Financial Analysis and Project Selection

Chapter five

Financial analysis and project selection

Financial analysis is analytical work required to identify the critical variables which are useful for likely to determine the success or failure of an investment. Its concern is to determine, analyze and interpret all the financial consequences of an investment that might be relevant to and significant for the investment and financing decisions. This unit discusses the viability of projects from financial significance to stakeholders and to the economy in general. For this purpose different statements such as resource flow and financial statements how then are and financial analysis tools (NPV, IRR and payback period) are discussed in detail.

5.1 Purpose of financial analysis in project preparation

Investors transfer the liquid financial resources (his own personal selling or borrowed money) into production assets with the objective of producing and obtaining future benefits. This process is known as investment, along term commitment of scarce resources.

The long-term commitment by the investor needs the transformation of liquid financial resources (own or borrowed) into productive assets for financing an investment project. Project financing includes the design of proper financial structure, considering the adequacy of the financial plan, and the optimization of project financing from the different actors or beneficiaries point of view. Therefore, the scope and objective of financial analysis are to determine, analyze and interpret all the financial consequences of an investment that might be relevant for and significant for the investment and financing decisions.

Financial analysis is essentially undertaken for the following purposes:

It provides an adequate financing plan for the proposed investment
It determines the profitability of a project
It assists in planning the operation and control of the project by providing management information to both internal and external users
It advises on methods of improving the financial viability of a project entity
It illustrates the financial structure of the project and its existing and potential financial viability.

Therefore, the purpose of financial analysis is not just to document the expected impact of the project, liquidity, credit worthiness, financial efficiency, etc, of the various agents involved; it should also be part of the process of project design itself.

5.2 Methods of financial analysis

To assess financial viability of a project a range of tools and methods can be used and various types of financial statements can be prepared. This includes:

Resource flow statements
Profit and loss statements
Cash flow statements and
Balance Sheet

These statements are explained in detail below.

5.2.1 Resource Flow Statements

The starting point of the financial analysis of a project is drawing up of a statement of project cost and benefits. The benefit and cost items included in the statement should include only those items, which are incremental. The resource flow statement shows: (1) the list of resources used in the project and (2) the resources generated by the investment on the project.

The major elements of resource flow statements are:

Investment costs: investment costs cover capital expenditure items such as land, buildings, equipment and furniture etc. It includes three group of costs:
1. Initial fixed investment costs. This includes investment made for the acquisition of land, development of land for construction purpose, civil works (laying the foundation), equipment and machinery costs, installation of the machines or the plant, vehicle, furniture, building etc. All these above costs are subject to depreciation except land which is depleted over time.
2. Pre-production capital expenditure. The pre-production capital expenditure includes:

Research and development
Pre-feasibility or feasibility study cost
Training costs incurred before the commencement of the operation
Recruitment of personnel costs
Arrangement for marketing of the product such as early advertisement to inform the public in advance before the actual distribution of the product to the market
Arrangements for supplies etc.
1. Working capital. Working capital is simply a revolving fund. It is the difference between current asset and current liability. This is known as a circulating fund because at the end of the project's life it can be put as a benefit of the project. Defining the working capital requirement appropriately is important because many projects fail while they are in operation due to shortage of cash or working capital. The amount of the total working capital required depends upon the operating costs for the project.

There are three basic components of physical working and capital inventories needed for production to be continuous. These are:

Initial stock and materials
Work-in-process and
Stock of outputs

When these three components of working capital have been estimated, they can be summed to give the total working capital requirements in any year. The working capital resources that need to be included in a project statement are the incremental amount (additional commitment of resources) as the inventories build up or vary from year to year.

Table 71: Project Investment Costs ('000 Birr)

Item	Project Year
Item	1	2	3	4	5	N
Land preparation	X	X	X	X	X
Building	X	X	X	X	X
Equipment	X	X	X	X	X
Vehicles	X	X	X	X	X
Working Capital	X	X	X	X	X
Other costs	X	X	X	X	X
Total	XX	XX	XX	XX	XX	XX

Generally speaking, the amount of funds required for operating needs varies from time to time in every business. But a certain amount of assets in the form of working capital are always required; if the business has to carry out its functions efficiently and without a break. The two types of requirements are permanent (fixed) and variable.

The permanent working capital in that part of capital which is permanently locked up in the circulation of current assets and in keeping it moving. On the other hand, variable working capital changes with the volume of the output of the project.

Operating Costs/Production Costs. Operating costs can be divided into two: Fixed and Variable components. Variable working capital includes items such as materials, power, labor inputs required for manufacture which will vary directly with the volume of production while fixed costs will include maintenance, administration and managerial charges, etc. which will be relatively fixed with respect to the volume of production.

The total operating costs will then be the sum of the fixed and variable costs and will increase over the operating years until full utilization of the investment asset is reached.

Table 7.2 Project Operating Costs Schedule

No	Years Items	1	2	3	4	5	N
	Capacity Utilization Rate (%)	50%	75%	80%	85%	90%	100%
1	Raw material
2	Labor
3	Utilities
4	Repair
5	Maintenance and Repair
6	Factory Overhead
	Factory Costs (1-6) (a)	XX	XX	XX	XX	XX
7	Administrative costs
8	Sales costs
9	Distribution cost
	Operating Costs (7-9) (b)	XX	XX	XX	XX	XX
10	Depreciation (c)
11	Interest expenses (d)
	Total production
	Cost (a + b + c + d) (Bold)	XX	XX	XX	XX	XX

Note: n represents the number of periods covered in the project appraisal.

As it is shown in the above schedule, operating cost includes: cost of production/cost of sales, administrative expenses, selling expenses, depreciation on fixed assets, and write off of preliminary and preoperative expenses.

a) Cost of Production

The cost of production includes

Material cost
Wages including salaries for executives
Utilities
Repairs and maintenance
Factory over heads. These items include expenses for the factory as:
- rent, for factory, if any
- insurance premium for factory assets and factory workers
- postage, telephone, fax, e-mail, etc, in the factory
- traveling expenses
- depreciation of plant and machinery and other factory equipment;
- proportionate management expenses, which may be charged to factory on the basis of time spent by management on the project operation.

b) Administrative Expenses

This represents all indirect expenses incurred in the organization including estimates for

salaries of all indirect staff
postage, telephone, fax, e-mail etc
traveling expenses
insurance other than for the factory assets
rent, rates, taxes, electricity etc and
depreciations of all fixed assets other than factory assets other than factory fixed assets

c) Selling Expenses

This represents estimated expenses in sales divisions as per projected organizations and includes the items:

salaries and personnel cost for sales staff and managers as planned
publicity, advertisement, exhibitions, etc.
subsidies, commissions, discounts to dealers, etc.
administrative expenses of sales office including rent.

d) Depreciation

Depreciation expenses represent consumption of utility units contained in an asset. It relates to the cost center where such assets are installed.

e) Production Build Up

In the first years of operation, a project may not be 100% build up or it may not utilizes the full capacity. It build up over the years of its operation. From the technical details of the plant and machinery and the available other resources as manpower, space etc. an estimation of the plant’s installed capacity is worked out. Once the installed capacity is worked out, estimation is made about the plant’s operation achieving from the initial zero to eighty or ninety percent of the installed capacity. The peak is achieved in a span of three or four years from the start in the phase manner – like 50%, 60%, 75%, 90% of the installed capacity – estimated by year 1, 2, 3, and 4 respectively. The capacity utilization factor is included in the projects operating costs schedule.

3. Benefits

Benefits of a project can be several. For example, a range of different farm products in an agricultural project, or cost savings as well as production benefit from a transport infrastructure project. The different benefits will all be variable with respect to their associated costs, and hence, total benefits will also be variable.

Benefits can be direct (production output) which may include items like:

main product
by product
residual and other income

Benefits can also be indirect or external. For example, in a road projects reducing transportation costs, reducing operating costs for maintenance of vehicles and saving time of the society are indirect benefits of the project.

Benefits are associated with the capacity utilization factor to which operating costs were also related. When the value and timing of investment costs of and operating costs have been determined the net benefits of the project can be calculated. The net benefit is computed by simply subtracting the investment, operating and working capital costs from benefits.

The following table depicts the complete project resource statement, which brings together the investment costs, operating costs, working capital and project benefits.

Table 7.3 Project Resource Statements

No	Project Period Items	1	2	3	4	5	6
1	Land preparation
2	Buildings
3	Equipment
4	Vehicles
5	Total investment cost (1 + 2 + 3 + 4)
6	Factory costs
7	Administrative costs
8	Selling expenses
9	Depreciation
10	Total operating costs (6 + 7 + 8 + 9)
11	Incremental working capital
12	Benefits
13	Net Benefits

The net benefits are negative in the first year’s whiles investment is taking place, and become positive when the utilization of the new assets is building up.

Example on resource flow statement

Assume Zebra PLC has spent birr 75,000 on research in developing a new product. For the purpose of financial analysis, the following information has been collected:

The fixed cost that will be incurred due to the product is birr 10,000 top cover insurance and maintenance of new equipment
Advertising the new product will total birr 75,000 in first year, birr 50,000 in the second year and birr 60,000 in the third year.
The new machinery will have to be purchased at cost of birr 650,000 and depreciates for the next three years at straight line method and expected to have salvage value of birr 50,000 at the end of third year.
Sales of this product were estimated to be birr 2,000,000 in first year, birr 3,000,000 and birr 4,000,000 in third years.
Variable costs to manufacture and sell this product were estimated to be 70% of the sales in each year.
In addition to the main product, the organization gets benefit by selling by products. Birr 25,000,10,000 and 15,000 in first, second and third years respectively

prepare the resource flow of the project and give decision to accept or reject the project based on this analysis. Answer: (385,000), 660,000 and 955,000 for first, second and third respectively

5.2.2 Project Financial Statements

Financial analysis also involves formulation of various financial statements, which enable project owners and other interested stakeholders to know whether the projects worthy or not. Most commonly prepared financial statements are balance sheet, loss and profit statement, and cash flow statements.

Profit and Loss Statements

The main purpose of profit and loss or trading profit and loss account in short income statement is to calculate the profit or loss of enterprise or project. It is the measure of the profitability of the project. Firms are required by law to prepare an income statement at the end of each year to report to stakeholders on the performance and profitability of the project and at the same time it is used to calculate the tax liability to the government. Borrowers also use this income statement as the base to grant loans. An example of typical income statement is given below.

XYZ Project

Profit and Loss Statements

No	Project Period Items	1	2	3	4	5	6	n
1 2	Total sales Variable production cost
3 4 5	Gross profit (1-2) Other production costs Corporate tax
6 7	Net profit after tax (3 – (4 + 5) Dividend
8	Retained profit (6-7)

The format of the profit and loss account varies according to who is preparing it and for what purpose, and on the type of activity, be it manufacturing, retail or service projects. Gross profit is calculated by deducting direct production costs (cost of sales) from sales revenue. Net profit item (6) in the above schedule is calculated by deducting other operation costs, such as over head costs including depreciation, loan interest and corporate tax from gross profit. The last part of P/L account is the appropriation account, which shows how much of the net profit is retained to be reinvested in the project and how much is distributed to stockholders.

Balance Sheet

Balance sheet is a statement of the assets and liabilities of the enterprise and gives "the net worth" an enterprise at a point of time. It is prepared to present a picture of the firm on one day in the year. The information represents the account balances recorded and does not indicate exact economic values.

The balance sheet shows the way in which a project is financed, whether by sponsors, lenders or creditors and how these funds have be employed. The sources of funds, even where they represent the capital invested by shareholders are regarded as the liabilities of the company and the use to which funds have been put are the assets.

The Balance Sheet is the key to understanding the financial position of a project or enterprise unlike the profit and loss account, which shows how well a project has performed over a period of time; the balance sheet is a measure of what the project is worth at a particular point in time. This is done by comparing assets (what the project owns) and liabilities (what the project owes). Balance sheet is usually prepared annually for project analysis and it is considered by commercial bankers to be one of the most important statement when deciding whether or not to invest in an existing project.

Balance sheets are presented in a number of different formats. An example of a typical vertical format is shown below.

XYZ Project

Balance Sheet

On Sene 30, 1996 E.C

No	Years Items	1	2	3	4	5	6
1	Current Assets:
2	Cash
3	Inventories and supplies
4	Accounts receivables
5	Total current assets (2+3+4)
6	Fixed assets:
7	Building
8	Machinery and equipment
9	Other assets
10	Total fixed assets
	(7 + 8 + 9)
11	Accumulated depreciation
12	Net book value of assets
	(10 – 11)
13	Current liabilities:
14	Short term loan
15	Loan
16	Tax payable
17	Total current liability
	(14 + 15 + 16)
18	Networking capital
	(5 – 17)
19	Employment of funds
	(18 + 12)
20	Funds employed:
21	Owners equity
22	Retained earnings
23	Term loans
24	Total funds
	(21 + 22 + 23)

Cash flow statement

Finance is considered by many as the lifeblood of an organization or any project. A well designed project may fail due to insufficient cash for its day to day operation. Therefore, a project planner has to develop some techniques of forecasting cash in flows and out flows. Cash flow statement is a basis for showing the cash flows associated with operating resources, funding and investment.

Cash flow statements are prepared for two reasons:

First, it is prepared for financial planning purpose: in this case, the purpose is to know the liquidity position of the project. It helps project planners to identify potential periods of cash shortages and enables them to plan appropriate responses designed to remove such shortages or how to utilize excess amount of fund during the life of the project.

Secondly, cash flow statement may be prepared for the purpose of Net Present Value (NPV) and Internal Rate of Return (IRR) calculation. The purpose here is to measure the overall profitability of the project.

In general, cash flow statement is the main tool of financial planning and is sometimes referred to as the "Source and application of funds statement". An example of a typical cash flow statement is given below:

XYZ Project

Cash Flow Statement for Financial Planning ('000)

No	Years Items	1	2	3	4	5	6	n
1	Cash in flows
2	Financial sources:
3	Loans
4	Equity
5	Bank over draft
6	Supplies
7	Credit
8	Total in flow (2 + 3 + 4 + 5 + 6)	XX	XX	XX	XX	XX
9	Cash out flows:
10	Operating costs (fixed and variable)
11	Debt service (Interest plus loan repayment)
12	Corporate tax
13	Total assets
14	Dividend
15	Working capital (physical and financial)
16	Surplus or deficit (Net cash flow)
	(7 – 14)
17	Cumulative cash balance (15₁ + 15₂ + 15₃ etc)

The following schedule shows the cash flow statement prepared for NPV and IRR calculation.

XYZ Project

Cash Flow Statement for NPV and IRR Calculation

No	Years Items	1	2	3	4	5	6	7
1	Cash in flows	XX	XX	XX	XX	XX	XX	XX
2	Cash out flow: total investment outlay operating costs corporate tax total cash out flow	XX	XX	XX	XX	XX	XX	XX
3	Net cash flow (1 – 2)	XX	XX	XX	XX	XX	XX	XX
4	Present value (PV)	XX	XX	XX	XX	XX	XX	XX

Present value is the net cash flow of the project over its life subject to discounting. If you are given the discounting rate say 10%, you can calculate discounting factors and then the present value of the net cash flow of the project. Example: if the Net cash flow of the project is in its first year of operation is Br. 100,000 and discounting rate is 10%, the present value of this sum of money (at Zero period) is given by the formula:

Where:

A = Amount

r = discounting rate

PV = present value

n = number of periods for which the amount of money is discounted

(1 + r)^-n = is the discounting factor.

PV = A (1 + r)^-n

PV = 100,000 (1 + 0.1)^-1

= 100,000 (1.1)^-1 or

= 100,000

1.1

= 90909.09Br

The value of the discounting factor (1+i)^-n can be determined either using a calculator or a financial table prepared for this purpose.

The cumulative cash flow must always show a positive balance. Because, a negative amount indicates that the project has run out of cash. Cash flow statement records (cash in flow and out flow) are presented on the cash basis of accounting not on the accruals concept, hence it does not give an indication of profitability. It simply tells you the amount of cash available at any one point in time and whether it is sufficient to be able to meet commitments as they fall due. It is possible for a project to be profitable yet find itself short of cash when it is needed to meet different types of operational commitments such as interest and loan repayments. This may be because sales revenue has not been collected.

As it is shown in the above schedule, CFS can be prepared for IRR and NPV calculation purpose to see whether the project is profitable or not. If a project has a negative cash flow but is acceptable in terms of its IRR and NPV and profitable in terms of the net profit figures then there are a number of options the project analyst can consider to improve the liquidity position of the project. These are:

increase owners equity
increase long term and short term borrowing
increase credit purchases
reduce credit sales/discounts
acquire machines and equipments on a rent or lease basis than purchase
increase the grace period on loan
increase loan repayment period
reducing the amount of working capital
improve inventory management etc.

Supporting statements/schedules

To prepare the three main financial statements the following supporting schedules and additional information are required:

Depreciation schedule: it calculates the total amount of depreciation for all project assets. This balance is deducted from the net profit figures in the income statement. Therefore, in order to be able to complete the income statement the annual total depreciation charges need to be calculated. Depreciation is a means of charging the cost calculated. Depreciation is a means of charging the cost of an asset against profit over a number of years. In other words, it is a way of spreading costs over the entire life of the assets used to produce the goods/services.

There are several methods employed to calculate depreciation and the choice depends on the preferences of the project analyst and the requirements of the taxation department of the government.

Taxation: the income statement is used to calculate the project's tax liability to the government. The analyst should check for the rate (which is governed by the government), tax holidays (number of years the project may be free from paying tax) and whether or not losses from previous years can be carried foreword.
Loan repayment schedule: in this schedule the loan disbursement and loan repayment conditions should be stated and understood very well. Because, the terms of the loan will affect the benefits received by the lender and by the borrower.

5.3 Measures of project worth

Measures of project worth are measures that tell you whether a project is worth undertaking form a particular viewpoint. All such measures are concerned with the question "are the benefits greater than the costs?" There are different ways of measuring project worth, which may fall under two categories, that is discounting cash flow methods and non discounted (traditional) methods. They are briefly explained here in after.

5.3.1 Non-Discounted Measure of Project Worth

Payback period

Payback period is one of the simplest method to find out the period by which the investment on the project may be recovered from the net cash inflows, i.e., gross cash in flow less the cash outflows. In short it is defined as the period required to recover the original investment cost. Payback period starts with a preconceived notion that the management wants to recover the cost of investment within a "specific period". When the analysis under such system shows that the payback period is less than such "specified period", decision may be taken in favor of the investment for such project.

The basic drawbacks of this method of financial analysis are:

The payback period is a very crude measure of project worth because it completely ignores benefits/ cash flows after the period when the initial investment has been repaid. Hence, it would be a very unreliable means for comparing two different investments with different time profiles. It discriminates heavily against projects with a long gestation period.
It ignores the time value of money

In spite of all the drawbacks mentioned above, this method is easy to understand, quick in calculations and emphasizes in liquidity. The decision on "short term" investment can be taken based on this method of financial analysis. There are two methods in use to calculate the payback period.

Unequal cash flows: In this situation the pay back period id calculated as:

Where

E = number of years immediately preceding the year of final recovery

B = the balance amount to be recovered

C = cash flow during the final recovery

Payback period = E + B/C

Example: A company is considering investing on a particular project. The alternative projects available are: Project A that costs Br. 100,000, and Project B that Costs Br. 70,000. The net cash in flows estimates are as follows:

Net Cash Inflow

Year Project A Project B

1 30,000 7,000

2 30,000 15,000

3 35,000 20,000

4 35,000 56,000

5 40,000 45,000

Which project is good?

Solution:

Year	Project A		Project B
Year	Net cash inflow	Accumulated Net cash inflow	Net cash inflow	Accumulated Net cash inflow
1	30,000	30,000	7,000	7,000
2	30,000	60,000	15,000	22,000
3	35,000	95,000	20,000	42,000
4	35,000	130,000	56,000	98,000
5	40,000	170,000	45,000	143,000

Payback period for Project A:

Payback period

= 3 years + 5000*

35,000

= 3.14 year or 3 years and 2 months

Payback period for Project B

PP = 3 years + 28,000

56,000

= 3.5 year or 3 years and 6 months

Note: * represent the balance to be recovered from the cash inflow in period four; i.e.,

100,000 – 95,000 = 5,000

Uniform Cash flows

Where the annual cash flows are uniform, payback period can be calculated using the formula:

PP = Original Investment

Annual Cash Flows

Example: A project requires an investment of Br. 200,000. It is expected to generate an annual cash flow of Br. 50,000 per year over the life of the project. How long will it take to recover the investment?

PP = Original Investment

Annual Cash Flows

= 200,000 Br

50,000

= 4 Years

B) Benefit cost ratio (B/C)

This is a measure of efficiency and used for comparison of different projects. It is given by the formula:

B/C = Benefits

Cost of the project

N.B. This approach can also be used to calculate discounted benefits and costs.

In general, non-discounted measures of project worth can be regarded as simplified short cuts that can be used for rough approximations and decision making on small investments but they are not appropriate quick look at on a feasibility viability of the project before you go to detail analysis of the project carried out.

5.3.2 Discounted Measure of Project Worth

Before we are going to discuss discounted financial analysis techniques, let us discuss briefly the concepts of discounting and compounding.

Money is one of the basic resources of an organization that has a time value. The time delay between an outlay and its effect is the main reason for discounting and compounding future benefits and costs.

To allow for the changes in the time value of money, the terms "present value" and "future value" are used. To calculate the present value of future costs and benefits their future values are "discounted" – reduced from constant price values – back to the present using a discount rate. The concept of compounding is the opposite of discounting whereby in compounding, the present value grows to a future value because of the accumulation of interest.

Compound Interest

Compound interest can be calculated using the following formula:

Where

r = annual interest rate

t = time in years

Fv = future value

PV = present value

Future value = Present value x Compound factor

FV = PV (1 + r)^t

Example: What will be the value of Br. 100,000 deposit in an account which pays 10% interest compounded for a period of three years time?

Solution:

PV = Br. 100,000

r = 10%

t = 3 years

FV = 100,000 (1 + 0.1)³

= 100,000 (1.1)³

= 133,100 Br

This is the amount that the account accumulates after three years the difference between the original sum of money 100,000 Br. and 133,100 i.e., 33, 100 birr is the interest earned during the period.

Discounting

The discount rate is the reciprocal of the compound factor and it is given by the following formula:

PV = FV or FV (1 + r)^-t

(1 + r)t

Example: what will be the present value of the profit of Br. 100,000 generated in the third year of a project if the discount rate is 10%?

Solution: Fv = 100,000 Br. r = 10%

t = 3 years Pv = ?

PV = 100,000 (1.1)^-3

= Br. 75,000

In a net shell, when you have streams of costs and benefits (cash inflows) for a project, and you also have a measure of time preference (i.e., rate of discount) we can then discount the cost and benefit streams to arrive at their discounted value as it is shown above. This procedure is often described as "Discounted Cash Flows" or DCF.

The commonly used discounting methods are:

Net Present Value (NPV)
Internal Rate of Return (IRR) and
Benefit Cost Ratio (BCR)

These are discussed in brief below.

Net Present Value (NPV): is the net sum of total discounted benefits (cash inflows) and total discounted costs. It represents the present worth of an investment in excess of the investment itself. The NPV method is a system of finding out the excess (or short) of the present value of the earnings from the investments over and above the present value of the investment itself.

Steps to find out the NPV

Find the project costs
Find the future cash flows as estimated for the projected business, net of cash outflows
Select an appropriate rate and a period to be considered for such evaluation to find the present value of the future cash flows for the period by discounting by the selected rate
Where:

CF = Cash inflows at different periods

r = discounting rate

C₀ = cash outflow in the beginning

NPV = Net Present Value

t = time period

Find out the difference between the present value of cash inflows (net) and the investment cost (present value of investments over the life of the project).This difference represents NPV.

This calculation can be represented algebraically as:

The decision rule here is to accept a project if the NPV is positive and reject it if it is negative. A project who NPV approaching zero is a marginal project. The planner has to remodify, otherwise it will be very risk to take such projects.

Comments on the NPV Method

The NPV is easy to understand and calculate from the figures available in the project schedule.
The basic drawbacks in this method are:
- Estimation of a discounting rate, which can be very much subjective, or need to be obtained externally such as National Bank.
- The measure fails to indicate which project uses capital more efficiently or which projects are closer to the margin of acceptability.
  1. Internal Rate of Return (IRR): is defined as the discount rate the net present value is zero. IRR method finds out the rate at which – when applied on future cash inflows – the present value of such inflows taken together should equal with the present value of the cost of investment. It is called "Internal", as it is purely related to the return of the particular projected investment only. In other words it is the rate at which the project investment is just recovered. In essence it measures the efficiency of capital. To calculate IRR we can use interpolation method using the following formula:

Lower discounting rate (DR)

Difference between discount rates

IRR = + ´

As you can see in the formula, you need to have two net present values i.e., positive and negative NPVs that can be determined by the trial and error method. The higher the discount rate is the lower NPV and the lower the discount rate is the higher the NPV. Interpretation should be attempted arithmetically over a range of discount rates.

Example 1: NPV calculation

AMA company is considering to invest in a particular project. The initial investment cost is Br. 100,000. It is expected that the project may generate a benefit for 5 years as shown below:

Year Operating cost Annual cash inflow

1 Br. 100,000 --

2 6,000 Br. 20,000

3 10,000 30,000

4 2,000 40,000

5 1,000 35,000

The discounting rate is 10%

Required: Calculate the NPV

The approach is discounting the cost and revenue streams separately. This is shown as follows.

Year	Cost	Revenue (Cash in flows)	Present Value Factor	PV of Cost	PV of Revenue
0	Br. 100,000	--	1	Br. 100,000	--
1	6,000	Br. 20,000	0.9091	5,454.6	Br. 18,182
2	10,000	30,000	0.8264	8,264	24,792
3	2,000	40,000	0.7513	3,756.5	30,052
4	1,000	40,000	0.6830	1,366	27,320
5	1,000	35,000	0.6209	620.9	23,905
Total				Br. 119,462	Br. 124,251

Net present value of the project = PV of Revenue – PV of Costs

= 124,251 – 119,462

= Br. 4,789

Decision: If you are talking about only one project, the decision is to accept this project since its NPV is positive (Br. 4,789).

A project's NPV varies with the discount rate usually the higher the discount rate then the smaller the NPV. NPV method is used widely because it provides an absolute measure of the surplus generated by the project. A project is acceptable at a given discount rate if the NPV is positive.

Example 2: IRR Calculation

Using the same project data as in the example 1 above, determine the IRR? New line IRR can be estimated approximately by interpolation from a few NPV calculations. This interpolation is done mathematically. The arithmetic rule for interpolation between two discount rates, one of which gives a positive NPV and the other of which gives a negative NPV, is as follows:

IRR = Lower rate DR + Difference between ´

Where: DR = Discount rate

Using the above data, it was found that the NPV at 10% was Br. 4789. Adopting a second trial rate of discount 12%, the NPV is found to be (Br. 3201) which is negative.

Year	Cost	Revenue	Present Value Factor	PV of Cost Br.	PV of Revenue Br.
0	100,000	--	1	100,000	--
1	6,000	20,000	0.8929	5,357	18,182
2	10,000	30,000	0.7972	7,972	24,792
3	5,000	40,000	0.7118	3,559	30,052
4	2,000	40,000	0.6355	1,271	27,320
5	1,000	35,000	0.5674	567	23,905
Total				Br. 118,726	Br. 115,525

NPV at a 12% rate in 115,525 – 118,726 = (Br. 3201)

4789

4789 –(-3201)

Therefore, IRR lies between 10% and 12% using the above formula; you can calculate IRR of the project as follows:

4789

7990

IRR = 10% + (12% - 10%) ´

= 10% + 2

= 10% + 2(0.5994)

= 10 + 2(0.5994)

= 11.2%

The IRR of the project is, therefore 11.2%. If the cost of capital is less than 11.2 it can be accepted? If it is above , it should be rejected

III. Net Benefit-Cost Ratio

Net Benefit Cost Ratio (NBCR) linked to BCR. It is the ratio between NPV and initial investment

NBCR= NPV/I

Where NBCR= net benefit cost ratio

I= initial investment

NPV = net present value

Three decision rules associated with NBCR criterion are

If NBCR is greater than zero, the project is accepted.
If the NBCR is equal to zero, the firm is indifferent to the project.
If the NBCR is less than zero, the project is rejected.

Example: Consider the two mutually exclusive projects X and Y with the following cash flow streams. The cost of capital for both the projects is 14%.

Year Project X Project Y

Cash PVIF Present Cash PVIF Present

Flow @14% value Flow @14% value

0 -155, 000 - 48,000

1 38,000 0.877 33,326 13,500 0.877 11,839.5

2. 44,000 0.769 33,836 14,700 0.769 11,304.

3. 49,000 0.675 33,075 17,300 0.675 11,677.5

4. 54,500 0.592 32,264 18,800 0.592 11,129.6

5. 60,000 0.519 31,140 20,500 0.519 10,639.5

163,641 56,590.4

The NBCR of both the projects is calculated as follows:

Project X = Present Value / Initial Investment

= 163641/155000 = 1.05575

Project Y = Present Value / Initial Investment

= 56590.4/48000 = 1.17896

Though the NBCR of both the projects is more than 1, Project Y should be accepted as it has a higher BCR than Project X.

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Project Analysis Chapter Five.doc

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Financial Analysis and Project Selection

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