Wyklad 5 (2017)
dodatek dla osob ktore znaja j. angielski
Investment decisions and capital budgeting
Learning Objectives:

to understand the nature of capital investments

to introduce the concept of equity ownership

to understand the time value of money

to explain simple methods of investment evaluation techniques

to understand life cycle costing

to explain the nature of portfolio investments.
Contents
1 Managerial Perspective
2 Calculations of the Value of an Investment
3 The Cost of Capital
4 Life Cycle Costing
5 Portfolio Investment
6 Concluding Comments
1 Managerial Perspective
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In particular, we consider how the business owner-manager calculates the return on
his/her equity capital. Since it is his/her job to determine what products to produce,
what prices to charge for them, which factor services to employ and at what cost,
1
Throughout most of the preceding Topics, it was assumed that economic decisions
were taken in a nearly deterministic environment, that is, all outcomes of decision
making were known with near certainty. Thus, all decision makers were assumed to
have nearly complete knowledge of past, present and future events, activities and their
outcomes, and all that knowledge was available at zero cost. In this Topic we consider
some of the problems arising when the assumption of perfect knowledge is relaxed
and review simple methods for dealing with limited knowledge.
he/she must also pay himself/herself for services rendered. In earlier Topics, this form
of payment was referred to as 'profits', which were described as return on equity
capital (own money and effort) contributed by the owner-manager. We assume that a
particular amount of that equity capital is provided to facilitate the activity under
consideration so that the business objective of the owner-manager is to maximise the
total return on the equity capital provided.
Capital Budgeting
So far in our discussion of pricing no account has been taken of the time dimension of
decisions. However, suppliers/businesses need to make investment decisions that
incur costs both initially and over a number of years, but that have payoffs in the
future. In order to maximise returns on equity capital (profits), the business owner
needs to evaluate investment projects taking into account revenues and costs that are
spread over time. This process of evaluating expected returns on various investment
opportunities is called capital budgeting.
Capital budgeting is of crucial importance to a firm. It is used in planning for:

replacement of old equipment;

adoption of new production techniques;

capacity expansion;

development of new products; and

compliance with government regulations.
Profitability, growth and even survival depend on how well management meets the
challenge implied in capital budgeting.
The Nature of Profits
Another issue that calls for clarification concerns the nature of business profits and
the business owner's equity capital. Up to this point, it has not been explained what
suppliers have to do to earn their profits. In particular, the nature of profits has to be
explained.
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In this interpretation, profits arise because the business owner (equity holder) has to
enter, beforehand, into contractual arrangements with all owners of factors of
production (input suppliers) who participate in the activity. As the equity holder, the
business owner bears the difference between the anticipated cost of these inputs and
the expected revenue. The contracted factor owners include workers (owners of
2
First, the business owner (manager) must calculate before the event (ex ante) all
expected costs as the anticipated value of his/her contractual commitments to factor
owners over some pre-specified period of time. He/she must also calculate the
expected revenue, that is, the expected value of sales. As long as the expected revenue
exceeds the expected costs, the business is expected to be profitable. It is this ex ante
profit that is maximised as the expected return on equity capital contributed by a
business owner.
human capital who provide all the labour services needed), suppliers of materials,
lessors of equipment, providers of financial capital, and so on. In each case, the
business owner or his representative has to enter into a contractual arrangement
whereby he/she promises to pay an agreed sum of money (wage, rent, etc.) per unit of
factor input provided in exchange for a particular quantity of input to be supplied by
the contracted factor owner. For example, a worker may be hired for $50 per hour for
30 hours a week. The sum of these ex ante commitments is the ex ante cost of the
activity.
The actual profits after the event (ex post profits) depend on the outcome of the
activity under consideration. In an uncertain world, this ex post result is likely to
differ from what was anticipated. For example, product prices and quantities of output
sold may differ from those previously expected and the ex post revenue may differ
from what was anticipated beforehand. Similarly, some input owners may fail to
honour their undertaking to supply particular quantities of inputs at agreed prices or
they may allow for some degradation of the quality of inputs supplied. Thus, the ex
post costs may differ from those anticipated beforehand. Hence, the business owner
(equity holder) must bear the risk that ex post outcomes could differ from ex ante
calculations.
Here we come to the second interpretation of profits as the ex post difference between
actual costs and actual revenues. As noted, there is likely to be a difference between
ex ante and ex post profits. This difference is a windfall which can be negative, zero
or positive, and which, by definition, cannot be maximised. That is, the final outcome
of an activity is only known when the books are closed, as it were, and all relevant
costs and revenues are enumerated. In that sense, the business owner bears the
risk/uncertainty that the actual outcome of activity differs from the anticipated costs
and revenues. The necessity to bear the difference between anticipated and actual
profits is inherent in business ownership (equity holding). This is because the business
owner makes legally binding promises (eg. contracts of employment) to pay the hired
factor owners for their supplies of goods and services used by the business but can
only recover these costs when the business turns out sufficient volume of sales and
brings high enough revenue.
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However, to assure the factor owners that promises to pay them are credible, the
owner must also provide some collateral, ie. funds to be used to pay factor owners in
the event the actual revenue falls short of the actual cost. This takes the form of
3
The role of the business owner is now more apparent. He/she is ultimately responsible
for arranging, ex ante, all contracts of employment with factor owners providing
inputs into the business and, where appropriate, customers. This explains why the
control of the business activity, that is, the right to hire and fire factor services, is
vested in the owner of the business. To ensure that the suppliers of factor services
comply with their contractual undertakings, the business owner must be able to
monitor their activities and validate the quality and quantity of factor services/goods
provided. If need be, for example when some factor owners shirk or default in some
other way on their contractual obligations, the business owner must be able to
revise/terminate the relevant contractual arrangements and seek damages. [This direct
control over factor inputs may be delegated in that the owner (principal) may hire a
salaried manager to act as his/her agent.]
equity capital. The latter is contributed to the business by the owner on the
understanding that the return on it can only be determined ex post, that is, after the
activity is completed and fully accounted for (all other factor owners are paid, etc.). In
this respect, equity capital is different from debt capital, whereby money is borrowed
for a period of time from financial institutions or individuals on (ex ante) agreed terms
(eg. at an agreed interest rate). In the latter case, the amount borrowed has to be repaid
to the lender over the duration of the loan (with interest). Equity capital, on the other
hand, is not repaid over some pre-agreed period. It may only be returned to its owner
(equity holder) when the business is closed and all the attendant liabilities are fully
met, or when there are sufficiently high profits to pay the equity holder both the
equivalent of his/her initial equity investment in the business and some rate of return
on that investment.
In this Topic, we are only concerned with the anticipated returns on equity capital. To
make rational investment decisions, the owner (or manager as the owner's
representative) must determine the opportunity cost of equity capital and assess
returns offered by various, sometimes mutually exclusive, investment opportunities. If
the available amount of equity capital is limited (capital rationing), the investor must
also rank the available investment opportunities to select those that offer the prospect
of the highest return.
Finally, the separation between ownership and management (principal and agent)
creates a rather complex institutional environment in which capital budgeting
decisions may be made. For example, the ownership structure of a business enterprise
may be so diffuse that its managers may 'hijack' the decision making process and treat
the providers of equity capital, the shareholders, in exactly the same way as they treat
other factor owners (other stakeholders in the business). In such circumstances, the
assumption that business managers maximise ex ante profits may not be appropriate.
In reality, the business objectives of firms may be quite complex with the need to
meet profit expectations of shareholders being only one item on the managerial
agenda (a constraint to be satisfied rather than the main objective of the business).
2 Calculation of the Value of an Investment
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In estimating revenues and costs over time (cash flows), guidelines must be followed.
These are:
 incremental costs and returns should be measured, ie. sales revenues and costs
that are specific to a particular investment opportunity/project;
4
Evaluation of Investment Opportunities
One of the most difficult parts of capital budgeting is estimating the future returns on
and costs of investment opportunities (projects). These are necessarily unknown at the
time investment decisions are being made and require forecasting a number of
variables - sales levels, engineering requirements, cost estimates. Decisions also need
to be taken on how much analysis to undertake to get these estimates. Detailed and
expensive analysis is required when the opportunity cost of the project is very high.
Where the opportunity cost of a project is low, less can justifiably be spent on
estimation. There is a trade-off between forecasting accuracy and the cost of making
the forecast.

cash

in cash flow calculations depreciation should not be included. It affects cash
flow only through its effect on taxes.
flows
should
be
estimated
on
an
after-tax
basis;
and
Discounting
Once estimates of anticipated future costs and revenues (benefits) have been obtained
from forecasts, they are compared to establish if the project is worthwhile. However,
this calls for more than a simple summation of costs and revenues before proceeding
to a decision. Costs and revenues must be subjected to a process of discounting
before they are compared. Discounting is a process that converts future dollars into
current values. Its purpose is to place the dollar values of future returns and costs on a
basis that is comparable with the dollar value of current returns and costs. Clearly, a
dollar you have in hand today means more to you than a dollar you cannot have for
ten years from now. Most people exhibit 'time preference': they prefer to have things
or money now rather than at a future date.
The logic of discounting future costs and receipts is that it is always possible to earn
an interest payment by postponing expenditure of money currently held, and thus
money only available in the future is of less value than money held now. For example,
compare $100 earned on a project in three years' time to $100 in hand now. Assuming
that the investor can earn 15% compound interest on the $100 currently held, in three
years' time that money will grow to $152 - considerably more than the $100 earned
three years from now from the project. The $100 now is more valuable than the $100
earned later.
Similarly, a cost of $100 now differs from an outlay of $100 in three years' time. If
expenses do not occur for three years the firm is able to use the $100 to earn interest
prior to incurring the outlay. At 15% compound interest the $100 will have grown to
$152 to pay for $100 worth of expenses. If the costs occur in the current period there
is no opportunity to earn an interest payment. Future outlays are less expensive than
current outlays of the same dollar amount.
If both costs and revenues are of less value when they arise in the future, they require
some adjustment to establish their current worth. This is the process of discounting
and their current worth is known as their present value. The rate at which they are
discounted is related to the rate of interest that could be earned elsewhere.
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5
Net present value
A well-established technique for determining the worth of an investment project is to
calculate the net present value of the project. The net present value (NPV) of a
project is the present value of all future revenues minus costs discounted at the firm's
cost of capital, minus the initial cost of capital. This is net cash flow or anticipated
profit on equity provided by the business owner of the project (see Transparencies 14).
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6
Internal Rate of Return
An alternative evaluation method is to calculate the internal rate of return. The
internal rate of return (IRR) of a project is the discount rate that equates the present
value of the cash flow generated by the project to the initial cost of the project (see
Transparencies 5-7).
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7
The IRR measures the return on the investment (the business owner's equity capital),
with more profitable investments generating higher returns. The firm should
undertake those projects where the IRR is greater than or equal to the discount rate the
firm uses to evaluate the cost of its capital (the marginal cost of capital). This reflects
the opportunity cost of employing equity capital in the activity under consideration as
opposed to the best opportunity for its employment elsewhere. If you could lend your
own money at 10% you would expect to earn at least 10% if you employed it in your
own business.
It should be noted that in the case of mutually exclusive projects - only one project
can be undertaken out of two or more proposals (eg. two different ways of building a
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8
Comparison of NPV and IRR
Although the two techniques have been given as alternatives, as long as a single
project or independent projects are evaluated, the NPV and IRR methods will lead to
the same decision concerning whether the project should proceed (see Transparency
8). The NPV is only positive if the IRR is greater than the firm's discount rate. The
rule that the investor should invest if the NPV is positive is equivalent to the rule that
it should invest if the IRR is greater than the discount rate. A third way of expressing
the rule is to state that the investor should invest up to the point where the marginal
return on investment equals the marginal costs of investment.
bridge) - the two techniques may give contradictory results. The project with the
higher NPV may have the lower IRR or vice versa. In this case, the project with the
higher NPV should be chosen. Both methods implicitly assume re-investment of cash
flows at the nominated rates - cost of capital for NPV, internal rate of return for IRR.
It is preferable to assume the lower rate of return for reinvestment of cash flows and
therefore the NPV method should be used to choose between mutually exclusive
projects.
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9
Capital Rationing
The above rule is not followed when investments are of unequal size and there is
capital rationing. Capital rationing can arise when management wishes to avoid the
strains that rapid expansion may bring with it or to avoid being over-exposed in
unfavourable market conditions (see Transparency 9). When investors cannot
undertake all projects with positive NPVs, they may rank projects according to their
profitability index (PI) and choose the projects with the highest index. The
profitability index measures relative profitability ie. net cash flow per dollar cost of
investment. Two small projects may each have smaller NPVs than a large project, but
together may increase the net worth of the firm more than the large project.
Transparency 10 ranks various investment projects A to E by their expected return.
The size of each project in $m is indicated by the thickness of the line for each
project. Project B is the smallest of the projects but is expected to yield the second
highest return. The marginal cost of capital (opportunity cost), at 6%, is also shown as
a horizontal red line. Projects A to D yield rates of return that exceed the marginal
cost of capital and should be pursued. Project E should be abandoned.
10
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Payback Period
Another popularly used capital budgeting procedure is the payback period criterion.
Under this rule, if the investment generates a net flow of returns that covers the initial
cost before some arbitrarily set time period, it should be followed (see Transparency
11). For example, if a project cost $300,000 and had returns of $50,000 in each
succeeding year, it will be undertaken if the manager has set a payback period of 6
years but not if a period of 4 years has been set. This procedure ignores the time
value of money (cash flow is not discounted), so although it is extensively used, it is
inferior to either NPV or IRR.
Present Value of Perpetual Returns
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11
See Transparency 12.
3 The Cost of Capital
The cost of raising capital to invest is an essential element of the capital budgeting
process, using either the NPV or IRR methods of evaluation. We now turn to consider
how the cost of raising capital is estimated.
Businesses raise capital from many sources - externally from the issuing of debt and
sale of stock (common and preferred) and internally from the use of retained earnings.
The cost of using retained earnings is the opportunity cost (the foregone return) on
investing these funds outside the business. The cost of using external funding is the
lowest rate of return that will ensure that lenders or shareholders keep their funds in
the business.
We can simplify by considering the cost of capital under two broad headings - the
cost of debt, ie. raising money by borrowing, and the cost of equity, ie. raising
money by extending ownership through the sale of shares.
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12
The Cost of Debt
The incremental cost of debt (we are concerned with new investments, so are
concerned with the marginal cost of debt, not the average cost) is the interest paid to
lenders of new debt, net of tax (see Transparency 13). Since the interest payments on
borrowed funds are allowed as a tax deduction from the firm's income, the after-tax
rate of interest is the true cost of debt. For example, if the firm borrows at 15% but
faces a 40% marginal tax rate on its taxable income, the after-tax cost of the funds is
not 15% but 15% - (40% of 15%) = 15% - 6% = 9%. More generally, the after-tax
cost of debt = interest rate (1 - tax rate).
Purchasing stock in a business entails accepting some risk of not getting a return.
Dividends vary with the company's profits, so an investor assumes the risk associated
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13
The Cost of Equity
The cost of equity capital is the rate of return the firm must offer stockholders to
induce them to invest in the firm (see Transparencies 14-15). There is no tax
adjustment to the cost of equity as dividends paid are not allowed as a tax deduction.
(However, the firm may pre-pay income tax due on the dividend and distribute
dividend payments to shareholders with the income tax pre-paid.)
with its performance. He/she will want a return that allows for the riskiness of
investing in a particular business rather than purchasing government securities
(assumed to be risk free). Thus the return on equity, RE, can be considered as having
two components, a risk-free rate, RF, which is what could be earned if investing in
government bonds, and a risk premium, RP, that is the additional compensation
required for accepting the risk of the business.
RE = RF + RP
The risk free rate is taken as the rate available on Treasury bills. However, calculating
the risk premium is less straightforward and there are different methods for
calculating it. Two methods are shown below (see Transparencies 16-18).
Method A - Risk Free Rate Plus Risk Premium
The risk premium can be considered as having two components. First, there is the risk
involved in investing in the business rather than buying government bonds. This is
usually measured as the difference between the return on government bonds and that
on the company's borrowing Ri (eg. bonds). Secondly, when businesses borrow from
lenders they incur an obligation to pay an interest payment to the lenders; dividend
payments are made only after interest payments are met. Therefore there is a risk
involved in purchasing the stock of the company rather than lending to the company.
This additional risk in purchasing the company's stock rather than bonds is measured
by the historical difference between yields on stocks and bonds issued by private
companies, ie. at about 4%.
For example, if the return on government bonds is 10% and the return on the firm's
bonds is 13%, the total risk premium is
RP = (Ri - RF) + 4% = (13% - 10%) + 4% = 7%
and the cost of equity is
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14
RE = RF + RP = 10% + 7% = 17%.
Method B - Capital Asset Pricing Model (CAPM)
This commonly used model takes into account the risk differential between a
particular company's stock and that of the stock of private companies in general, as
well as the differential between the company's stock and government securities. The
former differential is measured by a company's beta coefficient, which is the ratio of
the variability of return (eg. as measured by the coefficient of variation) on its stock
to the variability in the average return on the stock of all companies. A beta
coefficient of 1.0 means that the company's stock is as variable in its return as the
average; a coefficient of less than 1.0 indicates less variability (less risk); greater than
1.0 indicates more variability (greater risk).
Using this model, the cost of equity capital to the business is measured by
RE = RF + beta (RM - RF),
where RM is the average return on the stock of all companies. The second term is the
beta coefficient times the risk premium on average stock, ie. the risk premium on
holding stock of a particular business. Therefore the cost of equity is equal to the risk
free rate plus the particular company's risk premium.
For example, if the return on government bonds is 10%, the average return on stocks
is 17% and the beta coefficient for a particular firm is 0.75, then the cost of equity to
the firm is
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15
RE = 10% + 0.75 (17% - 10%) = 10% + 5.25% = 15.25%.
The Aggregate Cost of Capital
The overall cost of capital is a weighted average of the cost of debt and the cost of
equity, where the weights are the proportions of the company's overall capital that
comes from the respective financing methods (see Transparency 19). For example if
the cost of debt is 8% and the cost of equity is 15%, and 30% of the company's capital
comes from debt, 70% from equity, the cost of capital is
R = 8% x 0.30 + 15% x 0.70 = 12.9%.
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16
Since debt financing is cheaper than equity finance, businesses will lower their cost of
capital by incurring some debt. This does not imply however, that businesses should
aim for debt financing exclusively. As companies increase the proportion of their debt
financing, lenders see the business as being more risky to lend to. Consequently,
lenders require a higher risk premium from heavily indebted companies, and the
marginal cost of capital increases.
4 Life Cycle Costing
A particular area of capital budgeting that has become increasingly popular is life
cycle costing (LCC). This is usually defined as the sum of all funds expended in
support of the activity over its life time, that is, from its conception and through
development, implementation, operation to the end of its useful life (including the
cost of activity termination). LCC seeks to optimise the full, life-long cost of an
activity or an asset by attempting to identify ex ante all significant costs involved
during its life. If there are alternative activities to be considered, LCC allows their
ranking on the basis of the full cost of ownership. The least (LCC) cost option is then
selected.
In principle, LCC is a truncated version of capital budgeting in that it deals with the
flow of costs over the project life cycle but not the flow of revenues (benefits). In
practice, LCC is often applied as a (full) capital budgeting technique in that
revenues/benefits are treated as negative costs. However, in many applications where
benefits are less tangible than the costs (eg. weapons acquisition projects), it is
implicitly assumed that benefits are identical under each option whilst costs vary. In
practice, however, differences between activities/projects in terms of benefits are well
understood but poorly quantified. Hence the emergence of various 'value-for-money'
evaluations where 'money' usually means LCC and 'value' some (rather intangible)
notion of benefit.
5 Portfolio Investment
Diversification of risky activities and business ventures by acquiring portfolios of
varied activities, assets or lines of business is a method of reducing investment risk.
By avoiding putting all their investment eggs in one (project) basket, investors can
balance the average expected return and the average risk across a range of the
available investment opportunities.
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Suppose investment opportunities A and C are two (statistically) independent
investment opportunities, say shares in companies A and C respectively. By investing
all their investment resources in either A or C, investors can only achieve their lower
(risk-return) preference objectives (I or II). Suppose B represents a combination of
shares in C and A. This offers lower returns than C only but is also less risk than C
17
Consider Figure 1 below, which shows how risks can be spread through a portfolio of
risky activities. In the Figure, the investor's best investment opportunities are shown
as a curve linking the best available investment options (ABC). This curve is the
investor's risk-return investment opportunity frontier ABC. Other available options, to
the right of ABC, such as the investment opportunity D, either offer more risk for any
given rate of return or lower return for a given level of risk. Options to the north and
west of ABC are unattainable. The investor's preference for risk bearing is shown as
the risk-return preference curves I, II and III. Given the available investment
opportunities, investors strive to reach their highest risk-return preference curve. In
this case, this is III (since IV is beyond his/her reach and I and II are less preferable).
The shape of this curve shows the investor's preference for risk. In this case, the
investor is risk averse and any increase in the riskiness of his investment activity must
be compensated by an increase in the expected return at an increasing rate.
only. It also offers more preferable combination of risk and return than A. By
combining shares in A and C into a portfolio of investments, B, investors may achieve
a preferred balance between risk and return compared with dedicating all their
resources to one investment opportunity.
Figure 1
Portfolio of Risky Activities/Investments
Rate of Return (%)
IV
III
II
I
Investor’s Risk-Return Curves
C
Investor’s Risk-Return
Opportunity Frontier
B
D
A
Measure of Risk (eg. Variance
of Returns)
The above illustration explains why various portfolio arrangements are used to tailor
risk-return combinations to the requirements of particular investors (eg. pension
funds, equity holding trusts, and individuals). The application of portfolio analysis
also enables companies to pool statistically independent risks and spread the cost of
risk bearing over a large number of risk-averse individuals. This explains, in part,
equity capital that is provided in the form of marketable shares, so that each share can
be acquired or sold by an otherwise impecunious shareholder.
6 Concluding Comments
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Such opportunities are not available in the public sector where all assets are
collectively owned even if 'divided' between various government agencies and
enterprises.
18
All economic activities can be represented as investments in that they all involve the
use of resources over time. Considerations of 'time' are therefore most important and
the evaluation of economic activities should allow for the time value of money.
Class participants may now reflect on the nature of various institutional arrangements
that allow for better risk sharing and risk tailoring. Joint holdings of assets by
household members go some way in this direction but share 'trusts' and 'funds' allow
for better tailoring of risk-return combinations. The marketability of equity capital
provides more choice for investors whilst its 'securitisation' allows many individuals
to acquire small quantities of equity in different enterprises.