Capital investment appraisal - part 2
by Samuel O Idowu
01 Sep 2000
In Capital Investment Appraisal 1, a second article, was promised which would look at projects with unequal lives, taxation and the impact of inflation. Students at this stage of their studies should be aware that
questions in this area would not always be straightforward.
This second article intends to focus on some of these complications which may be introduced into capital investment appraisal questions. It is hoped that by working through the author;s approach in the following
example, students will learn the techniques required in tackling questions of this sort and be able to apply them in an examination environment.
Before looking at the example, let us say a word or two about them.
Unequal life projects
When considering possible investment projects, it is often the case that competing projects are not of the same life span. For example, an organisation may have to choose between two projects in which project A might have a useful life of, say, five years whilst another competing project, B may have a useful life of seven years. To simply compare the net present values of the two projects without looking at the unequal life span will not be comparing like with like. Under normal circumstances
project B will have a higher net present value, as it has the opportunity of generating cash for two additional years. To recommend undertaking project B solely, on the basis of the higher net present value may not be based on a sound reason. This is because there is a possibility that
the net cash inflow generated from project A at the end of its five-year
life could be reinvested elsewhere for the two equivalent additional years generating additional NPV which may total more than project B;s
NPV. This fact is often ignored as only the net present values of projects at the end of their respective lives are compared.
What needs to be done is to express the two projects in equal terms. If
two or more unequal life projects being considered had the same level
of risk, then it will be appropriate to use the Equivalent Annual Cost
to compare net Approach also known as Annual Equivalent Annuity Method
present values of costs on an annualised basis. If the projects had different levels of risk then the appropriate approach will be to assume
Infinite Re-investment for each project and calculate their net present values to infinity.
These two approaches will now be examined in detail.
The equivalent annual cost (EAC) approach
This approach computes the present value of costs for each project over a cycle and then expresses the present value in an annual equivalent cost using the appropriate annuity factors for each cycle. The annual equivalent of NPVs of the two or more projects can then be compared. Having
calculated the EAC for each cycle and each project, then compare the EACs. The project that has the lowest EAC over the cycles is the better one if lowest outlay is the objective or the higher EAC would be preferred if the highest revenue were the objective.
Infinite re-investment approach
This approach is appropriate when projects of unequal lives and unequal risks are being considered. The first step to take will be to establish the net present value of the projects in the normal way and then calculate
the net present value of projects to infinity using the formula:
NPV µ = NPV of project/PV of annuity for the life of project at discount rate
Discount rate for the project
The project, which has the highest NPV to infinity, is the one to recommend.
Project appraisal under inflation
Inflation is a state of affairs under which prices are constantly rising. When this happens the purchasing power of money depreciates. The currency will buy fewer goods and services than previously and consequently the real returns on investments will fall. Investors understandably, will expect to be compensated for the fall in the value of money during inflation. When appraising investment opportunities the appraiser requires an understanding of three discount rates. These are Money Rates,
Real Rates and Inflation Rates. Money rate (also known as Nominal rate) is a combination of the real rate and inflation rate and should be used to discount money cash flows. If on the other hand you were given real cash flows these must be discounted using the real discount rates. In order to be able to use either of these two rates, you need to know how to calculate both of them. They can be calculated from the following formula, devised by Fisher
1 + m = (1 + r) x (1 + i)
m = money rate
r = real rate
i = inflation rate
From the above formula it is possible to calculate m, r and i if you were given information about two of the three variables. For example if you were told that the money rate was 20% and real rate was 12% the inflation
rate will be calculated as follows:
i = 1 + m ; 1
1 + r
i = 1 + 0.20 ; 1
1 + 0.12
i = 1.0714 ; 1
Equally m and r could be calculated as follows.
m = (1.12 x 1.0714) ; 1
(1.19999) ; 1
r = 1.20 ; 1
When the appropriate discount rate has been established the present value
factors of this rate at different time periods can be obtained from the present value table or the present value factors calculated using the following formula:
1 1 1 1 1
(1+r) (1+r)2 (1+r)3 (1+r)4 (1+r)5 ;etc
Where r = discount rate.
Present value tables are only available for whole numbers, so if your r is not a whole number you will have to use the formula to calculate the required present value factors. Let us calculate for example the present value factors of 7.14% for years 1 to 5.
1 1 1 1 1
(1.0714) (1.0714) 2 (1.0714) 3 (1.0714) 4 (1.0714)5 ;etc
0.933 0.871 0.813 0.759 0.708
Having either obtained or calculated the present value factors for the relevant discount rates, these are then used to discount the future cash flows to give the net present values of the projects. It is important to understand when to use which rate. If the question gives you money cash flows, then use the money rate; if the question gives real cash flow it follows then that the real rate must be used. To confuse one with the other would give the wrong answer.
Effects of taxation on project appraisal
Investment in capital assets has taxation implications, which should be included in the analysis. To ignore the effect of taxation could affect the quality of the decision, which is consequently made about an investment opportunity. If the resulting project from the appraisal is profitable then taxation becomes payable on these profits thus reducing the net cash inflows by the amounts of tax payable. Capital allowances
are given by the Inland Revenue at about 25% on a reducing balance basis over the life of the project. Capital allowances reduce the amount of tax which becomes payable. If the project has a terminal value at the end of its useful life, it will be necessary to establish whether this gives rise to a balancing allowance or a balancing charge. Net cash inflows are used in pay back, net present value and Internal rate of return methods. If the entity will not be in a tax-paying position during the entire life
the project then it is known as tax exhausted and tax can be ignored of
but this situation is most unlikely to occur.
Now that we have looked at these possible areas of complication let us look at a fictitious company we shall call Samco Plc.
Samco Plc is a manufacturer of electric drills. The company has
just developed two new models of electric drills. Model 1 is called Automatic and model 2 is called Super. Senior managers have resolved that if production were to commence in making the automatic model, 200,000 drills per annum will be produced and
sold over the next five years at a price of ?200 per drill, whereas if production were to commence with the super model, 150,000 drills per annum will be sold over the next seven years at a price of ?140 per drill. Budgeted operating costs of each
of the two models at today;s prices are as stated below:
Automatic model ?
Direct material 70
Direct Labour 20
Fixed production overhead
Selling, Distribution etc 20
Net Cash inflow per unit = (?200 ; ?140) = ?60
Super model ?
Direct material 20
Direct labour 12
Variable overhead 15
Fixed production overhead
Selling, distribution, etc.
Net Cash inflow per unit = (?140 ; 70) = ?70
An extension will be required to the existing property for production to commence at a cost of ?20m if the automatic model was the preferred choice. If the super model was the preferred option then the extension will only cost ?17m. Corporation tax is paid at 30%. Shareholders of Samco Plc expect a money rate of return of 15.5% per annum after tax from projects similar to the automatic model but 20% for projects similar to the super model. Inflation is expected to be at 5% per annum for the next seven years. Operating cash flows for the purposes of the above information can be assumed to take place at year-ends. There
is a one year delay in the payment of taxation to the tax authorities.
Your task is to use the net present value method to justify which of the two models Samco Plc should undertake having taken in to consideration all available information. You are told that
the two projects are mutually exclusive.
The following approach should be taken.
Net Cash inflow before Taxation
but with Inflation allowance
?200 ; ?140 = (?60 x 1 = ?12.60m
200,000) x 1.05
2 ?12.60m x 1.05 = ?13.23m
3 ?13.23m x 1.05 = ?13.89m
4 ?13.89m x 1.05 = ?14.59m
5 ?14.59m x 1.05 = ?15.32m
1 25% x ?20m ?5m
2 75% x ?5m ?3.75m
3 75% x ?3.75m ?2.81m
4 75% x ?2.81m ?2.11m
5 Balancing Allowance
= ?6.33m (?20m ; ?13.67m) Year Net Cash Inflow Capital Allowance Taxable Profit Tax @ 30%
1 ?12.60m ?7.6m ?2.28m
2 ?13.23m ?3.75m ?9.48m ?2.84m
3 ?13.89m ?2.81m ?11.08m
4 ?14.59m ?2.11m ?12.48m
5 ?15.32m ?6.33m ?8.99m ?2.70m Cash
Year 0 1 2 3 4 5 6 Extensi (20) on
Operati 12.6 13.23 13.89 14.59 15.32 ng CFs
Taxatio 2.28 2.84 3.32 3.74 2.70 ; n
Net O. (20) 12.6 10.95 11.05 11.27 11.58 (2.70) CFs
factors 1 0.866 0.750 0.650 0.562 0.487 0.421 @ 15.5%
(20) 10.91 8.21 7.18 6.33 5.64 (1.14) Net
t Value =
?70 = = 1 (?70 x ?11.03m
?11.03m = 2 x 1.05 ?11.58m
?11.58m = 3 x 1.05 ?12.16m
?12.16m = 4 x 1.05 ?12.77m
?12.77m = 5 x 1.05 ?13.41m
?13.41m = 6 x 1.05 ?14.08m
?14.08m = 7 x 1.05 ?14.78m Capita
Allowanc Year es
25% x 1 ?4.25m ?17m
75% x 2 ?3.19m ?4.25m
75% x 3 ?2.39m ?3.19m
75% x 4 ?1.79m ?2.39m
5 75% x ?1.34m
75% x 6 ?1.01m ?1.34m
g 7 allowanc
(?17m ; = ?3.03m
profit and tax
Capital Net cash Taxable Year allowancTax @ 30% inflow profit e
1 ?11.03m ?4.25m ?6.78m ?2.03m
2 ?11.68m ?3.19m ?8.39m ?2.52m
3 ?12.16m ?2.39m ?9.77m ?2.93m
4 ?12.77m ?1.79m ?10.98m ?3.29m
5 ?13.41m ?1.34m ?12.07m ?3.62m
6 ?14.08m ?1.01m ?13.07m ?3.92m
7 ?14.78m ?3.03m 11.75m ?3.53m Cash
Year 0 1 2 3 4 5 6 7 8
atin 11.03 11.58 12.16 12.77 13.41 14.08 14.78
Taxa 2.03 2.52 2.93 3.29 3.62 3.92 3.53
O. (17) 11.03 9.55 9.64 9.84 10.12 10.46 10.86 (3.53)
fact1 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 ors @
PVs (17) 9.19 6.63 5.58 4.74 4.07 3.50 3.03 (0.82)
Now that we have established the Net Present Values of the two projects, it will be wrong of us to just compare the NPVs and conclude that merely because the super model has a higher NPV than the automatic model then it is the better of the two projects. This may well be the case, but we will not know this for certain until we have expressed the net present values of the two projects to infinity. This is because the two projects have unequal lives and different levels of risk. Let us now calculate their present values to infinity so that we can be in a better position to recommend the more appropriate one to the Board of Samco plc. Net present value to infinity
= NPV of the project/PV of annuity of appropriate years and NPV µ rate