1. INVESTMENT CRITERIA
A major problem of CBA is selecting an appropriate investment criterion in order to make the best decision given the scarcity of resources. The main criteria used in decision making include;
The Net present value (NPV) that’s the discounted approach
Benefit – Cost Ratio
Internal Rates of Return
Pay Back Period
Domestic Resource Cost

2. Time 1 2 3 4 5 6 B-C Project A -100 50 80 100 150 -50 380 Project B
THE NET PRESENT VALUE
Consider the following projects; two Projects , A and B
Time 1 2 3 4 5 6
B-C
Project A
-100 50 80
100
150
-50
380
Project B
-20

3. NPV CONTS.
 TIME
Time is really important in making decision on project choice. From the table, the distribution of revenue (benefit) over time is different for the 2 projects. The idea of net present value (NPV) is therefore to try to expresses all future values in terms of the present. That is, to make the values occurring at different times comparable at least with respect to the present time.
The basic notion of the NPV approach is that present consumption yields more satisfaction than the same amount of future consumption. We must therefore convert all future values into the present by discounting the future stream of income for a given stream of incomes.

4. Where r is the discount rate.
The formulae for the discounting process is:
(Bo-Co)+(B1-C1)/(1+ r) + (B2-C2)/(1+r)2 +….+ (Bn-Cn)/(1 + r)n
That is NPV =
Where r is the discount rate

5. NPV CONTS.
The most important issue in this criterion is the choice of the appropriate discount rate. More importantly the discount rate must reflect the society time preference values; that is, today’s amount paid in the future year. Assuming that the values of the project above are discount at a discount rate of 10% the results would be as follows;

6. Time 1 2 3 4 5 6
B-C
Project A
-100
45.4
66.1
75.1
102.5
93.2
-28.2
254.1
Project B
90.9
82.6
68.3
62.1
-11.3
267.3

7. NPV CONTS. Using NPV approach B would be selected.
The NPV criteria can be used in 3 different situations;
In decision concerning a single project
In the ranking of multiple projects
Decision relating to mutually exclusive projects
Decision relating to a single project falls within the accept or reject context. Where we accept a project when NPV is positive (NPV>0) reject when NPV is negative that’s (NPV<0) and when NPV = 0 indifferent
Ranking of projects
The NPV can also be used in ranking projects; where in this case the project with the highest NPV is ranked 1st and the others follows; supposing 3 projects XYZ with the ff benefits and cost.

8. Project
GPV(C)
GPV(B)
NPV
B/C X
100
200 2 Y 50
110 60
2.2 Z
120 70
2.4

9. NPV CONTS.
The NPV can also be used in the ranking or projects, from the data above and by using NPV the projects would be ranked as XYZ. However, given the differences in cost, Project X may not necessarily by the best.
By considering the benefit cost-ratio approach, project Z is more beneficial followed by Y and X. Supposing the initial cost for the project is ¢100 million to spend. It would be better to consider the implementation of the projects Y and Z when considering the initial cost. It implies it is better to have a combination of projects than to have a single project with a higher NPV.
The implication is that, in making decisions regarding single projects and using NPV, one may make inefficient decisions. It is better to rather have combination of projects.

10. NPV CONTS. MUTUALLY EXCLUSIVE PROJECTS
Two projects A and B are usually exclusive if accepting to invest into project A strictly implies rejecting project B and vice versa. But the problem in using NPV concerning mutually exclusive projects is the problem of comparability since they might not be of the same scale and may have difficult initial cost. In order to make them comparable, the said projects are normalized. For example, if the cost of A is ¢100m and the benefit is ¢180m then NPV equals ¢80m project B on the other hand cost ¢50m with a benefit of ¢95m then on the basis of NPV and being mutually exclusive we accept project A and reject project. But the question of comparability arises.

11. Cost A ≠ Cost B
Cost of project A = 2 (Cost of project B)
¢100m = 2 (¢50)m
Benefit A ≠ benefit B
¢180 = ¢2(95)
¢180m = ¢190m

12. INTERNAL RATE OF RETURN (IRR)
The internal rate of return of a given project may be defined as that rate of discount which reduces the NPV of the future stream of income generated by the project to zero. It is calculated by equating the discounted value of the net benefits from the projects to the initial capital outlay and solving the resultant equation rate for the discount rate r*

13. IRR =

14. The decision rule is that if the generated discount rate from the project (r*) is greater than the predetermined rate i.e.
If r* < r we reject the project
If r*> r we accept the project
If r* = r we are indifferent
Use the formulate below to calculate the r*

15. r*=[rh- (rh-r1)] NPVh/(NPVh + NPV1)]

16. where rh is the higher discount rate
r1 is the lower discount rate
NPVh is the absolute value of the NPV associated with the higher discount rare or absolute value of the negative NPV
NPV1 is the NPV for the lower discount rate

17. PROBLEMS OF USING THE NPV AND THE IRR
Both assume complete information over the entire life of the project which may not be so in the real world.
Both may exist in markets where conditions are prefect but in real world existence of monopoly and price control for example results in imperfect markets.
These approaches assume there are no uncertainties among project which is in untrue in the real world
IRR if the discount rate varies from one period to the other there is obviously no single discount rate which can be compared to the value of the r*
IRR is sensitive to the economic life and scale of the project. That is the IRR tends to over estimate the value of benefits for short term projects but projects with longer gestation periods tends to suffer when the IRR is used.

18. THE PAY BACK PERIOD
This is the period over which the initial investments of the project could be recouped. Usually, an arbitrary pay back limit or times is set and the project is selected if the difference between the sum of the NPV and initial cost of the investment turns positive before that period.
That is, when :

19. ∑NPV – C0 > 0

20. Consider the table that follows:

21. Time 1 2 3 4
NPV -
100
200
400
500 Co
1000
NPV-Co
-1000
-900
-700
-300

22. From the data above if the arbitrary pay back period is set at 2 years then the project would not be implemented. In effect, this criterion discounts returns after the Pay back period to existing values of time. If net benefits occur after the pay back period, they are regarded as windfall gains and if net cost occurs after the pay back period it is simply hope that, they would not affect the initial investment outlay.
The main problem of using this criterion is that
It may create the tending of opting for projects with short life span since it is possible to recover the initial cost of investment within that period.
The use of the pay back period approach may be inconsistent with objective of maximizing NPV over the entrée life span of the project. It is however often useful in areas where benefits can be recovered within the shortest possible time and using the capital outlay for another project.

23. BALANCE OF PAYMENT CONSIDERATION
Resource allocations implied in project allocation some time have BOP effects. From the point of view of developing continues, foreign exchange is always a scarce resource and for those matter BOP effects of allocation decision has to be incorporated into the investment criteria.
This may be done by upgrading foreign exchange generated by projects and adding the opportunity cost of implies of the project. Where the opportunity cost of imports satisfying the requirement of the projects may be calculated as the amount of exports that would have to be shipped abroad to meet the additional imports. For example if it may cost ¢600 million terms of export to impact a ¢500 with of requirement, then the opportunity cost of the import is the ¢600.
A formal approach of analyzing the BOP implication of the project the brow test or the Domestic Resource Cost Ratio (DRCR) where the domestic resource cost of a project is the domestic cost of a dollar of foreign exchange generated or saved by the project.

24. The application f this term yields an own foreign exchange for the project when compared with the market determined exchange rate may lead to the selection of rejection of the project.
There are 3 types of domestic resources cost analysis
The immediate impact analysis which is based on current price and an single period operation only.
Future impact analysis where we make use of discounted values.
Limited use approach which is concerned with projects that produce fully traded and nearly fully traded goods.
CALCULATING THE DIRECT RESOURCE COST (DRC)
In calculating DRC the following information are necessary;
The cost insurance freight (c.i.f.) price of a amount of the product expressed in foreign exchange.
The foreign exchange cost incurred in purchasing the output domestically (the cost of input imports)
The domestic cost of the output that’s the cost of local inputs
The opportunity cost of capita

25. Output (Tones) $/T Gross $
Poultry feed ,600
Livestock feed ,360
$594,960

26. From the above analysis it will cost the give economy $594,960 to import both poultry and livestock feed should we decide to produce this product locally, the ff would be the cost

27. Imported materials $
Soya bean oil 39,900
Feed meal 35,500
Mineral premix 3,500
Vitamin premix 9,400
Others 9,500
94,300
Contingency (10%) 9430
$103,730

28. it would cost the given economy $103,730 to import inputs for this final product. The difference of $491,230 is termed the foreign exchange saved by the project or the New Foreign Exchange Savings.

29. Local material
Maize 226,000
Oyster shells ,000
Groundnut cake 322,000
Brain 10,580
Common salt
Labour and overhead
Labour cost ,900
Packaging 1,150
Insurance and Handling
Utilities (H20, health, phone)
Admins & selling
Maintenance, depreciation
Interest
¢569,280

30. Total Domestic Cost (TDC)= 569,280
Domestic Cost ratio= TDC/ Total foreign Exchange saving
DCR= 589,258/ 491,230
=1.158
Compare this own generated exchange rate with the market exchange rate

31. Decision rule
If market exchange rate E*> E (Project exchange rate) accept the project
If market exchange rate E*< E (Project exchange rate) reject the project