Financial Analysis of Projects

Profitability Models Present & Future Value Benefit / Cost Ratio Payback period Internal Rate of Return Annual Value

Net Present Value Net Present Value - Present value of cash flows minus initial investments. Opportunity Cost of Capital - Expected rate of return given up by investing in a project. 4

Net Present Value A: Profit = - $50 + $60 = $10 Example Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value? Initial Investment Added Value $50 $10 A: Profit = - $50 + $60 = $10 6

Net Present Value Example Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return? This is the definition of NPV Initial Investment Added Value $50 $4.55 8

NPV = PV - required investment Net Present Value NPV = PV - required investment 11

Net Present Value Terminology C = Cash Flow t = time period of the investment r = “opportunity cost of capital” The Cash Flow could be positive or negative at any time period. 12

Net Present Value Net Present Value Rule Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value. 13

Net Present Value Example You have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building? 14

Net Present Value Example - continued 0 1 2 3 $466,000 Example - continued $450,000 $16,000 $16,000 $16,000 0 1 2 3 You have a cost of capital of 7 %. 15

Net Present Value Example - continued 0 1 2 3 Present Value 14,953 $466,000 Example - continued $450,000 $16,000 $16,000 $16,000 0 1 2 3 Present Value 14,953 13,975 380,395 $409,323 16

Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building? 17

Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building? 18

Present Value Example Initial Investment: $100,000 Project Life: 10 years Salvage Value: $ 20,000 Annual Receipts: $ 40,000 Annual Disbursements: $ 22,000 Annual Discount Rate: 12% What is the net present value for this project? Is the project an acceptable investment?

Present Value Example Solution Annual Receipts $40,000(P/A, 12%, 10) $ 226,000 Salvage Value $20,000(P/F, 12%, 10) $ 6,440 Annual Disbursements $22,000(P/A, 12%, 10) -$124,000 Initial Investment (t=0) -$100,000 Net Present Value $ 8,140 Greater than zero, therefore acceptable project

Future Value The future value method evaluates a project based upon the basis of how much money will be accumulated at some future point in time. This is just the reverse of the present value concept. FV T = 0 +/- Cash Flows

Future Value Example Initial Investment: $100,000 Project Life: 10 years Salvage Value: $ 20,000 Annual Receipts: $ 40,000 Annual Disbursements: $ 22,000 Annual Discount Rate: 12% What is the net future value for this project? Is the project an acceptable investment?

Future Value Example Solution Annual Receipts $40,000(F/A, 12%, 10) $ 701,960 Salvage Value $20,000(year 10) $ 20,000 Annual Disbursements $22,000(F/A, 12%, 10) -$386,078 Initial Investment $100,000(F/P, 12%, 10) -$310,600 Net Future Value $ 25,280 Positive value, therefore acceptable project Can be used to compare with future value of other projects

PV/FV No theoretical difference if project is evaluated in present or future value PV of $ 25,282 $25,282(P/F, 12%, 10) $ 8,140 FV of $ 8,140 $8,140(F/P, 12%, 10) $ 25,280

Annual Value Sometimes it is more convenient to evaluate a project in terms of its annual value or cost. For example it may be easier to evaluate specific components of an investment or individual pieces of equipment based upon their annual costs as the data may be more readily available for analysis.

Annual Analysis Example A new piece of equipment is being evaluated for purchase which will generate annual benefits in the amount of $10,000 for a 10 year period, with annual costs of $5,000. The initial cost of the machine is $40,000 and the expected salvage is $2,000 at the end of 10 years. What is the net annual worth if interest on invested capital is 10%?

Annual Example Solution Benefits: $10,000 per year $10,000 Salvage $2,000(P/F, 10%, 10)(A/P, 10%,10) $ 125 Costs: $5,000 per year -$ 5,000 Investment: $40,000(A/P, 10%, 10) -$ 6,508 Net Annual Value -$1,383 Since this is less than zero, the project is expected to earn less than the acceptable rate of 10%, therefore the project should be rejected.

Other Investment Criteria Internal Rate of Return (IRR) - Discount rate at which NPV = 0. 19

Other Investment Criteria Internal Rate of Return (IRR) - Discount rate at which NPV = 0. Rate of Return Rule - Invest in any project offering a rate of return that is higher than the opportunity cost of capital. 20

Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? 21

Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? 22

Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? IRR = 12.96% 23

Internal Rate of Return IRR=12.96% 24

Rate of Return Rule The rate of return is the discount rate at which NPV equals zero. If the opportunity cost of capital is less than the project rate of return, then the NPV of the project is positive. The NPV rule and the rate of return rule are positive.

Payback Method Payback Period Time until cash flows recover the initial investment of the project. 27

Payback Method Payback Period - Time until cash flows recover the initial investment of the project. The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this statement. 28

Payback Method Example The three project below are available. The company accepts all projects with a 2 year or less payback period. Show how this decision will impact our decision. 29

Payback Method Example The three project below are available. The company accepts all projects with a 2 year or less payback period. Show how this decision will impact our decision. Cash Flows Prj. C0 C1 C2 C3 Payback NPV@10% A -2000 +1000 +1000 +10000 B -2000 +1000 +1000 0 C -2000 0 +2000 0 30

Payback Method Example The three project below are available. The company accepts all projects with a 2 year or less payback period. Show how this decision will impact our decision. Cash Flows Prj. C0 C1 C2 C3 Payback NPV@10% A -2000 +1000 +1000 +10000 2 B -2000 +1000 +1000 0 2 C -2000 0 +2000 0 2 31

Payback Method Example The three project below are available. The company accepts all projects with a 2 year or less payback period. Show how this decision will impact our decision. Cash Flows Prj. C0 C1 C2 C3 Payback NPV@10% A -2000 +1000 +1000 +10000 2 +7,249 B -2000 +1000 +1000 0 2 - 264 C -2000 0 +2000 0 2 - 347 32

Payback Period

Book Rate of Return Book Rate of Return - Average income divided by average book value over project life. Also called accounting rate of return. 33

Book Rate of Return Book Rate of Return - Average income divided by average book value over project life. Also called accounting rate of return. Managers rarely use this measurement to make decisions. The components reflect tax and accounting figures, not market values or cash flows. 34

Internal Rate of Return Example You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised proposal (I). Using IRR, which do you prefer?

Internal Rate of Return Example You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised proposal (I). Using IRR, which do you prefer?

Internal Rate of Return Pitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem. Pitfall 2 - Lending or Borrowing? With some cash flows (as noted below) the NPV of the project increases as the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. Pitfall 3 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates. The following cash flow generates NPV=0 at both (-50%) and 15.2%.

Project Interactions When you need to choose between mutually exclusive projects, the decision rule is simple. Calculate the NPV of each project, and, from those options that have a positive NPV, choose the one whose NPV is highest. 35

Mutually Exclusive Projects Example Select one of the two following projects, based on highest NPV. assume 7% discount rate 36

Investment Timing Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision. A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow. 38

Investment Timing Example You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer? 39

Investment Timing Example You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer? Year Cost PV Savings NPV at Purchase NPV Today 0 50 70 20 20.0 1 45 70 25 22.7 2 40 70 30 24.8 3 36 70 34 Date to purchase 25.5 4 33 70 37 25.3 5 31 70 39 24.2 40

Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine. 42

Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method. Year Mach. 1 2 3 4 PV@6% Ann. Cost D -15 -4 -4 -4 E -10 -6 -6 - 9.61 -11.45 -25.69 -21.00 45

Equivalent Annual Cost Example (with a twist) Select one of the two following projects, based on highest “equivalent annual annuity” (r=9%). 2.82 2.78 .87 1.10 47

Capital Rationing Capital Rationing - Limit set on the amount of funds available for investment. Soft Rationing - Limits on available funds imposed by management. Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market. 48

Profitability Index

Project Interactions When you need to choose between mutually exclusive projects, the decision rule is simple. Calculate the NPV of each project, and, from those options that have a positive NPV, choose the one whose NPV is highest. 35

Numeric Models: Scoring In an attempt to overcome some of the disadvantages of profitability models, particularly their focus on a single decision criterion, a number of evaluation/selection models hat use multiple criteria to evaluate a project have been developed. Such models vary widely in their complexity and information requirements. The examples discussed illustrate some of the different types of numeric scoring models.

Some factors to consider

Unweighted 0–1 Factor Model A set of relevant factors is selected by management and then usually listed in a preprinted form. One or more raters score the project on each factor, depending on whether or not it qualifies for an individual criterion. The raters are chosen by senior managers, for the most part from the rolls of senior management. The criteria for choice are: (1) a clear understanding of organizational goals (2) a good knowledge of the firm’s potential project portfolio. Next slide: The columns are summed, projects with a sufficient number of qualifying factors may be selected. Advantage: It uses several criteria in the decision process. Disadvantage: It assumes all criteria are of equal importance and it allows for no gradation of the degree to which a specific project meets the various criteria.

Unweighted Factor Scoring Model X marks in 0-1 scoring model are replaced by numbers, from a 5 point scale.

Weighted Factor Scoring Model When numeric weights reflecting the relative importance of each individual factor are added, we have a weighted factor scoring model. In general, it takes the form where Si the total score of the ith project, Sij the score of the ith project on the jth criterion, and Wj the weight of the jth criterion.

Constrained Weighted Factor Scoring Model Additional criteria enter the model as constraints rather than weighted factors. These constraints represent project characteristics that must be present or absent in order for the project to be acceptable. We might have specified that we would not undertake any project that would significantly lower the quality of the final product (visible to the buyer or not). We would amend the weighted scoring model to take the form: where Cik 1 if the i th project satisfies the Kth constraint, and 0 if it does not.

Example: P & G practice Would not consider a project to add a new consumer product or product line: that cannot be marketed nationally; that cannot be distributed through mass outlets (grocery stores, drugstores); that will not generate gross revenues in excess of $—million; for which Procter & Gamble’s potential market share is not at least 50 percent; and that does not utilize Procter & Gamble’s scientific expertise, manufacturing expertise, advertising expertise, or packaging and distribution expertise.

Final Thought Selecting the type of model to aid the evaluation/selection process depends on the philosophy and wishes of management. Weighted scoring models preferred for three fundamental reasons. they allow the multiple objectives of all organizations to be reflected in the important decision about which projects will be supported and which will be rejected. scoring models are easily adapted to changes in managerial philosophy or changes in the environment. they do not suffer from the bias toward the short run that is inherent in profitability models that discount future cash flows.