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UNIT 7 METHOD OF PROJECT EVALUATION
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3.0 MAIN CONTENT 3.1 Payback Period
In this method, one should choose the projects which can repay the amount invested within a chosen number of years e.g. below are the returns from two enterprises.
S/N CROP LIVESTOCK
1.
2.
3.
4.
5 Total
3000 3000 4000 2000 1000 13000
3000 3000 3000 3000 3000 15000
If N10000 is invested in each enterprise in year 0, and we take three years payback period, crop will be chosen enterprise while in five years payback, livestock will be chosen enterprise.
3.2 Peak-Period Method
It is a guide to the average profitability of a project.
S/N CROP LIVESTOCK
1.
2.
3.
4.
5 Total
3000 3000 4000 2000 1000 13000
3000 3000 3000 3000 3000 15000
The level of profit in the best year is expressed as a rate of return on the sum invested e.g. the best year in the above table is the 3rd i.e.
4000/10000 = 40% and any of the years for livestock i.e. 3000/10000 = 30%.
3.3 Average Profit Method
The methods consider profit over the whole period of project life and expresses it as a rate of return on invested capital e.g. in the example above, profitability for crop = N3000 and N5000 for livestock.
S/N CROP LIVESTOCK
1.
2.
3000 3000
3000 3000
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3.
4.
5 Total
4000 2000 1000 13000
3000 3000 3000 15000
The average profit for crop = N3000/5 and N5000/5 for livestock.
3.4 Inadequacy of the Methods
These methods are faulty in that they did not consider the time value of money. They assume N1 today is equivalent to N1 next year or in three years time. This is wrong in that N1 today is worth more than N1 next year. However, discounting method overcomes these shortcomings.
THE DISCOUNTING METHOD: Here, the future is taken care of, the method considers all returns over the life span of the project in their present value (PV) i.e. what returns expected from the project in future are worth today.
PV = future nominal value (1 + r)n
Where r = interest rate and it is expressed as a percentage
PV = (future nominal value) (discount factor). Discount factor may be found in calculation tables. These concepts are better than the methods earlier treated in that discounting is embedded in them. Concepts to be calculated under the method include:
a. NPV = Net present value b. IRR = Internal rate of return c. BCR = Benefit cost ratio
NPV of a project is the value today of the surplus that the firm makes over and above what it could make by investing as its marginal rate.
n
t r
Ct NPV Bt
1 (1 )
Bt = benefit in each project year Ct = Cost in each project year n = number of years
r = interest (discount) rate t = individual project year
IRR of a project is the interest rate of return, which is the rate that is being earned on capital.
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0
) 1
1 (
n
t r
Ct NPV Bt
IRR
Bt = benefit in each project year Ct = Cost in each project year n = number of years
r = interest (discount) rate t = individual project year
BCR of a project is the total discounted benefit divided by total discounted cost.
n
t r
BCR Bt
1 (1 )
n
t r
Ct
1 (1 )
3. 5 Investment Decision Criteria
(a) IRR - A project should be undertaken if the IRR is above the interest rate charge by the bank.
(b) NPV - A project should be undertaken if the NPV is positive.
(c) BCR - A project should be undertaken if the BCR is greater than 1. If it is equal to 1, it may be considered if there is wide unemployment but when it is below 1, it is batter to save the money at the prevalent interest rate than to invest. Profit as mentioned in the above scenario is not used in an accounting sense but a net flow of funds i.e. all revenues from the sale minus all costs including initial investment that took place. The scrap value of equipment should be added to the last year of project life and no deduction should be made for depreciation as it is entered for by the internal rate of return (IRR).
3.6 Calculation of NPV, BCR, IRR
To estimate NPV and BCR, a discount rate must be given. This is usually related to the interest rate operating in the open market e.g. If the current interest rate in Nigeria is about 15%, the discount factor (DCF) at 15% is used.
Table showing, cash flow and analysis for mixed farming
Yea r
Cost s
Reven ue
Increment al benefit
Discou nt factor at 15%
Discou nt costs
Discou nt revenu e
NP V at 15
%
1. 5000 2000 -2800 0.876 4350 1914
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2.
3.
4.
5
4000 3000 2000 2000
5000 4500 3500 4000
1000 1500 1500 2000
0.756 0.658 0.572 0.497
3024 1974 1144 994 11,486
3780 2961 2002 1988 12,645
243 6 756 987 858 994 1,15 9 From the calculations, NPV = N1159 i.e. summation of the discounted benefits.
t Discount
venue Discountre
BCR cos
486 , 11
645 ,
12
= 1.10
IRR is obtained by trial and error in that different discount factors are tried until one obtains a value where the NPV is zero or near zero.
Year Discount factors at 30%
NPV at 30%
Discount factors at 40%
NPV at 40%
1.
2.
3.
4.
5.
0.769 0.592 0.455 0.350 0.269
-2153.2 592.0 682.5 525.0 538.0 184.3
0.714 0.510 0.364 0.260 0.186
-199.2 510.0 546.0 390.0 372.0 -18.12 This table shows that IRR lies between 30% and 40%. Precisely IRR can be worked out by this formula
(DRN DRP)
DVP DVN
DRP DVP
IRR
(Absolute value) i.e. (40 30)
5 . 365
3 .
30184
= 30 + (0.504) (10) = 35.04%
IRR can be obtained as accurately as possible through the use of a computer programme. The IRR is compared with the cost of capital in order to arrive at an investment decision e.g. if the current interest rate is
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15% and the farm can earn 35% rate of returns, it means that project is very profitable i.e. for every N1 invested, investor will receive N1.35.
After paying 15kobo on the Naira to the lender, in this case which is the bank, he will be better off by 20 kobo.
If the analyst wants to prepare a feasibility study for the bank, in addition to estimating all measures of project valuation described earlier, a financial plan is also prepared. This is sets out in detail, the amount of equity capital, loan capital, income as well as its sources, loan repayment schedule, the use to which loan will be put and what the overall cash flow for the investment period will look like. Usually, bank gives a moratorium (grace period) of a year especially year 0 when return may not be forthcoming for some projects. This year, the borrower pays only interest on the loan while principal is to be paid as from the second year.
SELF-ASSESSMENT EXERCISE Briefly discuss the following:
i. The payback period ii. Peak profit method
iii. The average profit method iv. The discounting method.
4.0 CONCLUSION
You have learnt about the payback period, peak profit method, the average profit method, the discounting method and their inefficiencies.
5.0 SUMMARY
In this unit, you have learnt that:
A project should be undertaken if the IRR is above the interest rate charge by the bank.
A project should be undertaken if the NPV is positive.
A project should be undertaken if the BCR is greater than 1. If it is equal to 1, it may be considered if there is wide unemployment but when it is below 1, it is batter to save the money at the prevalent interest rate than to invest.
6.0 TUTOR-MARKED ASSIGNMENT
1. What is the discounting method trying to do?2. What is moratorium?
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7.0 REFERENCES/FURTHER READING
Reddy, S. S. & Ram, P.R. (2004). Agricultural Finance and Management. New Delhi. Oxford & IBH Publishing Co. PVT.
LTD.
Pandey, I. M. (2002). Financial Management. (8th ed.). New Delhi:
Vikas.
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