financial analysis of projects

Financial Financial Analysis of Analysis of

ProjectsProjects

Profitability ModelsProfitability Models

Present & Future ValuePresent & Future Value Benefit / Cost RatioBenefit / Cost Ratio Payback periodPayback period Internal Rate of ReturnInternal Rate of Return Annual ValueAnnual Value

Net Present ValueNet Present Value

Opportunity Cost of CapitalOpportunity Cost of Capital - Expected rate - Expected rate of return given up by investing in a project. of return given up by investing in a project.

Net Present Value - Present value of cash flows minus initial investments.


ExampleExample

Q: Suppose we can invest $50 today & receive Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value?$60 later today. What is our increase in value?

Initial Investment

Added Value

$50

$10

A: Profit = - $50 + $60 = $10


ExampleExample

Suppose we can invest $50 today and receive Suppose we can invest $50 today and receive $60 in one year. What is our increase in $60 in one year. What is our increase in value given a 10% expected return?value given a 10% expected return?

This is the definition of NPVThis is the definition of NPV

Profit = -50 +60

1.10$4.55

Initial Investment

Added Value

$50

$4.55


NPV = PV - required investmentNPV = PV - required investment

NPV CC

rt

t

0 1( )

NPV CC

r

C

r

C

rt

t

01

12

21 1 1( ) ( )...

( )


TerminologyTerminology

C = Cash FlowC = Cash Flow

t = time period of the investmentt = time period of the investment

r = “opportunity cost of capital”r = “opportunity cost of capital”

The Cash Flow could be positive or The Cash Flow could be positive or negative at any time period.negative at any time period.


Net Present Value RuleNet Present Value Rule

Managers increase shareholders’ Managers increase shareholders’ wealth by accepting all projects that wealth by accepting all projects that are worth more than they cost. are worth more than they cost.

Therefore, they should accept all Therefore, they should accept all projects with a positive net present projects with a positive net present value.value.


ExampleExample

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


0 1 2 3

$16,000$16,000$16,000

$450,000

$466,000

ExampleExample - continued - continued

You have a cost of capital of 7 %.


0 1 2 3

$16,000$16,000$16,000

$450,000

$466,000

Present Value

14,953

13,975

380,395

$409,323




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



If the building is being offered for sale at If the building is being offered for sale at a price of $350,000, would you buy the a price of $350,000, would you buy the building and what is the added value building and what is the added value generated by your purchase and generated by your purchase and management of the building?management of the building?NPV

NPV

350 00016 000

107

16 000

107

466 000

107

323

1 2 3,

,

( . )

,

( . )

,

( . )

$59,

Initial Investment:Initial Investment: $100,000$100,000 Project Life:Project Life: 10 years10 years Salvage Value:Salvage Value: $ 20,000$ 20,000 Annual Receipts:Annual Receipts: $ 40,000$ 40,000 Annual Disbursements:Annual Disbursements: $ 22,000$ 22,000 Annual Discount Rate:Annual Discount Rate: 12%12%

What is the net present value for this project?What is the net present value for this project?

Is the project an acceptable investment?Is the project an acceptable investment?

Present Value Present Value ExampleExample

Present Value Example Present Value Example SolutionSolution

Annual ReceiptsAnnual Receipts $40,000(P/A, 12%, 10)$40,000(P/A, 12%, 10) $ 226,000$ 226,000

Salvage ValueSalvage Value $20,000(P/F, 12%, 10)$20,000(P/F, 12%, 10) $ 6,440 $ 6,440

Annual DisbursementsAnnual Disbursements $22,000(P/A, 12%, 10)$22,000(P/A, 12%, 10) -$124,000-$124,000

Initial Investment (t=0)Initial Investment (t=0) -$100,000-$100,000

Net Present ValueNet Present Value $ 8,140$ 8,140 Greater than zero, therefore acceptable projectGreater than zero, therefore acceptable project

Future ValueFuture Value

The future value method evaluates a project The future value method evaluates a project based upon the basis of how much money will be based upon the basis of how much money will be accumulated at some future point in time. This accumulated at some future point in time. This is just the reverse of the present value concept.is just the reverse of the present value concept.

T = 0 +/- Cash Flows

FV

Initial Investment:Initial Investment: $100,000$100,000 Project Life:Project Life: 10 years10 years Salvage Value:Salvage Value: $ 20,000$ 20,000 Annual Receipts:Annual Receipts: $ 40,000$ 40,000 Annual Disbursements:Annual Disbursements: $ 22,000$ 22,000 Annual Discount Rate:Annual Discount Rate: 12%12%

What is the net future value for this What is the net future value for this project?project?

Is the project an acceptable investment?Is the project an acceptable investment?

Future Value ExampleFuture Value Example

Future Value Example Future Value Example SolutionSolution

Annual ReceiptsAnnual Receipts $40,000(F/A, 12%, 10)$40,000(F/A, 12%, 10) $ 701,960$ 701,960

Salvage ValueSalvage Value $20,000(year 10)$20,000(year 10) $ 20,000$ 20,000

Annual DisbursementsAnnual Disbursements $22,000(F/A, 12%, 10)$22,000(F/A, 12%, 10) -$386,078-$386,078

Initial Investment Initial Investment $100,000(F/P, 12%, 10)$100,000(F/P, 12%, 10) -$310,600-$310,600

Net Future ValueNet Future Value $ 25,280$ 25,280 Positive value, therefore acceptable projectPositive value, therefore acceptable project Can be used to compare with future value of other projectsCan be used to compare with future value of other projects

PV/FVPV/FV

No theoretical difference if No theoretical difference if project is evaluated in present project is evaluated in present or future valueor future value

PV of $ 25,282PV of $ 25,282

$25,282(P/F, 12%, 10)$25,282(P/F, 12%, 10) $ 8,140$ 8,140

FV of $ 8,140FV of $ 8,140

$8,140(F/P, 12%, 10)$8,140(F/P, 12%, 10) $ 25,280$ 25,280

Annual ValueAnnual Value

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

Annual Analysis ExampleAnnual Analysis Example

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

Annual Example SolutionAnnual Example Solution

Benefits:Benefits: $10,000 per year$10,000 per year $10,000$10,000

SalvageSalvage $2,000(P/F, 10%, 10)(A/P, 10%,10)$2,000(P/F, 10%, 10)(A/P, 10%,10) $ 125$ 125

Costs:Costs: $5,000 per year$5,000 per year -$ 5,000-$ 5,000

Investment:Investment: $40,000(A/P, 10%, 10)$40,000(A/P, 10%, 10) -$ 6,508-$ 6,508

Net Annual ValueNet Annual Value --$1,383$1,383

Since this is less than zero, the project is expected to earn less than the 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.acceptable rate of 10%, therefore the project should be rejected.

Other Investment Other Investment CriteriaCriteria

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

Other Investment Other Investment CriteriaCriteria

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

Rate of Return RuleRate of Return Rule - Invest in any project - Invest in any project offering a rate of return that is higher offering a rate of return that is higher than the opportunity cost of capital.than the opportunity cost of capital.

Rate of Return =C - investment

investment1

Internal Rate of ReturnInternal Rate of Return

ExampleExample

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


ExampleExample

You can purchase a building for You can purchase a building for $350,000. The investment will $350,000. The investment will generate $16,000 in cash flows (i.e. generate $16,000 in cash flows (i.e. rent) during the first three years. At rent) during the first three years. At the end of three years you will sell the end of three years you will sell the building for $450,000. What is the building for $450,000. What is the IRR on this investment?the IRR on this investment?0 350 000

16 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR


ExampleExample

You can purchase a building for $350,000. You can purchase a building for $350,000. The investment will generate $16,000 in The investment will generate $16,000 in cash flows (i.e. rent) during the first three cash flows (i.e. rent) during the first three years. At the end of three years you will years. At the end of three years you will sell the building for $450,000. What is sell the building for $450,000. What is the IRR on this investment?the IRR on this investment?0 350 000

16 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR

IRR = 12.96%


-200

-150

-100

-50

0

50

100

150

200

0 5 10 15 20 25 30 35

Discount rate (%)

NP

V (

,000

s)

IRR=12.96%

Rate of Return RuleRate of Return Rule

The rate of return is the discount rate The rate of return is the discount rate at which NPV equals zero.at which NPV equals zero.

If the opportunity cost of capital is If the opportunity cost of capital is less than the project rate of return, less than the project rate of return, then the NPV of the project is then the NPV of the project is positive.positive.

The NPV rule and the rate of return The NPV rule and the rate of return rule are positive. rule are positive.

Payback MethodPayback Method

Payback PeriodPayback Period

Time until cash flows recover the initial Time until cash flows recover the initial investment of the project.investment of the project.

Payback MethodPayback Method

Payback PeriodPayback Period - Time until cash flows - Time until cash flows recover the initial investment of the recover the initial investment of the project.project.

The The payback rulepayback rule specifies that a project specifies that a project be accepted if its payback period is less be accepted if its payback period is less than the specified cutoff period. The than the specified cutoff period. The following example will demonstrate the following example will demonstrate the absurdity of this statement.absurdity of this statement.

Payback MethodPayback MethodExampleExample

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


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

Cash FlowsCash FlowsPrj.Prj. CC00 CC11 CC22 CC33 PaybackPayback

NPVNPV@10%@10%

AA -2000-2000+1000+1000 +1000+1000 +10000+10000

BB -2000-2000+1000+1000 +1000+1000 0 0

CC -2000-2000 0 0 +2000+2000 0 0


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

Cash FlowsCash FlowsPrj.Prj. CC00 CC11 CC22 CC33 PaybackPayback

NPVNPV@10%@10%

AA -2000-2000 +1000+1000 +1000+1000 +10000+10000 22

BB -2000-2000 +1000+1000 +1000+1000 0 0 22

CC -2000-2000 0 0 +2000+2000 0 0 22


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

Cash FlowsCash FlowsPrj.Prj. CC00 CC11 CC22 CC33 PaybackPayback NPVNPV@10%@10%

AA -2000-2000 +1000+1000 +1000+1000 +10000+10000 22+7,249+7,249

BB -2000-2000 +1000+1000 +1000+1000 0 0 22 - - 264264

CC -2000-2000 0 0 +2000+2000 0 0 22 - 347- 347

Payback PeriodPayback Period

Book Rate of ReturnBook Rate of Return

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

Book Rate of ReturnBook Rate of Return

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

Managers rarely use this measurement to Managers rarely use this measurement to make decisions. The components reflect tax make decisions. The components reflect tax and accounting figures, not market values and accounting figures, not market values or cash flows. or cash flows.

Book rate of return =book income

book assets


ExampleExample

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

%29.14

0)1(

400350

1

IRR

NPV

%96.12

0)1(

466

)1(

16

)1(

16350

321

IRRIRRIRR

NPV


ExampleExample

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

Project C0 C1 C2 C3 IRR NPV@7%

H -350 400 14.29% 24,000$ I -350 16 16 466 12.96% 59,000$

Internal Rate of ReturnInternal Rate of ReturnPitfall 1 - Mutually Exclusive ProjectsPitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project.IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem.The following two projects illustrate that problem.

Pitfall 2 - Lending or Borrowing?Pitfall 2 - Lending or Borrowing? With some cash flows (as noted below) the NPV of the project With some cash flows (as noted below) the NPV of the project

increases as the discount rate increases. increases as the discount rate increases. This is contrary to the normal relationship between NPV and This is contrary to the normal relationship between NPV and

discount rates.discount rates.

Pitfall 3 - Multiple Rates of ReturnPitfall 3 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two different Certain cash flows can generate NPV=0 at two different

discount rates.discount rates. The following cash flow generates NPV=0 at both (-The following cash flow generates NPV=0 at both (-

50%) and 15.2%.50%) and 15.2%.

Project InteractionsProject Interactions

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

Mutually Exclusive Mutually Exclusive ProjectsProjects

ExampleExample

Select one of the two following Select one of the two following projects, based on highest NPV. projects, based on highest NPV.

assume 7% discount rateassume 7% discount rate

3.87300300300700

5.1183503503508003210

Slower

Faster

NPVCCCCSystem

Investment TimingInvestment Timing

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

Investment TimingInvestment Timing

ExampleExample

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

Investment TimingInvestment TimingExampleExample

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

YearYear CostCost PV SavingsPV Savings NPV at PurchaseNPV at Purchase NPV NPV TodayToday

00 5050 7070 2020 20.020.011 4545 7070 2525 22.722.722 4040 7070 3030 24.824.833 3636 7070 3434 Date to purchase Date to purchase 25.525.544 3333 7070 3737 25.325.355 3131 7070 3939 24.224.2

Equivalent Annual CostEquivalent Annual Cost

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

Equivalent annual cost =present value of costs

annuity factor

Equivalent Annual CostEquivalent Annual Cost

ExampleExample

Given the following costs of operating two Given the following costs of operating two machines and a 6% cost of capital, select the machines and a 6% cost of capital, select the lower cost machine using equivalent annual lower cost machine using equivalent annual cost method.cost method.

YearYear

MachMach.. 11 22 33 44 PVPV@6%@6% Ann. CostAnn. Cost

DD -15-15 -4-4 -4-4 -4-4

EE -10-10 -6-6 -6-6

-25.69

-21.00

- 9.61

-11.45

Equivalent Annual CostEquivalent Annual CostExample (with a twist)Example (with a twist)

Select one of the two following Select one of the two following projects, based on highest “equivalent projects, based on highest “equivalent annual annuity” (r=9%). annual annuity” (r=9%).

4.107.81.820

2.69.52.59.415

Project 43210

B

A

EAANPVCCCCC

2.82

2.78

.87

1.10

Capital RationingCapital Rationing

Capital RationingCapital Rationing - Limit set on the - Limit set on the amount of funds available for amount of funds available for investment.investment.

Soft RationingSoft Rationing - Limits on available - Limits on available funds imposed by management.funds imposed by management.

Hard RationingHard Rationing - Limits on available - Limits on available funds imposed by the unavailability of funds imposed by the unavailability of funds in the capital market.funds in the capital market.

Profitability IndexProfitability Index

ProfitabilityProject PV Investment NPV Index

L 4 3 1 1/3 = .33M 6 5 1 1/5 = .20N 10 7 3 3/7 = .43O 8 6 2 2/6 = .33P 5 4 1 1/4 = .25

Project InteractionsProject Interactions

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

Numeric Models: ScoringNumeric 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 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 X marks in 0-1 scoring model are scoring model are replaced by replaced by numbers, from a 5 numbers, from a 5 point scale. 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

1

n

i ij j

j

S S W

whereSi the total score of the ith project,Sij the score of the ith project on the jth criterion, andWj 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:

1 1

vn

i ij j ik

j k

S S W C

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 ThoughtFinal 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.

financial analysis of projects

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