d

4- 14. Project Investment Decision-Making

4.1 Net Present Value

4.2 Other Investment Criteria

4.3 Mutually Exclusive Projects

4.4 Capital Rationing

4.5 Discounted Cash Flows, Not Profits

4.6 Incremental Cash Flows

4.7 Treatment of Inflation

d

4- 24. Project Investment Decision-Making

4.8 Separate Investment & Financing Decisions

4.9 How Firms Organize the Investment Process

4.10 Some “What If” Questions4.10.1 Sensitivity Analysis4.10.2 Scenario Analysis

4.11 Real Options and the Value of Flexibility

d

4- 3

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

d

4- 4

Net Present Value

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

d

4- 5

Net Present Value

ExampleSuppose 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

Profit = -50 +60

1.10$4.55

Initial Investment

Added Value

$50

$4.55

d

4- 6

Net Present Value

NPV = PV - required investment

NPV CC

rt

t

0 1( )

NPV CC

r

C

r

C

rt

t

01

12

21 1 1( ) ( )...

( )

d

4- 7

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.

d

4- 8

Net Present Value

Net Present Value RuleNet 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.

d

4- 9

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?

d

4- 10

Net Present Value

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

$450,000

$466,000

0 1 2 3Present Value

14,953

13,975

380,395

$409,323

Example – continued(7% WACC)

d

4- 11

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?

d

4- 12

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?

NPV

NPV

350 00016 000

107

16 000

107

466 000

107

323

1 2 3,

,

( . )

,

( . )

,

( . )

$59,

d

4- 13

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; however time to “+” cash flow is a critically useful measure.

d

4- 14

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

Project C0 C1 C2 C3 Payback NPV@10%

A -2000 +1000 +1000 +10000

B -2000 +1000 +1000 0

C -2000 0 +2000 0

Payback Method

+ 7,249

- 264

- 347

2

2

2

d

4- 15

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.

Rate of Return =C - investment

investment1

d

4- 16

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?

d

4- 17

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?

0 350 00016 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR

IRR = 12.96%

d

4- 18

Internal Rate of Return

Calculating IRR by using a spreadsheet

Year Cash Flow Formula0 (350,000.00) IRR = 12.96% =IRR(B3:B7)1 16,000.00 2 16,000.00 3 466,000.00

d

4- 19

Internal Rate of Return

-200

-150

-100

-50

0

50

100

150

200

0 5 10 15 20 25 30 35

Discount rate (%)

NP

V (

,00

0s

)

IRR=12.96%

d

4- 20

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?

%29.14

0)1(

400350

1

IRR

NPV

%96.12

0)1(

466

)1(

16

)1(

16350

321

IRRIRRIRR

NPV

d

4- 21

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?

Project C0 C1 C2 C3 IRR NPV@7%

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

d

4- 22

Internal Rate of Return

Pitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project.

Pitfall 2 - Lending or Borrowing With some cash flows 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 (if there are future negative cash flows)

d

4- 23

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.

d

4- 24

Mutually Exclusive Projects

Example

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

assume 7% discount rate

3.87300300300700

5.1183503503508003210

Slower

Faster

NPVCCCCSystem

d

4- 25

Investment Timing

Sometimes you have the ability: - to defer an investment

- 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.

d

4- 26

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.

d

4- 27

Profitability 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

d

4- 28

Cash Flow vs. Accounting IncomeDiscount actual cash flowsUsing accounting income, rather than cash flow,

could lead to erroneous decisions.

ExampleA project costs $2,000 and is expected to last 2

years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income.

d

4- 29

Year 1 Year 2

Cash Income $1500 $ 500

Depreciation -$1000 -$1000

Accounting Income + 500 - 500

32.41$)10.1(

500

1.10

500=NPVApparent

2

Cash Flow vs. Accounting Income

d

4- 30

Today Year 1 Year 2

Cash Income $1500 $ 500

Project Cost - 2000

Free Cash Flow - 2000 +1500 + 500

14.223$)10.1(

500

)10.1(

1500-2000=NPVCash

21

Cash Flow vs. Accounting Income

d

4- 31

Incremental Cash Flows

Discount incremental cash flowsInclude All Indirect EffectsForget Sunk CostsInclude Opportunity CostsRecognize the Investment in Working CapitalBeware of Allocated Overhead Costs

Incremental Cash Flow

cash flow with project

cash flow without project= -

d

4- 32

Incremental Cash Flows

IMPORTANTIMPORTANT

Ask yourself this question

Would the cash flow still exist if the project does not exist?

If yes, do not include it in your analysis.If no, include it.

d

4- 33

Inflation

INFLATION RULEINFLATION RULEBe consistent in how you handle inflation!!Use nominal interest rates to discount

nominal cash flows.Use real interest rates to discount real cash

flows.You will get the same results, whether you

use nominal or real figures

d

4- 34Separation of Investment & Financing Decisions

When valuing a project, ignore how the project is financed.

Following the logic from incremental analysis ask yourself the following question: Is the project existence dependent on the financing? If no, you must separate financing and investment decisions.

d

4- 35

Capital Budgeting Process

Capital Budget - The list of planned investment projects.

The Decision Process1 - Develop and rank all investment projects2 - Authorize projects based on:

• Legal need • Core business• Production efficiency• Capacity requirements• NPV

d

4- 36

Capital Budgeting Process

Capital Budgeting ProblemsConsistent forecastsConflict of interestCorporate politicsForecast biasSelection criteria (NPV and others)

d

4- 37

How To Handle Uncertainty

Sensitivity Analysis - Analysis of the effects of changes in sales, costs, etc. on a project.

Scenario Analysis - Project analysis given a particular combination of assumptions.

Simulation Analysis - Estimation of the probabilities of different possible outcomes.

Break Even Analysis - Analysis of the level of sales (or other variable) at which the company breaks even.

d

4- 38

Sensitivity Analysis

Example

Given the expected cash flow forecasts listed on the next slide, determine the NPV of the project given changes in the cash flow components using an 8% cost of capital. Assume that all variables remain constant, except the one you are changing.

d

4- 39

Sensitivity Analysis

7805,400-FlowCash Net

780flowcash Operating

330after taxProfit

22040% @ .Taxes

550profitPretax

450onDepreciati

2,000Costs Fixed

13,000Costs Variable

16,000Sales

5,400-Investment

12-1 Years0Year

Example – continued (,000s)

NPV= $478

d

4- 40

Sensitivity AnalysisExample - continued

Possible Outcomes

1,9002,0002,100)Costs(000s Fixed

80%81.25%83%sales) of (%Cost Var

18,00016,00014,000)Sales(000s

5,0005,4006,200(000s)Investment

OptimisticExpectedcPessimistiVariable

Range

d

4- 41

Sensitivity AnalysisExample - continuedNPV Calculations for Pessimistic Investment Scenario

7806,200-FlowCash Net

780flowcash Operating

330after taxProfit

22040% @ .Taxes

550profitPretax

450onDepreciati

2,000Costs Fixed

13,000Costs Variable

16,000Sales

6,200-Investment

12-1 Years0Year

NPV= ($121)

d

4- 42

Sensitivity AnalysisExample - continued

NPV Possibilities

93047826)Costs(000s Fixed

1,382478788-sales) of (%Cost Var

2,1744781,218-)Sales(000s

778478121-(000s)

)000(

Investment

OptimisticExpectedcPessimistiVariable

sNPV

d

4- 43

Scenario Analysis

Combine alternative sensitivities on the key risk variables in your cash flow statement and their probabilities to develop a set of possible outcomes and probabilities.

d

4- 44

Flexibility & Real Options

Decision Trees - Diagram of sequential decisions and possible outcomes.

Decision trees help companies determine their Options by showing the various choices and outcomes.

The Option to avoid a loss or produce extra profit has value.

The ability to create an Option thus has value that can be bought or sold.

d

4- 45

Decision Trees

NPV=0

Don’t test

Test (Invest $200,000)

Success

Failure

Pursue project NPV=$2million

Stop project

NPV=0

d

4- 46

Real Options

1. Invest

2. Don’t Invest

3. Delay the Investment

4. Flexible Investment