to manufacture the 1,000th unit? Explain your answer.

Is it realistic? If not, why? f. As you are producing the 150th unit, you receive an immediate follow-on contract for

another 150 units. How many manufacturing hours should you estimate for the follow-on effort (using only the learning curves)?

g. Let’s assume that industrial engineering determines that the optimum number of hours (for 100 percent efficiency) of manufacturing is forty-five. At what efficiency factor are you now performing at the completion of unit number 150? After how many units in the follow-on contract will you reach the optimum level?

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