PROJECT APPRAISAL PLANNING AND CONTROL

1. CHAPTER 8
INVESTMENT CRITERIA

2. Outline
• Net present value
• Benefit cost ratio
• Internal rate of return
• Urgency
• Payback period
• Accounting rate of return
• Assessment of various methods
• Investment evaluation in practice.

3. 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.

4. 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

5. Net Present Value
n Ct
NPV =  – Initial investment
t=1 (1 + rt )t

6. NET PRESENT VALUE
The 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 -100.00
1 34.00 0.870 29.58
2 32.50 0.756 24.57
3 31.37 0.658 20.64
4 30.53 0.572 17.46
5 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

7. 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.

8. 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

9. 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

10. 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

11. 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

12. 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 100,000
Benefits: Year 1 25,000
Year 2 40,000
Year 3 40,000
Year 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 = 0,145
100,000
Pros Cons
Measures bang per buck Provides no means for aggregation
+ + +

13. 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

14. Calculation of IRR
You 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

15. 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 Smaller
X discount – discount
rate rate
Smaller
discount +
rate

16. Problems with IRR
• Non-Conventional Cash Flows
• Mutually Exclusive Projects
• Lending vs. Borrowing
• Differences between Short-term and Long-term
Interest Rates

17. 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

18. Mutually Exclusive Projects
C0 C1 IRR NPV
(12%)
P -10,000 20,000 100% 7,857
Q -50,000 75,000 50% 16,964

19. Lending vs Borrowing
C0 C1 IRR NPV
(10%)
A -4000 6000 50% 145
B 4000 -7000 75% -236

20. 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.

21. 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 0 417,000 117,000
0 = + + +
(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

22. 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?

23. 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

24. 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?

25. 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.

26. 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

27. 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

28. Accounting Rate of Return
The 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 tax
A :
Initial investment
Average income after tax
B :
Average investment
Average income after tax but before interest
C :
Initial investment

29. Average income after tax but before interest
D :
Average investment
Average income before interest and taxes
E :
Initial investment
Average income before interest and taxes
F :
Average investment
Total income after tax but before depreciation
– Initial investment
G :
(Initial investment / 2) x years

30. Assessment of Basic Evaluation Methods
Net present Benefit Internal Payback Accounting
value cost ratio rate of period rate of return
return
Theoretical considerations
1. Does the method consider all Yes Yes Yes No ?
cash flows
2. 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

31. 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

32. 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

33. 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

34. 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

35. 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.

36.  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.

37.  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.

38.  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