The Mathemagics of Costing Ngpes-Ed

The Mathemagics of Costing NGPES-Ed.

Part II: A Numerical Example

R. Noonan

VientianeOctober 22, 2004

A. Aim of this Paper

The aim of this paper is to illustrate with a single example the use of the GapProjector© program for estimation of the financing gap associated with an education sector development program. The example used here is estimation of the recurrent costs associated with the achievement of the NGPES target of increasing the primary school enrollment rate in the 47 poorest districts. The equations used in the GapProjector© program are given in Annex A.

B. The Scenario

All cost projections require assumptions. In the present case, the assumptions are intended to be as close to the actual situation as possible, given the limitations in the available data. The GapProjector© program is user-friendly and highly transparent. All assumptions are visible and can easily be manipulated. In the present example, the following assumptions are made.

•School age population ½(5-14) = 167,000 in 2002/2003.

•The annual population growth rate is 2.4% in 2002/03, falling to 2.3% in 2007/08.

•O&M expenditure/student = K 10,000/year.

•Administrative expenditure/student = K 10,000/year.

•Scholarship expenditure/student = K 0/year, rising to K 10,000 in 2004/05.

•Teacher salary = K 230,000/month.

•Non-teacher salary = K 230,000/month

•Pupil/Non-teaching staff ratio = 600.

•Mean class size = 24.

•Internal efficiency (inverse of repetition rate) = 60%.

•Gross enrollment 99,000 in 2002/03.

•Teachers serve on average 15 years.

The program allows the user to develop the scenario as shown in Table 1 below. In the present example, following on to NGPES of achieving 70 gross enrollment by 2006, participation rates must be increased. In the baseline case in Table 1, participation rates are held constant, and the target is not approached.
Table 2 shows the consequences of the baseline (no increase in participation rates) in terms of numbers of teachers and classes required, unit costs, etc. Table 3 shows a breakdown of the sources of the unit cost, and Table 4 shows a percent breakdown of the unit cost.
In preparing the scenario, any or all of assumptions listed above can be changed in Table 1, and the consequences are displayed in Tables 2 – 4, as shown in the table extracts below on page 6.
The program also displays a graph showing the total recurrent cost for the baseline case with the total recurrent cost for the scenario. Table 5 shows the total and cumulative incremental recurrent cost of the scenario.
The user is free to change the scenario as many times and as much as needed. In the present case, beginning with the assumptions shown above and the progressive increase in participation rates shown in the extract from Table 1, it can be seen that the total cumulative incremental recurrent cost of reaching target 70 percent enrollment in the 47 poorest districts by 2006 (actually the 2006/07 school year) is Kip 6.542 billion or about USD 600,000.
This cost estimate covers only the recurrent cost for operating the schools, including salaries, operation and maintenance, and scholarships. It does not cover the cost of textbooks because it is unclear who should bear the cost and whether textbooks should be considered a recurrent cost or an investment cost. The cost estimate given here does not include the investment costs of classroom construction or teacher training. In order to include these costs, issues of development strategy need first to be considered.

C. A Caution

The calculations given here are intended only for illustration. Although an attempt has been made to make the example as realistic as possible, the basis for the assumptions used is unreliable.
The issues concerning textbooks and teachers need to be resolved in order to provide credible estimates of the costs of reaching the NGPES targets

The estimations should be based on the concept of a “standard quality unit” (SQU) of schooling, under which every school-age child in a community has access to:

1 classroom (standard quality) +

1 teacher (standard level of qualifications) +

1 teacher’s guide (standard quality & lifetime) +

1 set of textbooks (standard quality & lifetime)

Here the user has increased participation rates in Table 1:

Here the outcomes are shown in Table 2:

Annex A: EQUATIONS

BASIC DEFINITIONS

AE=Administrative expenditure per student per year

CS=Average class size

EER=Effective Enrollment Ratio

GER=Gross Enrollment Ratio

HLS=Number of hours of learning time per week for students

HTD=Number of hours of teaching duty per week for teachers

NC=Number of classes

NER=Net Enrollment Ratio

NNT=Number of non-teaching staff

NT=Number of teachers

NTS=Average annual salary of non-teaching staff

NS=Number of students

OE=Operation and maintenance expenditure per student per year

PTR=Pupil/teacher ratio

PNTR=Pupil/non-teaching staff ratio

SE=Scholarship, stipend, grant expenditure per student per year

TS=Average annual teacher salary

UC=Unit cost

UT=Utilization of teachers

BASIC RELATIONSHIPS

CS = NC/NS(1)

PTR = CS  (HTD/HLS)  UT(2)

UT = (NC/NT)  (HLS/HTD)(3)

CALCULATING UNIT COSTS

Unit costs (UC) for any given level and kind of instruction can be seen as the following functions:

UC1 = TS/PTR + NTS/PNTR + OE + SE + AE,(4a)

or, given Equations (1) – (3),

UC2 = (TS/UT)  (HLS/HTD)  (1/CS) + NTS/PNTR + OE + SE + AE,(4b)

where

AE=Administrative expenditure per student per year

CS=Average class size

HLS=Number of hours of learning time per week for students

HTD=Number of hours of teaching duty per week for teachers