Example 10.1. Leastcost analysis
Two alternative onsite sanitation systems (A and B) are to be considered. The discount rate is taken to be 10%, the shadow exchange factor (SEF) for imported goods is 1.3, the shadow wage rate (SWR) for labour is 0.6, and the institutional and promotional costs are 30% of the initial capital cost. All costs are in dollars.
System A costs $ 71.80 at the initial construction stage and $ 10 for the use of a vacuum tanker every 5 years. The anticipated life of the system is 20 years. Note: the effects of inflation may be ignored.


Materials 
Labour 


Cost 
SEF 
Shadow cost 
Cost 
SWR 
Shadow cost 
Costs of pit: 
excavation 



5.00 
0.6 
3.00 

lining 
 bricks 
15.50 

15.50 





 cement 
5.00 
1.3 
6.50 




construction 



2.00 
0.6 
1.20 
Costs of slab: 
cement 
10.00 
1.3 
13.00 




steel reinforcing bar 
3.00 
1.3 
3.90 




aggregate 
0.50 

0.50 




construction 



2.00 
0.6 
1.20 


34.00 

39.40 
9.00 

5.40 
Total economic cost 
44.80 
Cost of superstructure (calculated in a similar manner) 
27.00 
Subtotal 
71.80 
Cost of institutional support and sanitation promotion (at 30%) 
21.50 
Total economic investment cost 
93.30 
System B costs $ 55 for pit, slab and superstructure at the initial stage, with the same amount for a new pit and superstructure after 10 years, at the end of the original design life.
Total economic cost 
55.00 
Total economic investment cost 
71.50 
(calculated in a similar manner to System A above) 

Leastcost analysis
System A 


System B 
Costs (a) 
Discounted costs (a) × DF 
Year 
Discount factor DF 
Costs (b) 
Discounted costs (b) × DF 
93.30 
84.80 
1 
0.909 
71.50 
65.00 
10.00 
6.20 
5 
0.621 


10.00 
3.90 
10 
0.386 
55.00 
21.20 
10.00 
2.40 
15 
0.239 


123.30 
97.30 (present value) 


126.50 
86.20 (present value) 
By leastcost analysis, the present value of system B is slightly less than the present value of system A. However, the difference is not enough to allow one system to be chosen in preference to the other on economic grounds alone.
Example 10.2. Total annual cost per household
The total annual cost per household (TACH) is determined by multiplying the present value of each system by the capital recovery factor (CRF). Using the formula given in the text, and at an interest rate of 10% over 20 years, CRF = 0.118.
From the figures calculated in Example 10.1:
System A 
System B 
Present value = $ 97.30 
Present value = $ 86.20 
TACH 
= 97.30 × 0.118 
TACH 
= 86.20 × 0.118 

= $ 11.50 per household per year 

= $ 10.20 per household per year 
Example 10.3. Financial and affordability analysis
Using the figures given in Example 10.1 for system A, it is assumed that the householder is contributing time to excavate the pit and to construct the slab and superstructure.

Financial costs to be paid by household 

$ 

Labour 
0.00 
(given by household) 
Bricks 
15.50 

Cement 
5.00 


10.00 

Steel 
3.00 

Aggregate 
0.00 
(collected by household) 
Total 
33.50 

Superstructure 
14.50 
(assumes household labour contribution of 12.50) 
Total 
48.00 

Determination of repayments
Assuming a subsidized interest rate of 5% with the loan to be paid off over two years:
Capital recovery factor 
= 0.538 
Annual loan repayments 
= 0.538 × $ 48.00 

= $ 25.80 
Check on affordability: annual average household income estimated for this example as $ 380.
_{}
This would normally be too high for a household to pay, so repayments over four years at a subsidized rate of interest of 3% should be considered:
Capital recovery factor 
= 0.270 
Annual repayments 
= 0.270 × $ 48.00 

= $ 13.00 
_{}
This may be acceptable, depending upon the cost of living, and repayments would be completed before the first pitemptying cost is incurred. As an alternative to subsidizing the rate of interest, it might be possible to sell the latrine slab at a reduced cost. It would be unwise to sell the cement or steel at reduced cost because of the dangers of the materials being used for other purposes. Another alternative is to encourage the use of different building materials to reduce the cost of the superstructure.
Affordability with loan at full rate of interest, repayable over 4 years, slab sold at half price and reduced cost superstructure:

Financial costs to be paid by household 

$ 

Labour 
0.00 

Bricks 
15.50 

Cement 
5.00 

Cement 
as half price slab 
6.50 

Steel 



Aggregate 
0.00 

Total 
27.00 

Superstructure 
9.50 
(reducedcost design) 
Total 
36.50 

Capital recovery factor 
= 0.315 
Annual loan repayments 
= 0.315 × $ 36.50 

= $ 11.50 
_{}
Determination of subsidy
With subsidized rate of interest: assuming a real interest rate of 10%, capital recovery factor = 0.315 for four years. Without subsidy, annual repayments would be $ 15.10. With a subsidized rate of interest of 3%, subsidy = $2.10 annually for four years in addition to the institutional and promotional costs paid by the agency of approximately $ 22.
With subsidized slab cost: the subsidy represents half the cost of a householder making a slab. Therefore the agency has to pay labour charges as well as half the material costs. Subsidy = $ 2.00, labour and materials = $ 6.50, total subsidy = $ 8.50, in addition to the institutional and promotional costs.