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Project Evaluation Criteria

MF 807: Corporate FinanceProfessor Thomas Chemmanur

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Corporate Finance

1. Investment Decision

(a) Capital Budgeting

(b) Long-term Investment Strategy 2. Financing Decision

(a) How Should Investment Be Financed? Internal or External Financing What is the Menu of Securities to Use for External

Financing? Stocks, Bonds, Preferred Stock, Convertible Debt

(b) Interactions between financing and investment decisions 3. Dividend or Payout Decision

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Corporate Finance

(a) Of Total Earnings, How Much (What Fraction) Should Be Paid Out and How Much Retained (Retained Earnings)?

(b) Once the Payout Ratio is Decided, What is the Method of Payout?

Cash Dividends Stock Repurchases

Open Market Repurchases Tender Offers

Fixed Price Dutch Auction

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Objective of Firm Manager

The objective of a firm manager is to maximize shareholder wealth

Equivalent to maximizing total value of the firm’s equity, or its stock price

The above can be thought of as a benchmark; there may be in deviations in practice

E.g. agency problems However, if the deviations are too much, the CEO can be fired,

by the board. Takeovers and leveraged buyouts can also discipline firm

management

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Capital Budgeting

Capital Expenditures Expected to generate cash benefits lasting longer than a year

Operating Expenditures Expected to generate benefits for less than a year

Capital expenditures are incurred to obtain capital assets used in the production of goods and services; summarized in capital budget

New machinery, real estate, construction of factories, replace machinery, expand product line

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Capital Budgeting is a Complex Process

1. Searching for new projects 2. Marketing and production analysis – cash flow

estimates 3. Preparation of cash budgets 4. Evaluation of project proposals 5. Control and monitoring of past projects

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Steps Involved in Evaluating Project Proposals

1. Estimate the cash flows involved at various points in time.

Include not only the benefits, but the investment required

2. Estimate the riskiness in project cash flows, and thus the appropriate discount rate to use.

3. Select projects, and amounts to be invested in each using appropriate evaluation criteria.

Keep in mind limitations in amount of investment

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Project Evaluation Criteria

Project Evaluation Criteria:• 1. NPV rule• 2. Internal Rate of Return• 3. Benefit to Cost Ratio

Ad-hoc Project Evaluation Rules• 4. Payback Period Rule• 5. Discounted Payback Period Rule• 6. Average Return on Book Value

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The Net Present Value Rule

If we assume a flat term structure:

Decision Rule:

i. Under No Capital Rationing: accept all projects with a positive net present value

ii. Under Capital Rationing: accept that combination of projects that gives the highest net present value

1 20 2

1 2

...(1 ) (1 ) (1 )

nn

n

CC CNPV I

r r r

1 2 3 ..... nr r r r r

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Example

NPVA+B = NPVA + NPVB

Investment Amount (Total) = $10,000.00 Optimal Combination I, III, IV. Why? NPV = $1450.00 Combination of I & III NPV = $1250.00 < $1450.00

Project Investment Required

NPV

I $5000.00 $800.00

II $5000.00 $400.00

III $3000.00 $350.00

IV $2000.00 $300.00

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Internal Rate of Return (IRR)

It is that rate of return at which this equation holds:

I.e. IRR is that discounting rate at which the net present value equals zero

Decision Rule:i. Under No Capital Rationing: Accept all projects with an

IRR above a certain cut-off of return, which depends on the riskiness of the project

ii. Under Capital Rationing: Accept that combination of available projects which satisfies the investment constraint and gives the highest IRR

1 20 2

...(1 ) (1 ) (1 )

nn

CC CI

IRR IRR IRR

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Example

I0 = $10,000; C1=$4,000; C2 = $3000 = C3 = C4 = C5

NPV at r = 12%

t = 0 1 2 3 4 5

-10,000 4000 3000 3000 3000 3000

4 ,12%

4000 110,000 3000 PVIFA

1.12 1.121

10,000 3571.43 3000 3.03731.12

$1707.05 0 ACCEPT PROJECT

yrsNPV

NPV

NPV

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Example

NPV @ 14%

NPV @ 15%

4 ,14%

4000 110,000 3000 PVIFA

1.14 1.141

10,000 3508.77 3000 2.91371.12

$1176.43 0 ACCEPT PROJECT

yrsNPV

NPV

NPV

4 ,15%

4000 110,000 3000 PVIFA

1.15 1.151

10,000 3478.26 3000 2.85501.15

$926.22 0 ACCEPT PROJECT

yrsNPV

NPV

NPV

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Example

Similarly: NPV @ 16% = $685.12 > 0 NPV @ 18% = $229.24 > 0 NPV @ 20% = -$195.05 < 0

Thus, IRR = 19% > Cutoff (Say 12%)

12 14 16 18 20

IRR 19%Discount Rate %

NPV($)

2000 -

1000 -

-1000 -

Note that, by definition, NPV falls to zero at the IRR discount rate

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Comparison of NPV and IRR

1. IRR Cannot Distinguish Between Lending and Borrowing In some cases (e.g. when initial cash flows are positive), this

may lead to acceptance of negative net present value projects: Example:

When we lend, we like a high return. When we borrow, we want to pay a low return.

Project C0 C1 IRR NPV@10%

A -1000 +1500 50% +364

B +1000 -1500 50% -364

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Comparison of NPV and IRR

2. Multiple IRRs when there is more than one change in the sign of project cash flows

Most projects have only one change in sign from negative to positive cash flow

Some projects may have negative cash flows later more than one change in sign, generating as many IRRs as there are changes in sign. (“Descartes Rule of Signs”)

What is the real IRR then? We have to appeal to NPV then.

C0 C1 C2 IRR NPV@10%

-4000 +25,000 -25,000 25% & 400%

-1934

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Comparison of NPV and IRR

25% 400% Rate of Return %

NPV($)

0

TWO SOLUTIONS TO THIS EQUATION: 25% and 400%

2

25,000 25,0004,000 0

(1 ) (1 )NPV

r r

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Comparison of NPV and IRR

3. Gives wrong rankings for mutually exclusive projects This is the case when the timing of cash flows of the two

projects under consideration is dissimilar

Project C0 C1 IRR NPV@10%

F -10,000 +20,000 100% +8182

G +20,000 +35,000 75% +11,818

75% 100% Rate of Return %

NPV($)

0

G

F

Fisher’s intersection

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Comparison of NPV and IRR

If the cost of capital is lower than the discount rate at the Fisher’s intersection, then choosing the project with the highest IRR means choosing the project that contributes the least to the firm’s equity value

4. Difficult to apply IRR when the term structure of interest rates is not flat unlike NPV, where this can easily be done.

Advantages of IRR No need to estimate cost of capital, at least in initial stages. It is a measure of profitability, accounting for the timing of cash

flows Of course, we do need a cost of capital estimate to decide on the

accept / reject threshold that we compare with the project IRR.

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Profitability Index or Benefit to Cost Ratio

P.I. = Present Value of Benefits from the Project

Present Value of Investment in the Project Decision Rule

i. Under No Capital Rationing: Accept All Projects with P.I. > 1

ii. Under Capital Rationing: Accept that combination of projects that satisfies the investment constraint and gives the highest P.I.

Example: Consider a project with initial investment of $35,000 and net

cash inflows of $9,000 per year for 6 years. The cost of capital is 12%

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Profitability Index or Benefit to Cost Ratio

Solution: PV of Benefits = 9000 [PVIFA: 12%, 6yrs]

= 9000[4.1114]

= $37,002.6 P.I. = 37,002 / 35,000 = 1.057 > 1 ACCEPT NPV = 37002.6 – 35,000 = 2000.6 > 0 ACCEPT IRR: That discount rate “r” at which

• 35,000 = 9000 [PVIFA: r, 6yrs]

• PVIFA = 35,000 / 9000 = 3.888

• IRR 14% > 12% ACCEPT

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The Payback Period Rule

1. Payback Period Number of periods required for project cash flows to add up to initial investment; i.e. smallest “n” for which: C1 + C2 + … + Cn > I0, holds.

Decision Rule: Accept projects with pay-back period less than a cut-off value.

Problems: (i) No discounting.(ii) Choice of cut-off period is arbitrary rejects positive NPV projects with cash flows after the

cut-off.

E.g. with a 2 year cutoff, Project A is accepted & B is rejected!Project I0 C1 C2 C3 Payback NPV @ 10%

A (400) 300 100 20 2 years -29.6

B (400) 100 100 500 <3 years +149.19

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Discounted Payback Period

Number of periods it takes for the sum of the present values of project cash flows to equal the initial investment. However, the problem of ignoring all cash flows after the cut-off remains.

PV of C1 = 300(PVIF) = 300/1.1 = 272.72

PV of C2 = 100(PVIF) = 100/1.12 = 82.64

PV of C3 = 20(PVIF) = 20/1.13 = 15.03

Note we would correctly reject Project A but we might also reject Project B if the payback period was only 2 years.

Project I0 C1 C2 C3 Payback NPV @ 10%

PV of A (400) 272.72 82.64 15.03 No Payback -29.6

PV of B (400) 90.90 82.64 375.65 <3 years +149.19

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Average Return on Book Value

Average return on book value: = average forecasted net income

average annual net book value of project investment

Example:Initial outlay = 6,000; straight-line depreciation Projected Income Statement:

Average annual net income = (500+600+1000)/3 = 700

Year 1 Year 2 Year 3

Revenue 2,500 2,600 3,000

Depreciation 2,000 2,000 2,000

500 600 1,000

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Example: Average Return on Book Value

It is assumed that depreciation takes place at the end of the year

Average of beginning and ending book values

Date 0 Date 1 Date 2 Date 3

Gross book value of investment 6,000 6,000 6,000 6,000

Accumulated Depreciation 0 2,000 4,000 6,000

Net book value 6000 4000 2,000 0

Year 1 Year 2 Year 3

Ave. Book value 5,000 3,000 1,000

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Example: Average Return on Book Value

Average book value = (6,000 + 4,000 + 2,000 + 0)/4 = 3,000 Average book rate of return = 700/3,000 = 23.33% This project would be undertaken if the target book rate of

return was less than 23.33% There are a number of problems with this criterion:

It considers only average return on book investment. No allowance is made for the fact that immediate receipts are more valuable than distant ones.

Average return does not depend on cash flows; it depends on the accounting concepts of net income and net book value. These in turn depend on arbitrary conventions adopted for depreciation and so on by the account.