Package {fpoValue}

fpoValue: Farmer Producer Organisation Economics and Member Benefit Accounting

Description

Tools to assess when collective marketing, aggregation, grading and bulk procurement through a farmer producer organisation (FPO) improve member-farmer returns.

Details

* [transaction_costs()] - per-farmer transaction costs of a marketing channel. * [aggregation_savings()] - scale economies from consolidated transport, bulk input purchase and grading. * [member_benefit()] - member-level distributional accounting that separates total FPO surplus from benefits received by farmers. * [break_even_volume()] - throughput, membership and procurement price needed for the FPO to break even. * [collective_marketing_scenarios()] - comparison of individual and collective marketing channels for the same members.

Quantities may be in any unit (for example quintals or tonnes) and prices and costs in currency per the same unit, provided they are used consistently.

Author(s)

Maintainer: Anbukkani Perumal anbueconomic@gmail.com [copyright holder]

Scale economies from aggregation

Description

Estimates the gross savings an FPO can generate by aggregating members' produce and purchases, from three sources:

Transport consolidation

Without the FPO, each member carries produce to the market in small vehicles. With the FPO, members carry produce to a nearby collection centre and the FPO moves the pooled volume in large vehicles. Trip-based costs make the per-unit cost of both legs depend on the quantity carried.

Bulk input procurement

A tiered discount schedule is applied to each member's own input purchase and to the pooled purchase.

Grading

Selling sorted grades instead of an ungraded lot earns a price premium per unit equal to the grade-weighted price minus the ungraded price, less any grading cost.

Savings are reported in total, per unit and per member. Transport savings are member-specific; the bulk leg is allocated in proportion to quantity, as are grading premiums. These are *potential* savings: whether members receive them depends on the FPO's pricing and dividend policy, which [member_benefit()] evaluates.

Usage

aggregation_savings(
  quantity,
  distance_market,
  distance_centre = 0,
  centre_to_market = NULL,
  small_capacity = 1,
  small_cost_per_km = 0,
  small_fixed_trip = 0,
  bulk_capacity = 10,
  bulk_cost_per_km = 0,
  bulk_fixed_trip = 0,
  input_quantity = 0,
  input_price = 0,
  discount_tiers = NULL,
  grade_shares = NULL,
  grade_prices = NULL,
  ungraded_price = NULL,
  grading_cost = 0
)

Arguments

Value

A list of class 'aggregation_savings' with 'by_source' (total and per-unit savings for transport, inputs and grading), 'by_member' (savings per member) and 'total'.

Examples

q <- c(4, 8, 15, 25, 60)
aggregation_savings(q, distance_market = 30, distance_centre = 3,
                    centre_to_market = 30, small_capacity = 5,
                    small_cost_per_km = 20, bulk_capacity = 100,
                    bulk_cost_per_km = 45,
                    input_quantity = c(2, 3, 5, 8, 20), input_price = 1300,
                    discount_tiers = data.frame(min_quantity = c(10, 30),
                                                discount = c(0.03, 0.06)),
                    grade_shares = c(0.5, 0.3, 0.2),
                    grade_prices = c(2000, 1600, 1100),
                    ungraded_price = 1550, grading_cost = 30)

Break-even throughput, membership and procurement price

Description

Finds the volume an FPO must handle to cover its fixed costs (and an optional surplus target) given the per-unit margin between its sale price and the price it pays members:

Q^{*} = \frac{F + T - M_{inputs}}{p^{sale} - p^{m} - h},

where F is fixed cost, T the surplus target and M_{inputs} the margin from the input business. It also reports the number of members needed at the average member volume, the margin of safety at the current volume, and the highest member price the FPO can pay at the current volume while breaking even, which bounds how much of the aggregation gain can be passed to farmers through prices.

Usage

break_even_volume(
  fixed_cost,
  sale_price,
  member_price,
  handling_cost = 0,
  input_margin = 0,
  target_surplus = 0,
  avg_member_volume = NULL,
  current_volume = NULL
)

Arguments

Details

All arguments are vectorised and recycled, so a grid of scenarios can be evaluated in one call.

Value

A data frame of class 'break_even_volume' with the inputs and 'unit_margin', 'break_even_volume', 'members_needed', 'margin_of_safety' (share by which current volume exceeds break-even) and 'max_member_price' (at the current volume). Break-even volume is 'Inf' when the unit margin is not positive and the costs are not already covered.

Examples

break_even_volume(fixed_cost = 6e5, sale_price = 1650,
                  member_price = c(1450, 1500, 1550),
                  handling_cost = 60, input_margin = 1e5,
                  avg_member_volume = 15, current_volume = 6000)

Compare individual and collective marketing scenarios

Description

Evaluates the same set of members under alternative marketing channels, for example individual sale to a village trader, individual sale in a wholesale market, FPO aggregation, FPO aggregation with grading, and an FPO contract with a processor or retailer. Each scenario is described by one row of 'scenarios':

scenario

Name.

member_price

Price received by members.

member_cost

Members' transaction cost per unit.

sale_price

Price realised by the FPO; 'NA' for individual channels.

handling_cost, fixed_cost, dividend_share

Optional FPO parameters (default 0).

Member net return is q_i(p^m - c^m) + D_i. For FPO channels the FPO surplus and patronage dividends are computed as in [member_benefit()]. Each scenario is compared with the 'baseline' scenario: the gain in members' net returns, the FPO's retained surplus, the total value created relative to the baseline, the member share of that value, the share of members better off, and the gain received by the smallest half of suppliers.

Usage

collective_marketing_scenarios(
  quantity,
  scenarios,
  baseline = NULL,
  group = NULL
)

Arguments

Value

A list of class 'collective_marketing_scenarios' with 'summary' (one row per scenario), 'member_returns' (matrix of member net returns, members by scenarios) and, if 'group' is given, 'group_gain' (gain per member by group and scenario). A 'plot()' method compares member gains and retained surplus across scenarios.

Examples

q <- c(5, 8, 12, 20, 35, 60)
sc <- data.frame(
  scenario = c("village trader", "mandi", "FPO pooled", "FPO graded"),
  member_price = c(1300, 1450, 1480, 1540),
  member_cost = c(10, 140, 40, 55),
  sale_price = c(NA, NA, 1650, 1760),
  handling_cost = c(0, 0, 60, 90),
  fixed_cost = c(0, 0, 8000, 12000),
  dividend_share = c(0, 0, 0.5, 0.5))
res <- collective_marketing_scenarios(q, sc,
         group = c("marginal", "marginal", "small", "small",
                   "medium", "large"))
res
plot(res)

Member-level distributional accounting of FPO benefits

Description

Separates the total surplus generated by a farmer producer organisation (FPO) from the benefits actually received by member farmers.

Usage

member_benefit(
  quantity,
  outside_price,
  member_price,
  sale_price,
  outside_cost = 0,
  member_cost = 0,
  handling_cost = 0,
  fixed_cost = 0,
  input_quantity = 0,
  input_market_price = 0,
  input_member_price = 0,
  input_bulk_price = 0,
  dividend_share = 0,
  dividend_rule = c("patronage", "equity", "equal"),
  equity = NULL,
  group = NULL,
  member_id = NULL
)

Arguments

Details

**FPO account.** The FPO buys members' produce at 'member_price', sells it at 'sale_price', incurs handling costs per unit and fixed operating costs, and may run an input business buying at 'input_bulk_price' and selling to members at 'input_member_price'. Its net surplus is

S = \sum_i q_i (p^{sale} - p^{m}_i - h) + \sum_i x_i (w^{m} - w^{bulk}) - F.

A share 'dividend_share' of positive surplus is distributed as dividends; the rest is retained.

**Member account.** Relative to the member's outside option (selling individually at 'outside_price' with transaction cost 'outside_cost' and buying inputs at 'input_market_price'), member i gains

B_i = q_i (p^m_i - p^{out}_i) + q_i (c^{out}_i - c^m_i) + x_i (w^{mkt} - w^{m}) + D_i.

**Value created** is \sum_i (B_i - D_i) + S, which equals \sum_i B_i plus retained surplus. The member share of value created shows how much of the FPO's economic contribution actually reaches farmers. Distribution across members is summarised by the Gini coefficient of benefits (when all benefits are non-negative), the concentration index of benefits ranked by quantity marketed (positive values mean benefits are concentrated among larger suppliers), the benefit share of the smallest half of suppliers compared with their quantity share, the share of members made worse off, and, if 'group' is given, benefit shares and benefit per member by group (for example marginal, small, medium and large farmers).

Per-member arguments accept a scalar or one value per member. Per-unit transaction costs can be taken from [transaction_costs()].

Value

A list of class 'member_benefit' with

members

Data frame of benefit components per member: 'price_gain', 'cost_saving', 'input_saving', 'dividend' and 'total'.

fpo

Named vector: output margin, input margin, fixed cost, net surplus, dividends paid and retained surplus.

value

Named vector: value created, total member benefit, retained surplus, member share of value created, member benefit per unit marketed.

distribution

List with 'metrics' and 'by_group'.

Examples

q <- c(5, 8, 12, 20, 35, 60)
size <- c("marginal", "marginal", "small", "small", "medium", "large")
mb <- member_benefit(q, outside_price = 1400, member_price = 1480,
                     sale_price = 1650, outside_cost = 140,
                     member_cost = 40, handling_cost = 60,
                     fixed_cost = 8000, input_quantity = q / 5,
                     input_market_price = 1350, input_member_price = 1300,
                     input_bulk_price = 1250, dividend_share = 0.5,
                     group = size)
mb
mb$distribution$by_group

Plot collective marketing scenarios

Description

Stacked bars of the gain in member net returns and the FPO's retained surplus, relative to the baseline, for each scenario.

Usage

## S3 method for class 'collective_marketing_scenarios'
plot(x, ...)

Arguments

Value

'x', invisibly.

Examples

sc <- data.frame(scenario = c("individual", "FPO"),
                 member_price = c(1400, 1480), member_cost = c(120, 40),
                 sale_price = c(NA, 1650), handling_cost = c(0, 60),
                 fixed_cost = c(0, 5000), dividend_share = c(0, 0.5))
plot(collective_marketing_scenarios(c(5, 10, 20, 40), sc))

Transaction costs of a marketing channel

Description

Computes, for each farmer, the full cost of selling through one marketing channel. Transport is trip-based, so costs per unit fall with the quantity carried per trip:

transport_i = trips_i \times (2\,d_i\,c_{km} + c_{trip}),\quad trips_i = \lceil q_i / capacity \rceil.

Other components are commission (a share of sale value), market fees and handling charges per unit, the opportunity cost of the farmer's time per trip, the value of produce rejected or unsold, and the interest cost of delayed payment.

Usage

transaction_costs(
  quantity,
  price,
  distance,
  vehicle_capacity = 1,
  cost_per_km = 0,
  fixed_per_trip = 0,
  commission = 0,
  market_fee = 0,
  handling = 0,
  time_hours = 0,
  wage = 0,
  rejection = 0,
  payment_delay = 0,
  interest_rate = 0.12,
  label = NULL
)

Arguments

Details

Call the function once for each channel (for example individual sale in a wholesale market and delivery to an FPO collection centre) and pass the resulting 'per_unit' costs to [member_benefit()] or [collective_marketing_scenarios()].

Value

A data frame of class 'transaction_costs' with one row per farmer: 'quantity', 'trips', 'transport', 'commission', 'fees', 'handling', 'time_cost', 'rejection_cost', 'delay_cost', 'total', 'per_unit' and 'share_of_value'.

Examples

q <- c(5, 12, 30, 80)
mandi <- transaction_costs(q, price = 1500, distance = 35,
                           vehicle_capacity = 10, cost_per_km = 25,
                           commission = 0.06, market_fee = 15,
                           time_hours = 8, wage = 50,
                           payment_delay = 7, label = "mandi")
centre <- transaction_costs(q, price = 1500, distance = 4,
                            vehicle_capacity = 10, cost_per_km = 25,
                            time_hours = 1.5, wage = 50,
                            payment_delay = 10, label = "FPO centre")
data.frame(quantity = q, mandi = mandi$per_unit,
           centre = centre$per_unit)