PART 2: CALCULATIONS PERFORMED BY WINDASI

Investments
Plan, zones and projects
Project indicators
Normal versus phased modes of calculation

In Part 1 we looked at how to organize and enter data and how to obtain results for a project using WinDASI. In this section we consider how to carry out some precise calculations for four topics, using concrete examples. The four topics are:

· Investments
· Plans, Zones and Projects
· Project indicators
· Normal and Phased Modes

Investments

Investment items are characteristic of investment projects. WinDASI has technical facilities that allow you to carry out special calculations for each investment item.

These calculations are explained in Box 1.

Box 1
Examples of Investment items

A farmer is going to purchase a new small tractor in the first year of the project. The characteristics of the tractor are:
Investment							Tractor
Life duration (years)							7
Lag in operation and maintenance (years)							1
Operation and maintenance (%)							15
Physical contingencies (%)							5
Residual value (%)							10
Price of the tractor ($)							5 000
WinDASI carries out calculations as follows:
Investment	Years
	1	2	3	4	5-7	8		9	10-12	13
Tractor	5 000	-	-	-	-	5 000		-	-	-
Unexpected costs	250	-	-	-	-	250		-	-	-
Maintenance	-	750	750	750	750	-		750	750	750
Residual value	-	-	-	-	-	-500		-	-	-1 785
Total investment cost	5 250	750	750	750	750	4 750		750	750	-1 035
Note: The above values are computed in the following way: · Tractor: this line contains the cost of the investment in year 1, i.e., when the tractor is purchased. In year 8 the tractor is replaced after 7 years of use (note that WinDASI automatically replaces the tractor). · Unexpected costs: the physical/price contingency of 250 is computed at 5% of the purchase cost of the tractor and it is included in the year that the tractor was purchased. This item allows you to include additional costs when there are price increases, unforeseen costs or underestimation of the investment. · Maintenance: the maintenance cost of 750 is computed at 15% of the purchase cost of 5 000. It is repeated each year starting from year 2, since the "Lag in operation and maintenance" is 1 year. · Residual value: this takes into account the value of the tractor at the end of its life (year 8) and at the end of the project life (year 13). The value of - 500 in year 8, computed at 10% of the purchase cost, is the estimated revenue produced by the sale of the old tractor at the time of its replacement (the negative sign indicates that they are inflows rather than costs). The value of - 1 785 takes into account the fact that at the end of the project (year 13) the tractor, purchased in year 8, has only been used for 5 years. Therefore, after 7 years, there is a residual value of 500 that has to be increased for the remaining 2 years of useful life. The software uses the following formula: Y = Rv + (Pv-Rv) * Rl/L where: Y = residual value at the end of the project Rv = residual value at the end of the investment life Pv = is the purchase value Rl = is the remaining life of the investment at the end of the project in years L = is the life duration of the investment in years The formula when applied to the tractor is thus: 500 + (5 000 - 500) * 2/7 = 1 785 The above calculations are carried out for investment items contained in Plans, Zones and Projects that contain investment items. If you wish to obtain a similar table using WinDASI, you can ask for "investments" and "values" (see Section 4.1 in Part 1). Note that the investment items of a project need not necessarily be placed under the Investments category. For example, if you have a time series of investment costs for which no life duration, maintenance costs or residual values are specified, you may include these investment costs as normal inputs of the project. WinDASI will include these costs among the project costs and all the indicators of the project will thus be correctly calculated.

Plan, zones and projects

As mentioned in Part 1, WinDASI carries out calculations at the Plan, Zone and Project levels.

In mathematical terms, a Plan is a linear combination of activities and investments; a Zone is a linear combination of Plans and Investments; and a Project is a linear combination of Zones and Investments. Thus we have:

P = a₁A₁ + a₂A₂ + ... + a_nA_n ... + b₁I₁ + b₂I₂ +... b_mI_m

where:

P	is the value of a Plan;
a1, a2, ... an....	are the coefficients specifying the number of units of each activity in the plan;
A1, A2, ... An....	are the activities specified in the data base;
I1, I2, ... In ....	are the investments items defined in the database; and
b1, b2, ... bm ....	are the coefficients specifying the number of units of each investment in the plan

We shall use a practical example (Box 2) to illustrate this concept.

Box 2
Main calculations performed in a plan

A farmer with 20 ha of land wants to shift from a wheat-based to a maize-based cultivation pattern. Let us use WinDASI to calculate the quantities and values of inputs and outputs over a 13-year period. Step 1: The project data have to be organized to match WinDASI requirements.
Name			Commodity prices
			Unit			Unit price ($)
Labour			days			0.8
Other inputs			$			1.0
Maize			tons			50
Wheat			tons			70
Note: (1) Prices here are considered constant throughout the project life
Activities Activity 1: Maize growing Unit 1 ha
		WoP	Year
			1	2	3	4	5	6-13
Labour (days)		30	35	35	35	35	35	35
Other inputs ($)		5	10	15	20	30	30	30
Yield (maize, tons)		07	0.9	1.1	1.3	1.5	1.5	1.5
Activities Activity 2: Wheat growing Unit 1 ha
		WoP	Year
			1	2	3	4	5	6-13
Labour (days)		45	50	50	50	50	50	50
Other inputs ($)		7	10	20	20	20	20	20
Yield (wheat, tons)		0.7	0.8	0.9	1.0	1.1	1.1	1.1
Plans Plan 1: One farmer Unit Farm
	WoP		Year
			1	2	3	4	5-13
A Wheat (ha)	15		10	5	2	2	2
A Maize (ha)	5		10	15	18	18	18
Step 2: Insert data according to the instructions given in Part 1. Step 3: Run WinDASI calculations for the Plan "One farmer," and try to obtain the quantities of inputs and outputs produced/consumed. To calculate total quantities of required labour, WinDASI takes the number of required labour days per hectare of maize or wheat, year by year (from the "Activity" data), and multiplies this by the number of hectares under each crop, year by year (from the "Plan" data), as shown below.
	WoP		Years
			1	2	3	4	5-13
1. Labour used
Maize	30 x 5		35 x 10	35 x 15	35 x 18	35 x 18	35 x 18
Wheat	45 x 15		50 x 10	50 x 5	50 x 2	50 x 2	50 x 2
Total	825		850	775	735	735	735
2. Other inputs consumed
Maize	5 x 5		10 x 10	15 x 15	20 x 18	30 x 18	30 x 18
Wheat	7 x 15		10 x 10	20 x 5	20 x 2	20 x 2	20 x 2
Total	130		200	325	580	580	580
3. Maize production
Maize	0.7 x 5		0.9 x 10	1.1 x 15	1.3 x 18	1.5 x 18	1.5 x 18
Total	3.5		9	16.5	23.4	27	27
4. Wheat production
Wheat	0.7 x 15		0.8 x 10	0.9 x 5	1.0 x 2	1.1 x 2	1.1 x 2
Total	10.5		8	4.5	2	2.2	2.2
Similarly, for the same plan you may calculate the Values of Commodities produced and consumed. WinDASI calculates the values of commodities produced and consumed by taking the total quantities you have just calculated and then multiplying by the appropriate prices (from the "Commodity" data). In this way, the total costs and benefits of the project are obtained year by year, as shown here below.
Costs	WoP	1	2	3	4-7	8	9-12	13
1) Labour	825 x 0.8	850 x 0.8	775 x 0.8	735 x 0.8	735 x 0.8	735 x 0.8	735 x 0.8	735 x 0.8
	660	680	620	588	588	588	588	588
2) Other inputs	130 x 1	200 x 1	325 x 1	400 x 1	580 x 1	580 x 1	580 x 1	580 x 1
	130	200	325	400	580	580	580	580
3) Total inputs	790	880	945	988	1 168	1 168	1 168	1 168
Production value
4) Maize	3.5 x 50	9 x 50	16.5 x 50	23.4 x 50	27 x 50	27 x 50	27 x 50	27 x 50
	175	450	825	1 170	1 350	1 350	1 350	1 350
	10.5 x 70	8 x 70	4.5 x 70	2 x 70	2.2 x 70	2.2 x 70	2.2 x 70	2.2 x 70
	735	560	315	140	154	154	154	154
6) Total production	910	1 010	1 140	1 310	1 504	1 504	1 504	1 504
7) Balance	910 - 790 = 120	1 010 - 880 = 130	1 140 - 945 = 205	1 310 - 998 = 312	1 504 - 1 168 = 336	1 504 - 1 168 = 336	1 504 - 1 168 = 336	1 504 - 1 168 = 336

Project indicators

(i) Project Life
(ii) Incremental Net Benefits
(iii) Cumulative Values
(iv) Net Present Value
(v) Switching Values
(vi) Switching Value Calculation
(vii) Comparing project alternatives: with-project versus without-project situations

After having computed total inputs consumed and outputs produced and related values for a Plan, Zone or Project, you can also get the related project indicators, namely:

· time series of costs and benefits;
· Net Benefits
· incremental Net Benefits; and
· Cumulative values.

(i) Project Life

Some of the most frequently used project indicators depend on the life of a project. WinDASI calculates all projects for a maximum duration of 30 years. However, you can choose to use a shorter project life if you so wish. Remember that the shorter the lifetime of a project, the smaller the project indicators, such as IRR, Cost/Benefit Ratio, Total Present Value, etc.

(ii) Incremental Net Benefits

While the Net Benefits are the difference between benefits and costs, the Incremental Net Benefits are the Net Benefits due to the project, i.e. the Net Benefits of the "with" project (WiP) situation minus the Net Benefits of the "without" project (WoP) situation. When it is assumed that the WoP situation is constant, the WoP is shown in the first column of each table. Later on, we will discuss how to analyse a project for which the WoP situation cannot be assumed constant. These Incremental Net Benefit values form the basis on which all the other indicators are built.

(iii) Cumulative Values

While the meaning and the economic interpretation of the Net Benefits and Incremental Benefits are evident, the flow of Cumulative Values are computed using the following formula:

C_t = C_t-1 + A_t

where:

Ct	Cumulative Value of year t; and
At	Incremental Net Benefit of year t.

These values are used in order to see how long it takes to recover project investments. Usually they are negative at the beginning of the project, when the investments are made, and they become positive when the investment costs are fully recovered. The cumulative value of the last year of the project is the total net benefit of the project.

(iv) Net Present Value

When you ask for the Net Present Value, you must specify the discount rate to be used in order to calculate the present values. If the rate is set at zero, you will obtain the same project indicators computed till now. The greater the discount rate used, the smaller the net present values of project benefit and the longer the recovery period for investments. If the cumulative values of a project remain always negative, it means that the project has a negative Total Present Value and is incapable of paying for the investments made.

WinDASI provides, for each year: Present Values, cumulative values of Net Project Benefits and Incremental Net Project Benefits.

(v) Switching Values

Under the heading "Project Indicators", WinDASI also calculates Switching Values, the IRR, the Benefit/Cost Ratio and the Total Present Value, which are the most common indicators used to measure a project's financial and economic profitability.

In this respect it is useful to remember some important points:

1. Financial indicators are obtained by selecting Financial prices in the calculation windows and economic indicators by selecting Economic prices, which should be entered in the commodities window.

2. All these indicators depend on project duration; by default WinDASI will use a project life of 30 years; if you wish to use a shorter project life you should enter the exact number of years in the Calculation Window.

3. Total Present Values, Benefit/Cost Ratio and Switching Values depend on the Discount Rate, and the larger the discount rate, the less favourable the indicators.

(vi) Switching Value Calculation

The switching value is computed as follows:

SW_i = (TPV/PV_i) × 100

where:

SWi	is the Switching Value (percentage) of the variable "i"
TPV	is the Total Net Present Value of the project
PVi	is the Net Present Value of the variable "i"

This formula is derived directly from the definition: "The Switching Value is the percentage of change of a cost or benefit that makes the Total Net Present Value equal to zero," as follows:

TPV - PV_i × k = 0

Where:

k	is a coefficient equal to SWi when multiplied by 100.

(vii) Comparing project alternatives: with-project versus without-project situations

A major objective of financial and economic analysis of a project is to investigate the profitability of a given investment scenario and, hopefully, to identify the "best" project alternative.

Without-project situation (WoP)

This process is achieved through a systematic comparison of project scenarios. The most important scenario to be analysed is the WoP situation, i.e. the situation that you would expect to happen in the project area if the project is not implemented. This scenario will then be taken as a basis for comparing all other project alternatives and, in general, when we talk about incremental costs or benefits, we are referring to the differences in costs and benefits between a given scenario and the WoP situation.

In many cases, the WoP situation is assumed to be constant over the project life and, for this reason, WinDASI offers the facility of introducing the related data in the first cell or column of the project data, just before the first year of the project. WinDASI then uses these data for computing the incremental values and the project indicators.

However, in certain cases, it is not possible to assume that a WoP situation is constant overtime, particularly in certain types of environmental projects where the situation is clearly deteriorating and the major objective of the project is to prevent the costs resulting from falling productivity of resources.

In this case, there is no possibility of using the WinDASI built-in facility for the WoP situation and you will have to build a specific scenario for the WoP situation, and a distinct scenario for each project alternative. The cells and columns reserved for the WoP situation will be set at zero.

Two ways of comparing WoP and WiP situations

In order to compare the WoP and WiP scenarios, you have the two possibilities below, the second one being easier to carry out.

1. In the same WinDASI file, insert data for Activities, Plans and Zones for both the WoP and WiP situations. You can then subtract the Plan, Zone or Project) of the WoP situation from the corresponding Plan Zone or Project of the WiP situation. The results will be the incremental costs and benefits due to the project.

2. Create a project data file for each scenario and use a spreadsheet to make the comparison. You can start with the WoP situation, define the Commodities, Activities, Plans and Zones, and compute the expected costs and benefits. By using the previous data file as a basis, you can build a project scenario describing the WiP situation, for which you can compute the related costs and benefits. The comparison between the various possible project scenarios of the WoP situation will be carried out in a second stage, using a spreadsheet.

Normal versus phased modes of calculation

WinDASI allows you to calculate total production and consumption in two different ways: either Normal or Phased.

Normal mode

The Normal Mode assumes a uniform build-up of the activities, etc. contained in a plan, and was the method used for the calculation illustrated in Box 2.

Phased mode

The Phased Mode of calculation allows for:

· different groups of farmers entering the project in different years. Those who enter the project in Year 1 will have different yields by Year 3 from those who enter the project in Year 3; and

· starting perennial activities like tree plantations, livestock production, etc., in different years of the project. Thus animals, trees, etc., can be introduced gradually into the project.

Where the Phased Mode is required, the letter C is placed in the first column and the level of the activity (or other plan component) is given in incremental terms, such as additional hectares planted for a perennial crop, or the new number of farmers joining a project each year.

Two examples showing the different calculations performed by WinDASI - according to whether Normal or Phased Mode is being used - are given below, in Boxes 3 and 4.

Box 3
Comparing Normal and Phased Mode of Calculation

Comparing two variants of a project, where:
	Variant 1: Normal mode - 100 farmers join the project in Year 1
	Variant 2: Phased mode:
		- 50 farmers join the project in Year 1;
		- 30 farmers join the project in Year 2; and
		- 20 farmers join the project in Year 3.
The expected build-up of yield of rice production per farm is given below.
Rice production per farm
			WoP	1		2		3		4				5-10
Rice/yield (ton)			5	6		7		8		9				9			9
Area planted (ha)			10	10		10		10		10				10			10
Total production			50	60		70		80		90				90			90
Plan for Variant 1: Normal Mode Plan: Total production. Unit: Project area
			WoP	1		2		3		4				5-10
N Rice farm			100	100		100		100		100				100			100
The computer will then perform the following calculation (to calculate total quantities of rice produced):
			WoP	1		2		3			4			5-10
Yield x farms			50x100	60x100		70x100		80x100			90x100			90x100			90x100
Total			5 000	6 000		7 000		8 000			9 000			9 000			9 000
Plan for Variant 2: Phased Mode Plan: Total production. Unit: Project area
			WoP	1		2		3				4			5-10
C Rice farm			0	50		30		20				0			0			0
Note that in the above Plan, data is entered in terms of incremental levels (new farmers joining the project), and therefore the total number of farmers undertaking the activity "production of rice" will be 100 from Year 3 onwards, as in normal mode. The computer will then perform the following calculations:
Table 1. Total production of rice using the Phased Mode
Group			WoP		1		2		3				4			5			6-10
Group 1 (50 farms)			50x50		50x60		50x70		50x80				50x90			50x90			50x90
Group 2 (30 farms)			30x50		30x50		30x60		30x70				30x0			30x90			30x90
Group 3 (20 farms)			20x50		20x50		20x50		20x60				20x70			20x80			20x90
Total			5 000		5 500		6 300		7 300				8 300			8 800			9 000
To understand the calculations performed by WinDASI when the Phased Mode is used, it may help if you imagine the farmers divided into three groups: · Group 1 enters the project in Year 1; · Group 2 enters the project in Year 2; and · Group 3 enters the project in Year 3. Each group continues to produce the output of the WoP situation until it joins the project (the first year each group joins the project is highlighted in Table 1 above). The build-up of yields affects the three groups in different years, according to when they entered the project. It is worth noting that full production is reached earlier when using the Normal Mode of calculation, and the increase in total production is smoother (more gradual) when using the Phased Mode.

Box 4
Milk production (Phased Mode)

Analysing a plan for a small livestock farm over a period of 14 years (Phased Mode) The first step in the analysis is to define the inputs required and the production of milk per cow.
Activity: Cows. Unit: 1-Cow
		C/P	1		2			3		4		5		6			7-14
Feed		C	2		2.2			2.5		2.5		2.5		2.5			0
Milk		P	800		1 000			1 500		2 000		2 000		2 000			0
Note that feed consumption and milk production are defined for each year for which the cow is kept by the farmer (Year 1 is the first year after the cow has been purchased and Year 6 is the last year before the cow is sold). Three cows are to be introduced in the first year of the project, and two in the second year. Each cow is kept for 6 years, and then sold and replaced by another. The Plan for the farm will have to use the Phased Mode of calculation (since Feed requirements and Milk output for each cow varies according to when the cow was purchased).
Plan: Small farmers
		0	1	2	3	4		5	6	7	8	9	10		11	12		13		14
Cows		-	3	2	-	-		-	-	3	2	-	-		-	-		3		2
Note: The plan has coefficients in Years 7, 8, 13 and 14 because we wish to replace the cows that will have been sold. The table below shows the details of the calculations for milk production. Each line refers to a new group of cows introduced into the project in the year specified at the beginning of the row.
Production of milk by small-scale farmers
	0		1	2	3		4	5	6	7	8	9	10	11		12		13	14
1	3x0		3x800	3x1000	3x1500		3x2000	3x2000	3x2000	3x0	3x0	3x0	3x0	3x0		3x0		3x0	3x0
2	2x0		2x0	2x300	2x1000		2x1500	2x3000	2x2000	2x2000	2x0	2x0	2x0	2x0		2x0		2x0	2x0
7	3x0		3x0	3x0	3x0		3x0	3x0	30	3x800	3x1000	3x1500	3x2000	3x2000		3x2000		3x0	3x0
8	2x0		2x0	2x0	2x0		2x0	2x0	2x0	2x0	2x800	2x1000	2x1500	2x2000		2x2000		2x2000	2x0
13	3x0		3x0	3x0	3x0		3x0	3x0	3x0	3x0	3x0	3x0	3x0	3x0		3x0		3x800	3x1000
14	2x0		2x0	2x0	2x0		2x0	2x0	2x0	2x0	2x0	2x0	2x0	2x0		2x0		2x0	2x800
Total	0		2400	4600	6500		9000	10000	10000	6400	4600	6500	9000	10000		10000		6400	4600
The table above shows the results of the calculation for milk production. Each line refers to a new group of cows introduced into the project in the Year specified in the first column.