Capital Budgeting, Investment Appraisal & Business Decisions.
Article by P McGillion, B.E, MBA, CDipAF, Dip.M, HDip(MS), CEng, Eur Eng, FIEI,
Examiner F1 Business Mathematics & Quantitative Methods
Section 1 of the syllabus sets out the examination requirements for Investment
Appraisal and NPV Analysis. These techniques are examined at competency
Level 2. This paper covers the basics of the topic without dealing with detailed
aspects of these areas not required for examinations such as the impact of
inflation, taxation, depreciation, grants and capital allowances. The content is
suitable for candidates sitting Formation 1 examination and is an introduction to
the subject area which is dealt with in detail in Managerial Finance at P1.
Introduction. Capital investment decisions involves a company making decisions about large
investment outlays in return for a stream of benefits in future years. The main feature between
short-term decisions and capital investment decisions (which are long-term) is time. Short-term
decisions involve a short time horizon, say one year, from the commitment of funds to the flow
of benefits. However, where capital investment decisions are made a significant period of time
may elapse, possibly a number of years, before the receipt of benefits. This time period involves
an interest cost which must be brought into the analysis. Companies may commit a large
proportion of the firm’s resources to investment in plant and machinery which may be
irreversible. In our analysis (for F1) we assume that all cash inflows and outflows are known
with certainty – a factor not realistic in the business world.
The rates of return which are available from investments in financial markets represent the
‘opportunity cost of an investment’ in capital projects, that is, if cash is invested in the capital
project it cannot be invested elsewhere to earn a return. A company should therefore invest in
capital projects only if they yield a return in excess of the opportunity cost of the investment.
This is also known as the minimum required rate of return, cost of capital, the discount rate or
the interest rate.
The objective in this section is to calculate and compare returns on an investment in a capital
project with an alternative investment in the financial markets. This comparison is made by
using discounted cash flow (DCF) analysis and concentrates on time value of money
techniques. There are two main forms of dcf:
- the net present value (NPV)
- the internal rate of return (IRR) methods.
A DCF analysis is the opposite of the concept of compounding interest. Compound interest can
be calculated in tabular format by reinvesting the interest earned each year to the previous
years investment or, in the case of many years, by using the formula: Vn = V0(1 + i)n, where Vn
denotes the future value of the investment in years, V0 denotes the amount invested at the
beginning of the period (year 0), i denotes the rate of return on investment, and n denotes the
number of years for which the money is invested. When making investment decisions, cash
inflows and outflows for different years, must be converted into a common value. This is done
by converting the cash flows into their respective values at the same point in time. The ‘point in
time’ at which the decision is taken is normally the present time or year 0. The process of
converting cash to be received in the future into a value at the present time by the use of an
interest rate is called discounting and the resulting present value is the discounted present
value. To calculate future values the formula above can be rearranged to produce the present
value formula: V0 = Vn/(1 + i)n
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By using discounted cash flow techniques and calculating present values we can compare the
return on an investment in capital projects with an investment in financial markets. The best way
of determining if a project yields an acceptable return is to calculate the net present value
(NPV). This is the present value of the net cash inflows less the project’s initial investment
outlay – the present value rule.
NPV = V1/(1 + i) + V2/(1 + i)2 + V3/(1 + i)3 + ---------- Vn/(1 + i)n – I0, where I0 represents the initial
outlay and V represents the future values received in years 1 to n. The present value for each
year can be found from ‘discount factor’ tables (available during examinations). These tables
are based on the present value of €1 received in n years time calculated according to the
present value formula.
Business decision rule: if the rate of return from the project is greater than the return from an
equivalent investment, the NPV will be positive. Alternatively, if the rate of return is lower, the
NPV will be negative. A positive NPV indicates that an investment should be accepted while a
negative value indicates that it should be rejected. When the NPV is positive the return on the
cash invested in the project is above the selected rate and vv.
When the annual cash flows are constant, the calculation of the net present value is simplified.
There are cumulative present value factors which can only be applied when the annual cash
flows are the same each year.
Internal Rate of Return. The IRR is an alternative technique for use in making capital investment
decisions which also takes into account the time value of money. The IRR represents the true
interest rate earned on an investment over the course of its economic life. This is also termed
the discounted rate of return. The IRR is the interest rate which, when used to discount all cash
flows resulting from an investment will equate the present value of the cash received to the
present value of the cash outlays. It is the discounted rate which will cause the net present
value of an investment to be zero. The IRR can be found by solving the value of i in the formula:
I0 = V1/(1 + i) + V2/(1 + i)2 + V3/(1 + i)3 + ---------- Vn/(1 + i)n.
This can be done in two ways
(i) By calculation: the IRR can be found by trial and error by using a number of discount factors
until the NPV equals zero. It is difficult to get an accurate value unless the discount values
are of constant amounts each year.
(ii) By interpolation: a number of discount rates are applied and the NPVs derived (a higher
discount rate gives a negative NPV while a lower discount rate gives a positive NPV). The
discount rates are then graphed against the NPVs. Where the line joining the NPVs crosses
the ‘discount rate’ axis, the NPV is zero. However, a formula using the interpolation method
is simplified to: [N2I1 –N1I2]/[N2 – N1] where N1 is the NPV at the low discount rate I2 and N2 is
the NPV at the higher discount rate I1.
Business decision rule: if the IRR is greater than the cost of capital, the investment is profitable
and will yield a positive NPV; if the IRR is less than the cost of capital the investment is
unprofitable and will result in a negative NPV.
If the funds for the investment are borrowed at a cost of capital of 15% and the derived IRR is
18%, the project will be profitable. The degree of profitability can be assessed by the fact that,
after paying the cost of capital a ‘net profit’ of 3% on the cash invested is obtained. When
comparing two projects, the IRR is used to identify the most profitable project.
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Comparison of NPV and the IRR. In the case of conventional projects, that is, where the initial
cash outflow is followed by a series of cash inflows, both NPV and IRR rules will lead to the
same accept/reject decisions. However, where projects are mutually exclusive (where the
acceptance of one excludes the acceptance of another, for example, the choice of one of many
different machines), it is possible for the NPV and the IRR methods to give different rankings.
The NPV may give a higher ranking to project A than B and the IRR may give a higher ranking
to project B than A. However, there are mechanisms for dealing with this situation which are
outside the scope of our syllabus.
In summary
-
NPV is technically superior to IRR: it reflects the scale of a project (discriminates between
projects with larger cash flows) while IRR does not
NPV is superior for ranking investments in order of attractiveness
Where discounts rates are expected to differ over the life of the project, these variations can
be included in NPV calculations
Where cash flows are conventional (initial outflows followed by a series of inflows), a single
IRR value is calculated.
Where cash flows are not conventional (vary during the period of the project) there may be a
number of different rates of return making it difficult to apply the IRR.
Which method should be used in any given situation? The argument used in favour of the IRR is
that a percentage return is understood in business and enables comparison with the cost of
borrowing while the NPV provides a ‘surplus’ but this is not quantified in terms of the magnitude
of the return. Although the NPV may be technically superior, surveys indicate that the majority of
decisions are based on the IRR method.
Every expenditure analysis involves the following components
- identification of all relevant elements (initial costs, cash flows, residual costs,
etc,)
- identification of all cash flows (both inflows and outflows and determining the
‘net cash flow’)
- the timing of cash flows (the end or beginning of a year)
- a procedure for evaluating the benefits relative to the costs.
Example.
This example sets out the principles outlined above and considers the key components
involved in the analysis.
A company is considering two investment plans. One plan requires an investment now of €7,500
and will provide a return of €10,400 in 5 years. The second plan requires 5 investments starting
with €2,000 now, €1,000 for the next 3 years and €1,500 in year 4. It will give a return of €8,500
in year 5.
Which investment should the company undertake if the cost of capital to the company is 6%?
What IRR would the second plan provide?
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Comparison of plans.
Year
Discount
Factor
(6%)
0
1
2
3
4
5
NPV
1.000
0.943
0.890
0.840
0.792
0.747
Plan 1
Net Cash
PV €
Flow €
(using
6% pv
factor)
(7,500) (7,500)
------------------------10,400
7,769
269
Plan 2
Net Cash
PV €
Flow €
(using
6% pv
factor)
(2,000)
(2,000)
(1,000)
(943)
(1,000)
(890)
(1,000)
(840)
(1,500)
(1,180)
8,500
6,350
497
Discount
Factor
(10%)
1.000
0.909
0.826
0.751
0.683
0.621
Plan 2
PV €
(using
10% pv
factor)
(2,000)
(909)
(826)
(751)
(1,025)
5,279
(232)
(a) Cols. 4 and 6 give the NPVs for the plans based on 6% cost of capital. Due to the higher NPV,
Plan 2 provides the better investment opportunity for the company.
(b) The IRR for plan 2 is 8.65%, using the interpolation method as set out in (ii) above.
References.
Refer to the core texts on the syllabus. The following may be of value for additional information.
Bradley, Teresa (2008), Essential Mathematics for Economics and Business, 3rd Ed, John Wiley &
Sons, England.
Burton, Glyn., Carrol, George., Wall, Stuart (2002), Quantitative Methods for Business &
Economics, Pearson Education Ltd, England.
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