MBA – IV SEMESTERFM-3: PROJECT FINANCE

UNIT IIILESSON 3.1

INVESTMENT CRITERIADISCOUNTED CASH FLOW

TECHNIQUES

MBA (Trimester)(MBA – Finance and MBA – Banking and Finance)

Module Title : Project Finance and Management

Term VUNIT III: – Project Market and Demand Analysis

Lesson 3.1 : Investment Criteria

Discounted Cashflow techniques

The key steps involved in determining whether a project is worthwhile or not are:

• Estimate the costs and benefits of the project.

• Assess the riskiness of the project.

• Calculate the cost of capital.

• Compute the criteria of merit and judge whether the project

is good or bad.

For pedagogic purposes, we find it more convenient to start with a discussion of the criteria of merit, referred to as investment criteria or capital budgeting techniques. A familiarity with these criteria will facilitate an easier understanding of costs and benefits, risk analysis, and cost of capital.

INVESTMENT CRITERIA

INVESTMENT CRITERIA

DISCOUNTING CRITERIA

NON-DISCOUNTING CRITERIA

NET PRESENT

VALUE

BENEFIT COST

RATIO

INTERNAL RATE OF RETURN

PAYBACK PERIOD

ACCOUNTING RATE OF RETURN

Net Present Value

n Ct

NPV = – Initial investment t=1 (1 + rt )t

NET PRESENT VALUEThe net present value of a project is the sum of the present values of all the cash flows associated with it. The cash flows are discounted at an appropriate discount rate (cost of capital)

Naveen Enterprise’s Capital Project

Year Cash flow Discount factor Present value 

0 -100.00 1.000 -100.001 34.00 0.870 29.582 32.50 0.756 24.573 31.37 0.658 20.644 30.53 0.572 17.465 79.90 0.497 39.71

Sum = 31.96

  Pros Cons

• Reflects the time value of money • Is an absolute measure and not a relative

• Considers the cash flow in its entirety measure

• Squares with the objective of wealth maximisation

Properties of the NPV Rule

• NPVs are additive

• Intermediate cash flows are invested at cost of capital

• NPV calculation permits time-varying discount rates

• NPV of a simple project decreases as the discount rate increases.

Rationale for the NPV Rule

Year 0

Year 1

O G F

H

D

Q

S

N

M R

P

L E Y

X

Z

Rationale for the NPV Rule

What do we find when we compare the three cases ? If you invest

an amount equal to DF in real assets you reach the consumption

frontier MN; if you invest an amount equal to DG in real assets

you reach the consumption frontier PQ; if you invest an amount

equal to DH in real assets you reach the consumption frontier RS.

Clearly, investment of an amount equal to DF in real assets is the

most desirable course of action since it takes you to the highest

consumption frontier.

Investment of an amount equal to DF in real assets, it may be

emphasised, is also the investment which has the highest net

present value

Modified NPV

The standard net present value method is based on the assumption that

the intermediate cash flows are re-invested at a rate of return equal to the

cost of capital. When this assumption is not valid, the re-investment rates

applicable to the intermediate cash flows need to be defined for

calculating the modified net present value

Steps in Calculating Modified NPV

Step 1: Calculate the terminal value of the project’s cash inflows using the explicitly defined reinvestment rate(s) which are supposed to reflect the profitability of investment opportunities ahead of the firm. n TV = CFt (1+r t)n-t t=1

Step 2: Determine the modified net present value

TV NPV* = - I

(1+ r)n

Benefit Cost Ratio PVB

Benefit-cost Ratio : BCR = I

PVB = present value of benefits I = initial investment

To illustrate the calculation of these measures, let us consider a project which is being evaluated by a firm that has a cost of capital of 12 percent.

Initial investment : Rs 100,000Benefits: Year 1 25,000

Year 2 40,000Year 3 40,000Year 4 50,000

The benefit cost ratio measures for this project are:

25,000 40,000 40,000 50,000(1.12) (1.12)2 (1.12)3 (1.12)4

BCR = = 1.145 NBCR=BCR-1 = 0,145100,000

Pros ConsMeasures bang per buck Provides no means for aggregation

+ + +

Internal Rate of Return

Net Present Value

Discount Rate

The internal rate of return (IRR) of a project is the discount rate that makes its NPV equal to zero. It is represented by the point of intersection in the above diagram

Net Present Value Internal Rate of Return• Assumes that the discount • Assumes that the net rate (cost of capital) is known present value is zero• Calculates the net present • Figures out the discount rate value, given the discount that makes net present rate value zero

Calculation of IRRYou have to try a few discount rates till you find the one that makes the NPV zero

Year Cash Discounting Discounting Discounting

flow rate : 20% rate : 24% rate : 28%

Discount Present Discount Present Discount Present

factor Value factor Value factor Value

0 -100 1.000 -100.00 1.000 -100.00 1.000 -100.00

1 34.00 0.833 28.32 0.806 27.40 0.781 26.55

2 32.50 0.694 22.56 0.650 21.13 0.610 19.83

3 31.37 0.579 18.16 0.524 16.44 0.477 14.96

4 30.53 0.482 14.72 0.423 12.91 0.373 11.39

5 79.90 0.402 32.12 0.341 27.25 0.291 23.25

NPV = 15.88 NPV = 5.13 NPV = - 4.02

Calculation of IRR

NPV at the smaller rate

Sum of the absolute values of the NPV at the smaller and the bigger discount rates

5.13 24% + 28% - 24% = 26.24%

5.13 + 4.02

Bigger SmallerX discount – discount rate rate

Smaller discount + rate

Problems with IRR

• Non-Conventional Cash Flows

• Mutually Exclusive Projects

• Lending vs. Borrowing

• Differences between Short-term and Long-term

Interest Rates

Non-Conventional Cash Flows

C0 C1 C2

-160 +1000 -1000

TWO IRRs : 25% & 400%

NPV

25% 400%

NO IRR : C0 C1 C2

150 -450 375

Mutually Exclusive Projects

C0 C1 IRR NPV(12%)

P -10,000 20,000 100% 7,857

Q -50,000 75,000 50% 16,964

Lending vs Borrowing

C0 C1 IRR NPV(10%)

A -4000 6000 50% 145

B 4000 -7000 75% -236

What Does IRR Mean?

There are two possible economic interpretations of internal rate of

return : (i) The internal rate of return represents the rate of return

on the unrecovered investment balance in the project. (ii) The

internal rate of return is the rate of return earned on the initial

investment made in the project.

What Does IRR Mean?

To understand the nature of these interpretations, consider a project with the following cash flows.

Year Cash flow 0 Rs.-300,000 1 0 2 417,000 3 117,000

-300,000 0 417,000 117,0000 = + + +

(1+r)0 (1+r)1 (1+r)2 (1+r)3

The internal rate of return of this project is the value of r in the expression

The value of r which satisfies the above expression is 30 percent

This figure, according to the first interpretation of internal

rate of return, reflects the rate of return on the unrecovered

investment balance. The unrecovered investment balance is

defined as :

Ft = Ft-1 (1+r) + Ct

What Does IRR Mean?

What Does IRR Mean?

Year Unrecovered investment Interest for the year Cash flow at Unrecovered investment

Balance at the beginning the end of balance at the end

the year of the year

Ft-1 Ft-1 (1+r) Ct Ft-1 (1+r) + Ct

 

1 Rs.-300,000 -90,000 0 -390,000

2 Rs.-390,000 -117,000 417,000 -90,000

3 Rs.-90,000 -27,000 117,000 0

Unrecovered Investment Balance

Now, let us consider the second interpretation according to which, the internal rate of return is the compounded rate of return earned on the initial investment, for the entire life of the project. This means that if a project involves an initial outlay of I, has an internal rate of return of r percent, and has a life of n years, the value of the benefits of the project, assessed at the end of n years, will be I(1+r)n . In our numerical example, where the initial investment is Rs.300,000, the internal rate of return of the project is 30 percent, and the life of the project is three years, the value of the benefits of the project, assessed at the end of three years, will be Rs.300,000 (1+0.30)3 = Rs.659,100.

The second interpretation of internal rate of return is based on the assumption that the intermediate flows of the project are re-invested at a rate of return equal to the internal rate of return of the project.

What Does IRR Mean?

What Does IRR Mean?

Which economic interpretation should we put on internal rate of

return ? Since it is often not possible for a firm to re-invest

intermediate inflows at a rate of return equal to the project’s internal

rate of return, the first interpretation seems more realistic. Hence, we

may view internal rate of return as the rate of return on the time-

varying, unrecovered investment balance in the project, rather than the

compounded rate of return on the initial investment. This point

deserves to be understood because the notion of internal rate of return

generally creates the impression that it is the rate of return earned on a

sustained basis on the initial investment over the life of the project.

Modified IRR

0 1 2 3 4 5 6

-120 -80 20 60 80 100 120 r=15% 115 - -69.6 r =15% r =15% 105.76

PVC = 189.6 r =15% 91.26 r =15% 34.98 Terminal value (TV) = 467 PV = 189.6 MIRR = 16.2% of TV NPV 0

Payback Period

Payback period is the length of time required to recover the initial

outlay on the project

Naveen Enterprise’s Capital Project

Year Cash flow Cumulative cash flow

0 -100 -100 1 34 - 66 2 32.5 -33.5 3 31.37 - 2.13 4 30.53 28.40

Pros Cons• Simple • Fails to consider the time

value of money• Rough and ready method • Ignores cash flows beyond

for dealing with risk the payback period• Emphasises earlier cash inflows

Accounting Rate of ReturnThe accounting rate of return, also referred to as the average rate of return on investment, is a measure of profitability which relates income to investment, both measured in accounting terms. Since income and investment can be measured variously, there can be a very large number of measures for accounting rate of return. The measures that are employed commonly in practice are :

Average income after taxA :

Initial investment 

Average income after taxB :

Average investment 

Average income after tax but before interestC :

Initial investment

Average income after tax but before interestD :

Average investment  

Average income before interest and taxesE :

Initial investment 

Average income before interest and taxesF :

Average investment

Total income after tax but before depreciation – Initial investment

G :(Initial investment / 2) x years

Assessment of Basic Evaluation Methods

  Net present Benefit Internal Payback Accounting value cost ratio rate of period rate of return

return

Theoretical considerations1. Does the method consider all Yes Yes Yes No ? cash flows2. Does the method discount cash flows at the opportunity Yes Yes No No No cost of funds ?3. Does the method satisfy the Yes No No ? ? principle of value additivity ?4. From a set of mutually exclusive projects, does the method choose Yes No No ? ? the project which maximises shareholder wealth ?

Practical considerations

1. Is the method simple ? Yes Yes Yes Yes Yes

2. Can the method be used with

limited information ? No No No Perhaps Yes

3. Does the method give a

relative measure ? No Yes Yes No Yes

Evaluation Techniques in India

A survey of capital budgeting practices in India, conducted by U. Rao Cherukeri, revealed the following:

• Over time, discounted cash flow methods have gained in importance and internal rate of return is the most popular evaluation method.

• Firms typically use multiple evaluation methods.

• Accounting rate of return and payback period are widely employed as supplementary evaluation methods.

• Weighted average cost of capital is the most commonly used discount rate and the most often used discount rate is 15 percent in post-tax terms.

• Risk assessment and adjustment techniques have gained popularity. The most popular risk assessment technique is sensitivity analysis and the most common methods for risk adjustment are shortening of the payback period and increasing the required rate of return

A survey of corporate finance practices in India by Manoj Anand, reported in the October-December 2002 issue of Vikalpa, revealed that the following methods (in order of decreasing importance) are followed by companies to evaluate investment proposals

% of companies considering as

Method very important or important

• Internal rate of return 85.00

• Payback period 67.50

• Net present value 66.30

• Break-even analysis 58.00

• Profitability Index 35.10

Evaluation Techniques in India

Evaluation Techniques in the US

A study conducted by William Petty and David Scott revealed the following:

Level of importance

Technique None Slight Moderate Fair High No response

 

Accounting return 12.35% 15.29% 17.06% 8.82% 3.53% 2.94%

on investment

Payback period 1.76 12.35 25.29 28.82 30.00 1.76

Net present value 8.82 16.47 20.59 15.29 33.20 5.29

Internal rate of 7.65 9.41 4.71 14.71 59.41 4.12

return

Profitability index 31.17 18.82 15.29 7.65 11.18 15.88

or benefit-cost ratio

Evaluation Techniques in Japan

Japanese firms appear to rely mainly on two kinds of analysis: (a) one year return on investment analysis and (b) residual investment analysis

Year Cash flow Imputed interest @ 10% Adjusted cash flow Residual investment

0 (1000) - - -

1 200 100 100 900

2 200 90 110 790

3 300 79 221 569

4 300 57 243 326

5 400 33 367 -

6 400 - - -

7 300 - - -

8 300 - - -

Residual Investment Analysis

SUMMARY• A wide range of criteria has been suggested to judge the worthwhileness of investment

projects. They fall into two broad categories : discounting criteria and non-discounting criteria. The important discounting criteria are : net present value, benefit cost ratio, and internal rate of return. The major non-discounting criteria are : payback period and accounting rate of return.

• The net present value (NPV) of a project is the sum of the present values of all the cash flows - positive as well as negative - that are expected to occur over the life of the project.

• The decision rule associated with the NPV criterion is : Accept the project if the NPV is positive and reject the project if the NPV is negative.

• NPV has certain properties that make it a very attractive decision criterion : NPVs are additive; the NPV rule assumes that the intermediate cash flows of a project are reinvested at a rate of return equal to the cost of capital; NPV calculation permits time varying discount rates

• The standard NPV method is based on the assumption that the intermediate cash flows are re-invested at a rate of return equal to the cost of capital. When this assumption is not valid, the investment rates applicable to the intermediate cash flows need to be defined for calculating the modified net present value.

• The benefit cost ratio is defined as the present value of benefits (cash inflows) divided by the present value of costs (cash outflows). A project is considered worthwhile if the benefit cost ratio is more than 1 and not worthwhile if the benefit cost ratio is less than 1.

• The internal rate of return (IRR) of a project is the discount rate which makes its NPV equal to zero. In the NPV calculation we assume that the discount rate is known and determine the NPV. In the IRR calculation, we set the NPV equal to zero and determine the discount rate that satisfies this condition.

• The decision rule for IRR is as follows : Accept the project if its IRR is greater than the cost of capital; reject the project if its IRR is less than the cost of capital.

• The IRR and NPV rules lead to identical decisions provided two conditions are satisfied. First, the cash flows of the project must be conventional, implying that the first cash flow (initial investment) is negative and the subsequent cash flows are positive. Second, the project must be independent meaning that the project can be accepted or rejected without reference to any other project.

• There are problems in using IRR when the cash flows of the project are not conventional or when two or more projects are being compared to determine which one is the best. In the first case, it is difficult to define 'what is IRR' and in the second case IRR can be misleading. Further, IRR cannot distinguish between lending and borrowing. Finally, IRR is difficult to apply when short-term interest rates differ from long-term interest rates.

• There are two possible economic interpretations of internal rate of return: (i) The internal rate of return represents the rate of return on the unrecovered investment balance in the project . (ii) The internal rate of return is the rate of return earned on the initial investment made in the project.

• Despite NPV's conceptual superiority, managers seem to prefer IRR over NPV because IRR is intuitively more appealing as it is a percentage measure. Is there a percentage measure that overcomes the shortcomings of the regular IRR? Yes, there is one and it is called the modified IRR or MIRR. It is calculated by solving the following equation :

Terminal value of cash inflows

Present value of cash outflows =

(1 + MIRR)n

• The payback period is the length of time required to recover the initial cash outlay on the project.

• According to the payback criterion, the shorter the payback period, the more desirable the project. Firms using this criterion generally specify the maximum acceptable payback period.

• Payback period is widely used because it is simple, both in concept and application, and it is a rough and ready method for dealing with risk. However, it has serious limitations : it does not consider the time value of money; it ignores cash flows beyond the payback period; it is a measure of capital recovery, not profitability.

• In the discounted payback period method, cash flows are first converted into their present values (by applying suitable discounting factors) and then added to ascertain the period of time required to recover the initial outlay of the project.

• The accounting rate of return, also called the average rate of return, is defined as

Profit after tax

Book value of the investment

• The accounting rate of return has certain virtues : it is simple to calculate; it is based on accounting information which is readily available and familiar to businessmen; it considers benefits over the entire life of the project. However, it has serious shortcomings as well: it is based upon accounting profit, not cash flow; it does not take into account the time value of money; it is internally inconsistent.

• The most popular methods for evaluating small sized projects are payback method and accounting rate of return method. For larger projects, IRR appears to be the most commonly used method.

• In the U.S, internal rate of return, net present value, accounting rate of return, and Payback period are the most popular methods of project appraisal.

• Japanese firms appear to rely mainly on two kinds of analysis: (i) one year investment analysis and (ii) residual investment analysis