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Ch 6 Project Analysis Under Certainty

Methods of evaluating projects when the future is assumed to be certain.

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Ch 6 Project Analysis Under Certainty

Study objectivesAfter studying this chapter the reader should be able to:

– Use the NPV model to evaluate projects under certainty– Apply the net present value, internal rate of return, payback

period and accounting rate of return criteria for investment decision- making under certainty

– Understand the reasons why the NPV criterion is generally the method of choice for project evaluation

– Apply the NPV criterion for ranking mutually exclusive projects and project retirement and replacement decisions

– Use the NPV model to evaluate replacement chain decisions.

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Certainty Assumption• Certainty means that although future flows

must be forecast or estimated, the estimated amounts will be received at the times they are expected to occur.

• Certainty makes the decision simple to model, and the outcome easy to accept.

• Under the assumption of certainty, future cash flows are to be discounted at a rate which represents the time value of money

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Certainty Assumption

For example:

Project Alpha requires an initial outlay of $900, will have cash inflows of $300 in year 1, $400 in year 2 and $600 in year 3. The discount rate is 8% per annum. The calculation is:

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Certainty Assumption• This positive result means that, by undertaking the project, the

firm’s wealth will increase by $197.01. Based on the NPV decision rule, the project should be undertaken.

• We have made several assumptions in formulating and using this NPV model and decision:– the amounts of the initial cash outflow and all future cash

flows are known with certainty.– the discount rate is constant and known with certainty– the initial capital outlay occurs at the beginning of year 1

and all operating cash flows occur at year end– cash outflows from the firm are treated as negative; cash

inflows are treated as positive– there are no constraints on the supply of capital, or on other

resources– the firm will accept all positive NPV projects.

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Net Present Value. The ideal investment decision making technique

is Net Present Value.

N P V measures the equivalent present wealth contributed by the investment.

NPV is given in

NPV -- relates directly to the firm’s goal of wealth maximization

-- employs the time value of money

-- can be used in all types of investments

-- can be adjusted to incorporate risk.

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Net Present Value.

• The NPV is calculated by discounting a project’s net cash flows at a specified rate. This rate – often called the discount rate, opportunity cost or cost of capital – refers to the minimum return that must be earned on a project in order to leave the firm’s market value unchanged.

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Net Present Value.Delta Project

• The NPV of this project can be computed by evaluating the cash flows. They begin with the initial outlay of $1,002,000 at EOY 0 and continue until EOY 8, at which time the asset salvage value is included. The NPV computation is:

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Net Present Value.Delta Project

• With this positive NPV, the project is acceptable.• We have used the risk-free rate of 5% per annum

as the required rate of return here, as the cash flows are assumed to be certain.

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Other project appraisal methods

• While the NPV criterion is the most appropriate method in most cases, the other discounted cash flow technique, the internal rate of return (IRR), is also frequently used, sometimes as a supplementary measure to NPV.

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CFO Decision Tools

Profitability Index, 12%

Payback, 57%

IRR, 76%

NPV, 75%

Book rate of return, 20%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Survey Data on CFO Use of Investment Evaluation Techniques

SOURCE: Graham and Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187-243.

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Other project appraisal methods

• Non-discounted cash flow methods such as payback period (PP) and accounting rate of return (ARR) have a number of serious defects but are still being used in practice in some situations.

• Sometimes PP is used in conjunction with NPV, particularly in making risky investment decisions. It is useful to understand these methods and their drawbacks so that the most appropriate method can be used for investment evaluation.

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Other Project Evaluation Techniques:

Discounted Cash Flow Techniques

Internal Rate of Return – calculates the discount rate that gives the project an NPV of $0. If the IRR is greater than the required rate, the project is accepted. IRR is given as % pa.

IOIRR

CF

IRR

CFNPV

......

)1()1()(0$ 2

21

1

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Internal rate of returnDelta Project

• Using i to represent the IRR, the equation for the IRR calculation using the same cash flows as employed in the NPV calculation (Table 6.1) is:

• The solution for i, calculated by the Excel IRR function, is 19.80%. Since this rate is above the required rate of 5%, the project is acceptable

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Internal rate of return

• The IRR remains in use because decision-makers are used to dealing in ‘rates of return’ rather than the more esoteric NPV.

• The IRR measure is useful for easily comparing the rate of return from the project being considered with various alternative returns.

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Other Project Evaluation Techniques:

Modified Internal Rate of Return – calculates the discount rate that gives the project an NPV of $0, when future cash flows can be re-invested at the Re-Investment Rate, a rate different from the IRR. If the MIRR is greater that the required rate, the project is accepted. MIRR is given as % pa.

IOIRR

RIRCF

IRR

RIRCFNPV

nn

......)1(

)1(

)1(

)1()(0$

2

)1(2

11

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Other Project Evaluation Techniques:

Non-Discounted Cash Flow TechniquesAccounting Rate of Return- measures the ratio of

annual average accounting income to an asset base value. ARR is given as % pa.

= % pa.Accounting income is different from cash flow.

For example, an outlay of $1,000 may earn $200, $500 and $700 as accounting income over three years. The ARR is calculated as:

ARR = [ (200 + 500 + 700) / 3] / 1000 = 46.66%

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Other Project Evaluation Techniques:

Non-Discounted Cash Flow TechniquesAccounting Rate of Return

• Now the merits of an investment project do not depend on how accountants classify the cash flows and few companies these days make investment decisions just on the basis of the Accounting rate of return

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Other Project Evaluation Techniques:

Payback Period– measures the length of time required to retrieve the initial cash outlay.

PB is given as number of years.

• For example, an outlay of $1,200 may generate cash inflows of $820, $450 and $300 over three years. The total cash inflow to the end of year 2 is $1,270, so the payback period would be within two years.

• There is no objective time criterion associated with payback, but a period of two to three years would be generally acceptable

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Other Project Evaluation Techniques:

• Payback Period : There are several problems with this measure:

1. The cash flows are not discounted. As the time value of money is not taken into account, the future cash flows cannot be related to the initial outlay.

2. The data outcome is not a decision variable. It does not relate to the firm’s goal of wealth maximization.

3. There is no objective measure of what constitutes an acceptable payback period.

4. Management may set an arbitrary target of say three years, but this value is not objectively related to the firm’s goal.

5. Cash flows occurring after the payback period are ignored. In the case where large outflows may occur on the termination of the project, such as the cost of rehabilitation of a mine site, a project may be erroneously accepted on the basis of a short payback term.

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Internal Rate of Return

Example

You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

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Internal Rate of Return

Example

You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

0)1(

000,4

)1(

000,2000,4 21

IRRIRRNPV

%08.28IRR

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Internal Rate of Return

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

10 20 30 40 50 60 70 80 90 100

Discount rate (%)

NP

V (

,000

s)

IRR=28%

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Internal Rate of ReturnPitfall 1 - Lending or Borrowing?• With some cash flows (as noted below) the NPV of the

project increases s the discount rate increases.

• This is contrary to the normal relationship between NPV and

discount rates.

364%50500,1000,1

364%50500,1000,1

%10@Project 10

B

A

NPVIRRCC

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Internal Rate of Return

Pitfall 2 - 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 IRR% of 8.49% and 31%.

270455190210

CCC

Cash Flows (millions of Australian dollars)

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Internal Rate of Return

Pitfall 2 - Multiple Rates of Return• Certain cash flows can generate NPV=0 at two different discount rates.

• The following cash flow generates NPV=$A 3.3 million at both IRR% of (-44%) and +11.6%.

150120120600

............ 10910

CCCC

Cash Flows (millions of Australian dollars)

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Internal Rate of ReturnPitfall 2 - Multiple Rates of Return• Certain cash flows can generate NPV=0 at two different discount rates.

• The following cash flow generates NPV=$A 3.3 million at both IRR% of (-44%) and +11.6%.

600NPV

300

0

-30

-600

Discount Rate

IRR=11.6%

IRR=-44%

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Internal Rate of Return

Pitfall 3 – No Internal Rate of Return• It is possible to have a zero IRR and a positive NPV

339500,2000,3000,1

%10@Project 210

NoneC

NPVIRRCCC

-210 455 -270 #NUM!

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Internal Rate of Return

Pitfall 4 - Mutually Exclusive Projects

• IRR sometimes ignores the magnitude of the project.

• The following two projects illustrate that problem.

818,11%75000,30000,20

182,8%100000,20000,10

%10@Project 10

E

D

NPVIRRCC

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Internal Rate of Return

Pitfall 4 - Mutually Exclusive Projects

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Internal Rate of Return

Pitfall 5 - Term Structure Assumption• We assume that discount rates are stable during the

term of the project. • This assumption implies that all funds are

reinvested at the IRR. • This is a false assumption.