Chapter 5 Net Present Value and Other Investment Criteria

OVERVIEW

This chapter reviews the NPV rule for capital budgeting. The NPV rule’s competitors— the book rate of
return, the payback period and the internal rate of return (IRR)—are discussed. These methods have a
number of shortcomings and therefore NPV comes out on top. It is shown that NPV is the most
appropriate method, so long as the objective is to maximize value. Discounted payback and modified
IRR methods are discussed briefly. The chapter ends with a discussion of capital rationing and
profitability index (PI).

LEARNING OBJECTIVES

 To understand the NPV method

 To understand the payback period, book rate of return and internal rate of return (IRR) methods
 To understand the advantages and disadvantages of the above mentioned methods and compare
them to the NPV method
 To understand capital rationing

CHAPTER OUTLINE

A review of the basics

Restates the reasons why capital projects should be judged by their NPVs, and emphasizes that the
discount rate should be the investor’s opportunity cost of capital. This section also introduces the
competitors to the NPV method namely; the payback period, book rate of return and the internal rate of
return. It emphasizes the importance of the value adding-up property of the NPV.

Payback period

Describes the payback and discounted payback rules. These rules ignore cash flows that occur after
payback. Also, the cutoff period is usually chosen arbitrarily. Discounted payback method is also
discussed briefly.
Internal rate of return

The internal rate of return (IRR) rule can give the correct accept-reject signal if used carefully. However,
there are a number of possible pitfalls:

 Cannot distinguish between lending and borrowing

 A project may have multiple IRRs.
 IRR often gives incorrect rankings for mutually exclusive projects, particularly if the projects
differ in scale (amount of initial investment required) or economic life.

The IRR, because it is a single number, can’t be applied where the situation calls for more than one
opportunity cost of capital. You may need to use more than one opportunity cost of capital if the term
structure is strongly upward sloping or downward sloping. The comparison becomes difficult as the
IRR can be thought of as a complex weighted average of the opportunity cost of capitals.

 The modified internal rate of return method is also discussed briefly.

Choosing capital investments when resources are limited

Simple capital rationing problems can be solved by trial and error or by ranking projects using
profitability index. This section also distinguishes between “soft” and “hard” rationing and discusses
whether value maximization remains the appropriate objective if hard rationing is encountered. Linear
programming methods are useful in solving multi-period capital constraints.

Decisions on investment, have to be based on the returns which that investment will make. If the
investment is unprofitable in the long run, it is unwise to invest in it..

The present value of the future investment is, or how long it will take to mature (give returns). It could be
much more profitable putting the planned investment money in the bank and earning interest, or investing
in an alternative project.

Typical investment decisions include the decision to build another grain silo, cotton gin or cold store or
invest in a new distribution depot. At a lower level, marketers may wish to evaluate whether to spend
more on advertising or increase the sales force, although it is difficult to measure the sales to advertising
ratio.

Capital Budgeting
Capital budgeting is an important process of any business activity. Vast amount of money can be easily
wasted if the investment turns out to be wrong . It is based on the concept of the future value of money
which may be spent now.

Various techniques are examined

Net present value

Internal rate of return and annuities

The timing of cash flows are important in new investment decisions.. One problem that developing
countries encountered is "inflation rates". in some cases, exceed 100% per annum. The topic will can
take this into account.

Capital budgeting versus current expenditures

A capital investment project can be distinguished from current expenditures by two features:

a) such projects are relatively large

b) a significant period of time (more than one year) elapses between the investment outlay and the receipt
of the benefits..

Systematic approach to Capital Budgeting.

Most organization will have in place procedures and methods for dealing with these decisions, namely

a) the formulation of long-term goals

b) the creative search for and identification of new investment opportunities

c) classification of projects and recognition of economically and/or statistically dependent proposals

d) the estimation and forecasting of current and future cash flows

e) a suitable administrative framework capable of transferring the required information to the decision
level

f) the controlling of expenditures and careful monitoring of crucial aspects of project execution

g) a set of decision rules which can differentiate acceptable from unacceptable alternatives is required.

The last point (g) is crucial and this is the subject of later sections of the chapter.
The classification of investment projects

a) By project size

Small projects may be approved by departmental managers.

Board of Directors' approval is needed for large projects, say, a million dollars or more.

b) By type of benefit to the firm

an increase in cash flow

a decrease in risk
an indirect benefit (restroom for employees , etc).

c) By degree of dependence

mutually exclusive projects (can execute project A or B, but not both)

complementary projects: taking project A increases the cash flow of project B.
substitute projects: taking project A decreases the cash flow of project B.

d) By degree of statistical dependence

Positive dependence
Negative dependence
Statistical independence.

e) By degree of statistical dependence

Conventional cash flow: only one change in the cash flow sign

e.g. -/++++ or +/----, etc

Non-conventional cash flows: more than one change in the cash flow sign,

e.g. +/-/+++ or -/+/-/++++, etc.

The economic evaluation of investment proposals

The analysis stipulates a decision rule for:

I) accepting or
II) rejecting

investment projects

The time value of money

Borrowing is only worthwhile if the return on the loan exceeds the cost of the borrowed funds. Lending is
only worthwhile if the return is at least equal to that which can be obtained from alternative opportunities
in the same risk class.

The interest rate received by the lender is made up of:

i) The time value of money: the receipt of money is preferred sooner rather than later. Money can be used
to earn more money. The earlier the money is received, the greater the potential for increasing wealth.
Thus, to forego the use of money, you must get some compensation.

ii) The risk of the capital sum not being repaid. This uncertainty requires a premium as a hedge against
the risk, hence the return must be commensurate with the risk being undertaken.

iii) Inflation: money may lose its purchasing power over time. The lender must be compensated for the
declining spending/purchasing power of money. If the lender receives no compensation, he/she will be
worse off when the loan is repaid than at the time of lending the money.

a) Future values/compound interest

Future value (FV) is the value in dollars at some point in the future of one or more investments.

FV consists of:

i) the original sum of money invested, and

ii) the return in the form of interest.

The general formula for computing Future Value is as follows:

FVn = Vo (l + r)n
where

Vo is the initial sum invested

r is the interest rate
n is the number of periods for which the investment is to receive interest.

Thus we can compute the future value of what Vo will accumulate to in n years when it is compounded
annually at the same rate of r by using the above formula.

Future values/compound interest

Exercise 1

i) What is the future value of $10 invested at 10% at the end of 1 year?
ii) What is the future value of $10 invested at 10% at the end of 5 years? (student should try to attempt the
answer using the first (i) as an example)

We can derive the Present Value (PV) by using the formula:

FVn = Vo (I + r)n

By denoting Vo by PV we obtain:

FVn = PV (I + r)n

by dividing both sides of the formula by (I + r)n we derive:

Rationale for the formula:

As you will see from the following exercise, given the alternative of earning 10% on his money, an
individual (or firm) should never offer (invest) more than $10.00 to obtain $11.00 with certainty at the
end of the year.

Now attempt exercise 2

Present value

i) What is the present value of $11.00 at the end of one year?

ii) What is the PV of $16.10 at the end of 5 years?

b) Net present value (NPV)

The NPV method is used for evaluating the desirability of investments or projects.
where:

Ct = the net cash receipt at the end of year t

Io = the initial investment outlay
r = the discount rate/the required minimum rate of return on investment
n = the project/investment's duration in years.

The discount factor r can be calculated using:

Examples:

N.B. introduce the net present value tables from any recognised published source.

Decision rule:

If NPV is positive (+): accept the project

If NPV is negative(-): reject the project

Now attempt exercise 3.

Exercise 3 Net present value

A firm intends to invest $1,000 in a project that generated net receipts of $800, $900 and $600 in the first,
second and third years respectively. Should the firm go ahead with the project?

Attempt the calculation without reference to net present value tables first.

c) Annuities
A set of cash flows that are equal in each and every period is called an annuity.

Example:

Year Cash Flow ($)

0 -800
1 400
2 400
3 400
PV = $400(0.9091) + $400(0.8264) + $400(0.7513)

= $363.64 + $330.56 + $300.52

= $994.72

NPV = $994.72 - $800.00

= $194.72

Alternatively,

PV of an annuity = $400 (PVFAt.i) (3,0,10)

= $400 (0.9091 + 0.8264 + 0.7513)

= $400 x 2.4868

= $994.72

NPV = $994.72 - $800.00

= $194.72

d) Perpetuities

A perpetuity is an annuity with an infinite life. It is an equal sum of money to be paid in each period
forever.

where:

C is the sum to be received per period

r is the discount rate or interest rate
Example:

You are promised a perpetuity of $700 per year at a rate of interest of 15% per annum. What price (PV)
should you be willing to pay for this income?

= $4,666.67

A perpetuity with growth:

Suppose that the $700 annual income most recently received is expected to grow by a rate G of 5% per
year (compounded) forever. How much would this income be worth when discounted at 15%?

Solution:

Subtract the growth rate from the discount rate and treat the first period's cash flow as a perpetuity.

= $735/0.10

= $7,350

e) The internal rate of return (IRR)

The IRR is the discount rate at which the NPV for a project equals zero. This rate means that the
present value of the cash inflows for the project would equal the present value of its outflows.

The IRR is the break-even discount rate.

The IRR is found by trial and error.

where r = IRR

IRR of an annuity:
where:

Q (n,r) is the discount factor

Io is the initial outlay
C is the uniform annual receipt (C1 = C2 =....= Cn).

Example:

What is the IRR of an equal annual income of $20 per annum which accrues for 7 years and costs $120?

=6

From the tables = 4%

Economic rationale for IRR:

If IRR exceeds cost of capital, project is worthwhile, i.e. it is profitable to undertake.

Internal rate of return

Find the IRR of this project for a firm with a 20% cost of capital:

YEAR CASH FLOW

$
0 -10,000
1 8,000
2 6,000
a) Try 20%
b) Try 27%
c) Try 29%

Net present value vs internal rate of return

Independent vs dependent projects

NPV and IRR methods are closely related because:

i) both are time-adjusted measures of profitability, and

ii) their mathematical formulas are almost identical.
So, which method leads to an optimal decision: IRR or NPV?

a) NPV vs IRR: Independent projects

Independent project: Selecting one project does not preclude the choosing of the other.

With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to
the same accept/reject decisions.

NPV vs IRR Independent projects

If cash flows are discounted at k1, NPV is positive and IRR > k1: accept project.

If cash flows are discounted at k2, NPV is negative and IRR < k2: reject the project.

Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e.

Similarly for the same project to be acceptable:

where R is the IRR.

Since the numerators Ct are identical and positive in both instances:

 implicitly/intuitively R must be greater than k (R > k);
If NPV = 0 then R = k: the company is indifferent to such a project;
Hence, IRR and NPV lead to the same decision in this case.

b) NPV vs IRR: Dependent projects

NPV clashes with IRR where mutually exclusive projects exist.

Example:

Mdis is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on
a prime site. The following information is available:

Initial Investment Outlay Net Inflow at the Year End

Project A -9,500 11,500
Project B -15,000 18,000

Assume k = 10%, which project should Mdis undertake?

= $954.55

= $1,363.64

Both projects are of one-year duration:

IRRA:

$11,500 = $9,500 (1 +RA)

= 1.21-1

therefore IRRA = 21%

IRRB:

$18,000 = $15,000(1 + RB)

= 1.2-1

therefore IRRB = 20%

Decision:

Assuming that k = 10%, both projects are acceptable because:

NPVA and NPVB are both positive

IRRA > k AND IRRB > k

Which project is a "better option" for Agritex?

If we use the NPV method:

NPVB ($1,363.64) > NPVA ($954.55): Agritex should choose Project B.

If we use the IRR method:

IRRA (21%) > IRRB (20%): Agritex should choose Project A. See figure 6.2.

NPV vs IRR: Dependent projects

Up to a discount rate of ko: project B is superior to project A, therefore project B is preferred to project A.

Beyond the point ko: project A is superior to project B, therefore project A is preferred to project B

The two methods do not rank the projects the same.

Differences in the scale of investment

NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:

Years 0 1 2 3
Project A -2,500 1,500 1,500 1,500
Project B -14,000 7,000 7,000 7,000

Assume k= 10%.
NPVA = $1,500 x PVFA at 10% for 3 years
= $1,500 x 2.487
= $3,730.50 - $2,500.00
= $1,230.50.

NPVB == $7,000 x PVFA at 10% for 3 years

= $7,000 x 2.487
= $17,409 - $14,000
= $3,409.00.

IRRA =

= 1.67.

Therefore IRRA = 36% (from the tables)

IRRB =

= 2.0

Therefore IRRB = 21%

Decision:

Conflicting, as:

NPV prefers B to A
IRR prefers A to B
NPV IRR
Project A $ 3,730.50 36%
Project B $17,400.00 21%

Scale of investments
To show why:

i) the NPV prefers B, the larger project, for a discount rate below 20%

ii) the NPV is superior to the IRR

a) Use the incremental cash flow approach, "B minus A" approach
b) Choosing project B is tantamount to choosing a hypothetical project "B minus A".
0 1 2 3
Project B - 14,000 7,000 7,000 7,000
Project A - 2,500 1,500 1,500 1,500
"B minus A" - 11,500 5,500 5,500 5,500

IRR"B Minus A"

= 2.09

= 20%

c) Choosing B is equivalent to: A + (B - A) = B

d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of
$11,500 of which $5,500 will be realised each year for the next 3 years.

e) The IRR"B minus A" on the incremental cash flow is 20%.

f) Given k of 10%, this is a profitable opportunity, therefore must be accepted.

g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.

h) At the point of intersection,

NPVA = NPVB or NPVA - NPVB = 0, i.e. indifferent to projects A and B.

i) If k = 20% (IRR of "B - A") the company should accept project A.

This justifies the use of NPV criterion.

Advantage of NPV:

It ensures that the firm reaches an optimal scale of investment.

Disadvantage of IRR:

It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the IRR
will prefer 500% of $1 to 20% return on $100. However, most companies set their goals in absolute terms
and not in % terms, e.g. target sales figure of $2.5 million.

The timing of the cash flow

The IRR may give conflicting decisions where the timing of cash flows varies between the 2 projects.

Note that initial outlay Io is the same.

0 1 2
Project A - 100 20 125.00
Project B - 100 100 31.25
"A minus B" 0 - 80 88.15

Assume k = 10%

NPV IRR
Project A 17.3 20.0%
Project B 16.7 25.0%
"A minus B" 0.6 10.9%

IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept
A, that is B + (A - B) = A. .

Timing of the cash flow

The horizon problem

NPV and IRR rankings are contradictory. Project A earns $120 at the end of the first year while project B
earns $174 at the end of the fourth year.

0 1 2 3 4
Project A -100 120 - - -
Project B -100 - - - 174

Assume k = 10%

NPV IRR
Project A 9 20%
Project B 19 15%

Decision:

NPV prefers B to A
IRR prefers A to B.

The profitability index - PI

This is a variant of the NPV method.

Decision rule:

PI > 1; accept the project

PI < 1; reject the project

If NPV = 0, we have:

NPV = PV - Io = 0
PV = Io

Dividing both sides by Io we get:

PI of 1.2 means that the project's profitability is 20%. Example:

PV of CF Io PI
Project A 100 50 2.0
Project B 1,500 1,000 1.5

Decision:

Choose option B because it maximises the firm's profitability by $1,500.

Disadvantage of PI:

Like IRR it is a percentage and therefore ignores the scale of investment.

The payback period (PP)

Payback can be defined as 'the time it takes the cash inflows from a capital investment project to equal
the cash outflows, usually expressed in years'. When deciding between two or more competing projects,
the usual decision is to accept the one with the shortest payback.

Payback is often used as a "first screening method". When a capital investment project is being
considered, the first question to ask is: 'How long will it take to pay back its cost?' The company might
have a target payback, and so it would reject a capital project unless its payback period were less than a
certain number of years.

Example 1:

Years 0 1 2 3 4 5
Project A 1,000,000 250,000 250,000 250,000 250,000 250,000

For a project with equal annual receipts:

= 4 years

Example 2:

Years 0 1 2 3 4
Project B - 10,000 5,000 2,500 4,000 1,000

Payback period lies between year 2 and year 3. Sum of money recovered by the end of the second year

= $7,500, i.e. ($5,000 + $2,500)

Sum of money to be recovered by end of 3rd year

= $10,000 - $7,500

= $2,500

= 2.625 years

Disadvantages of the payback method:

 It ignores the timing of cash flows within the payback period, the cash flows after the end of payback
period and therefore the total project return.

It ignores the time value of money. This means that it does not take into account the fact that $1 today
is worth more than $1 in one year's time. An investor who has $1 today can either consume it
immediately or alternatively can invest it at the prevailing interest rate, say 30%, to get a return of $1.30
in a year's time.

It is unable to distinguish between projects with the same payback period.

It may lead to excessive investment in short-term projects.

Advantages of the payback method:

Payback can be important: long payback means capital tied up and high investment risk. The method
also has the advantage that it involves a quick, simple calculation and an easily understood concept.

The accounting rate of return - (ARR)

The ARR method (also called the return on capital employed (ROCE) or the return on investment (ROI)
method) of appraising a capital project is to estimate the accounting rate of return that the project should
yield. If it exceeds a target rate of return, the project will be undertaken.

Note that net annual profit excludes depreciation.

Example:

A project has an initial outlay of $1 million and generates net receipts of $250,000 for 10 years.

Assuming straight-line depreciation of $100,000 per year:

= 15%
= 30%

Disadvantages:

It does not take account of the timing of the profits from an investment.

It implicitly assumes stable cash receipts over time.

It is based on accounting profits and not cash flows. Accounting profits are subject to a number of
different accounting treatments.

It is a relative measure rather than an absolute measure and hence takes no account of the size of the
investment.

It takes no account of the length of the project.

it ignores the time value of money.

The payback and ARR methods in practice

Despite the limitations of the payback method, it is the method most widely used in practice. There are a
number of reasons for this:

It is a particularly useful approach for ranking projects where a firm faces liquidity constraints and
requires fast repayment of investments.

It is appropriate in situations where risky investments are made in uncertain markets that are subject to
fast design and product changes or where future cash flows are particularly difficult to predict.

The method is often used in conjunction with NPV or IRR method and acts as a first screening device
to identify projects which are worthy of further investigation.

it is easily understood by all levels of management.

It provides an important summary method: how quickly will the initial investment be recouped?

Allowing for inflation

So far, the effect of inflation has not been considered on the appraisal of capital investment proposals.
Inflation is particularly important in developing countries as the rate of inflation tends to be rather high.
As inflation rate increases, so will the minimum return required by an investor. For example, one might
be happy with a return of 10% with zero inflation, but if inflation was 20%, one would expect a much
greater return.

Example:

MDIS is considering investing in a project with the following cash flows:

ACTUAL CASH FLOWS

Z$
TIME
0 (100,000)
1 90,000
2 80,000
3 70,000

MDIS requires a minimum return of 40% under the present conditions. Inflation is currently running at
30% a year, and this is expected to continue indefinitely. Should MDIS go ahead with the project?

Let us take a look at MDIS required rate of return. If it invested $10,000 for one year on 1 January, then
on 31 December it would require a minimum return of $4,000. With the initial investment of $10,000, the
total value of the investment by 31 December must increase to $14,000. During the year, the purchasing
value of the dollar would fall due to inflation. We can restate the amount received on 31 December in
terms of the purchasing power of the dollar at 1 January as follows:

Amount received on 31 December in terms of the value of the dollar at 1 January:

= $10,769

In terms of the value of the dollar at 1 January, MDIS would make a profit of $769 which represents a
rate of return of 7.69% in "today's money" terms. This is known as the real rate of return. The required
rate of 40% is a money rate of return (sometimes known as a nominal rate of return). The money rate
measures the return in terms of the dollar, which is falling in value. The real rate measures the return in
constant price level terms.
The two rates of return and the inflation rate are linked by the equation:

(1 + money rate) = (1 + real rate) x (1 + inflation rate)

where all the rates are expressed as proportions.

In the example,

(1 + 0.40) = (1 + 0.0769) x (1 + 0.3)

= 1.40

So, which rate is used in discounting? As a rule of thumb:

a) If the cash flows are expressed in terms of actual dollars that will be received or paid in the future, the
money rate for discounting should be used.

b) If the cash flows are expressed in terms of the value of the dollar at time 0 (i.e. in constant price level
terms), the real rate of discounting should be used.

In MDIS’ case, the cash flows are expressed in terms of the actual dollars that will be received or paid at
the relevant dates. Therefore, we should discount them using the money rate of return.

TIME CASH FLOW DISCOUNT FACTOR PV

$ 40% $
0 (150,000) 1.000 (100,000)
1 90,000 0.714 64,260
2 80,000 0.510 40,800
3 70,000 0.364 25,480
30,540

The project has a positive net present value of $30,540, so MDISshould go ahead with the project.

The future cash flows can be re-expressed in terms of the value of the dollar at time 0 as follows, given
inflation at 30% a year:

TIME ACTUAL CASH FLOW CASH FLOW AT TIME 0 PRICE LEVEL

$ $
0 (100,000) (100,000)
1 90,000 69,231

2 80,000 47,337
3 70,000 31,862

The cash flows expressed in terms of the value of the dollar at time 0 can now be discounted using the
real value of 7.69%.

TIME CASH FLOW DISCOUNT FACTOR PV

$ 7.69% $
0 (100,000) 1.000 (100,000)
1 69,231 64,246

2 47,337 40,804

3 31,862 25,490

30,540

The NPV is the same as before.

Expectations of inflation and the effects of inflation

When a manager evaluates a project, or when a shareholder evaluates his/her investments, he/she can only
guess what the rate of inflation will be. These guesses will probably be wrong, at least to some extent, as
it is extremely difficult to forecast the rate of inflation accurately. The only way in which uncertainty
about inflation can be allowed for in project evaluation is by risk and uncertainty analysis.

Inflation may be general, that is, affecting prices of all kinds, or specific to particular prices. Generalised
inflation has the following effects:

a) Inflation will mean higher costs and higher selling prices. It is difficult to predict the effect of higher
selling prices on demand. A company that raises its prices by 30%, because the general rate of inflation is
30%, might suffer a serious fall in demand.

b) Inflation, as it affects financing needs, is also going to affect gearing, and so the cost of capital.

c) Since fixed assets and stocks will increase in money value, the same quantities of assets must be
financed by increasing amounts of capital. If the future rate of inflation can be predicted with some degree
of accuracy, management can work out how much extra finance the company will need and take steps to
obtain it, e.g. by increasing retention of earnings, or borrowing.

However, if the future rate of inflation cannot be predicted with a certain amount of accuracy, then
management should estimate what it will be and make plans to obtain the extra finance accordingly.
Provisions should also be made to have access to 'contingency funds' should the rate of inflation exceed
expectations, e.g. a higher bank overdraft facility might be arranged should the need arise.

Many different proposals have been made for accounting for inflation. Two systems known as "Current
purchasing power" (CPP) and "Current cost accounting" (CCA) have been suggested.

CPP is a system of accounting which makes adjustments to income and capital values to allow for the
general rate of price inflation.

CCA is a system which takes account of specific price inflation (i.e. changes in the prices of specific
assets or groups of assets), but not of general price inflation. It involves adjusting accounts to reflect the
current values of assets owned and used.

At present, there is very little measure of agreement as to the best approach to the problem of 'accounting
for inflation'. Both these approaches are still being debated by the accountancy bodies.

Inflation

TA Holdings is considering whether to invest in a new product with a product life of four years. The cost
of the fixed asset investment would be $3,000,000 in total, with $1,500,000 payable at once and the rest
after one year. A further investment of $600,000 in working capital would be required.

The management of A Holdings expect all their investments to justify themselves financially within four
years, after which the fixed asset is expected to be sold for $600,000.

The new venture will incur fixed costs of $1,040,000 in the first year, including depreciation of $400,000.
These costs, excluding depreciation, are expected to rise by 10% each year because of inflation. The unit
selling price and unit variable cost are $24 and $12 respectively in the first year and expected yearly
increases because of inflation are 8% and 14% respectively. Annual sales are estimated to be 175,000
units.

TA Holdings money cost of capital is 28%.

Is the product worth investing in?

Capital Rationing

In some circumstances the business is unable or unwilling to undertake capital expenditures even though
it is a positive returns, it is called capital rationing,

If it is unable to raise finance because of limited funds, it is called hard capital rationing.

When the rationing is self imposed because lack of management expertise, we called it soft capital
rationing.
Investment appraisal and strategic planning

a) Establish mission and objectives

b) Undertake a position analysis
c) Identify and assess the strategic position
d) Select strategic position
e) Review and control.

Shareholder value analysis

We should now the following drivers relate them to the business

Increase in sales revenue growth rate

Operating profit margin
Corporation Tax rate
Investment in non current assets
Investment in working capital
Investment in working capital
The cost of capital the life of the projected cash flow

EVA

EVA = NOPAT – (R-C)

NOPAT – net operating profit
R required rate of return
C capital invested

Increase NOPAT This may be done by reducing expenses or by increasing sales revenue
Use capital invested more efficiently
Reduce the required rate of return for investors.

Assessment of the EVA approach to management

Eva is based on conventional financial statements , adjusted to remove the biases. Any adjustments to the
financial statements are matter of judgment which call into question the credibility of the economic value
added for a period that has been calculated
Managers are subject to a charge for the capital that has been invested. Before any increase in
shareholders wealth can be recognized, an appropriate deduction is made for the use of the business
resources.
For mutually exclusive projects, accept the project with the higher NPV. A project with higher NPV need
not be the one with a higher IRR. Again using the NPV method is easier. IRR does not have the value-
additive property.
Example

Project D has an IRR of 100% and NPV of + 8,182 at 10%.

Project E has an IRR of 75% and NPV of +11,818 at 10%
Alternate example:
Project C0 C1 IRR NPV at 25%

A –1 +2 100% +0.6

B –1 +4 300% +2.2

(A + B) –2 +6 200% +2.8

Adding the two NPVs gives the NPV of the combined project. This is called the value-adding property.
Adding the two IRRs does not give the IRR of the combined project.

The project with higher IRR need not be a better project. This is because of the reinvestment rate
assumption. In case of the NPV method and the MIRR method, the reinvestment rate is the cost of
capital. This is a more reasonable assumption than investing at the IRR, particularly for projects with
high IRRs.
Alternate Example:

Project C0 C1 IRR NPV at 25%

F – 20,000 +35,000 75% +8,000

E – 10,000 +20,000 100% +6,000

——————————————————————

F – E – 10,000 +15,000 50% +2,000 (Project F is preferred to project E).

IRR method cannot be applied to mutually exclusive projects. You can only compare two projects at a
time as shown above. It is much easier to use the NPV method and choose the project with the higher
(highest if there are more than two projects) NPV.

IRR method implicitly assumes that the project cash flows are reinvested at the IRR. This is not a realistic
assumption. It also assumes that the discount rates are stable during the term of the project.

Profitability index (PI) provides a tool for selecting among various projects when the firm is faced with
capital constraint.

Profitability index (PI) provides a tool for selecting among various projects when the firm is faced with
capital constraint. PI = NPV/(Investment). The combination B + C gives the highest NPV, given the
resource constraint. Choose the combination with the highest weighted average PI.

Here is another example. Choose the combination with the highest weighted average PI.
PI method indicates that B and C combination is better. It also has the highest NPV.

There is capital constraint for the firm.

Project: A B C D
PI 1.15 1.13 1.11 1.08

Investment 200 125 175 150

WAPI(BD) = (1.13)×(125/300) + (1.08)×(150/300) + (0.0)×(25/300) = 1.01.

($25,000 is invested in the financial market and therefore has zero NPV)
Weighted Average PI for B and C is (125/300) x 1.13 + (175/300) x(1.11) = 1.12

Weighted Average PI (BD) = 1.01

WAPI (A) = 0.77

WAPI(BC) = 1.12

Therefore, accept B and C combination.

KEY TERMS AND CONCEPTS

Payback period, discounted payback rule, book rate of return, internal rate of return, mutually exclusive
projects, modified internal rate of return, capital rationing, profitability index, soft rationing, hard
rationing.

CHALLENGE AREAS

Internal rate of return (IRR)

Modified internal rate of return (MIRR).

ADDITIONAL REFERENCES

Graham J.R and C.R. Harvey, “The Theory and Practice of Finance: Evidence from the Field,”

Journal of Financial Economics, 61(2001), pp. 187-243.

Copeland,T.E, J.F. Weston, and K. Shastri, “Financial Theory and Corporate Policy,” Fourth Edition,

Pearson Addison Wesley, Boston, 2005.

Benninga, S. Financial Modeling. 3nd Edition, Cambridge, MA: The MIT Press, 2008.

WEB LINKS

www.mcgraw-hill.co.uk/textbooks/brealey

www.smallbusinesslearning.net

www.cob.ohio-state.edu/~fin/overview.htm

www.cfo.com

http://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P67_The_theory_and.pdf

ADDITIONAL INTERNET ACTIVITIES

Go to www.studyfinance.com and study the material under capital budgeting.

Go to http://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P67_The_theory_and.pdf

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