# Evaluation of Public Alternatives¶

## Example 10.1 Page 138¶

In :
#initiation of variable
Ii=4000000.0;#in Rs.
AM=150000.0;#in Rs.
AFS=600000.0;#in Rs.
Einc=50000.0;#in Rs.
i=12.0;#in % per annum
n=15.0;#in years

#calculation
Cp=AM*(((1+i/100)**n)-1)/((i/100)*(1+i/100)**n);#in Rs
TPW=Ii+Cp;#in RS

#result
print "Total present worth of costs in RS. : ",round(TPW,3);

#Total present worth of fuel savings:
AI=600000.0;#in Rs.
G=50000.0;#in Rs.
i=12.0;#in % per annum
n=15.0;#in years

#calculation
A=AI+G*(((1+i/100)**n)-i*n/100-1)/(((i/100)*(1+i/100)**n)-i/100);#in RS
Bp=A*(((1+i/100)**n)-1)/((i/100)*(1+i/100)**n);#in Rs.
BCratio=Bp/(Ii+Cp);#unitless

#result
print "Present worth of fuel savings in Rs. : ",round(Bp,3);
print "BCratio : ",round(BCratio,3);
print"Since BC ratio is more than 1, the construction of the bridge across the river is justified.";

Total present worth of costs in RS. :  5021629.673
Present worth of fuel savings in Rs. :  5782527.265
BCratio :  1.152
Since BC ratio is more than 1, the construction of the bridge across the river is justified.


## Example 10.2 Page 139¶

In :
#initiation of variable
Ic=80000000.0;#in Rs.
Aps=6000000.0;#in Rs.
Afs=3000000.0;#in Rs.
Aib=5000000.0;#in Rs.
Arb=2000000.0;#in Rs.
Amc=3000000.0;#in Rs.
i=12.0;#in % per annum
n=50.0;#in years

#calculation
TAB=Afs+Aib+Arb;#in Rs.
PW_B=TAB*(((1+i/100)**n)-1)/((i/100)*(1+i/100)**n);#in Rs

#result
print "Total present worth of benefits in RS. : ",round(PW_B,3);

#Present worth of costs:
PW_C=Ic+Amc*(((1+i/100)**n)-1)/((i/100)*(1+i/100)**n)-Aps*(((1+i/100)**n)-1)/((i/100)*(1+i/100)**n);#in RS
BCratio=PW_B/PW_C;#unitless

#result
print "Present worth of costs in Rs. : ",round(PW_C,3);
print "BCratio : ",round(BCratio,3);
print "Since BC ratio is more than 1, the state govt. can implement the hydroelectric project.";

Total present worth of benefits in RS. :  83044984.884
Present worth of costs in Rs. :  55086504.535
BCratio :  1.508
Since BC ratio is more than 1, the state govt. can implement the hydroelectric project.


### Example 10.3 Page 140¶

In :
#initiation of variable
#alternative 1
P=3000000.0;#in Rs.
B=900000.0;#in Rs.
i=10.0;#in % per annum
n=5.0;#in years

#calculation
AE1=P*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);#in Rs
BCratio=B/AE1;#unitless

#result
print "Annual equivalent of initial cost in Rs. : ",round(AE1,3);
print "BCratio : ",round(BCratio,3);

#Alternative A2 :
P=6000000.0;#in Rs.
B=1500000.0;#in Rs.
i=10.0;#in % per annum
n=7.0;#in years

#calculation
AE2=P*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);#in Rs
BCratio=B/AE2;#unitless

#result
print "Annual equivalent of initial cost in Rs. : ",round(AE2,3);
print "BCratio : ",round(BCratio,3);
print "The benefit cost ratio of alternative 2 is more than that of alternative A1. Hence, alternative A2 is to be selected. The comparisoon is made on a 35 years period which is the minimum common multiple of the lives of alternative 1 and 2";

Annual equivalent of initial cost in Rs. :  791392.442
BCratio :  1.137
Annual equivalent of initial cost in Rs. :  1232432.998
BCratio :  1.217
The benefit cost ratio of alternative 2 is more than that of alternative A1. Hence, alternative A2 is to be selected. The comparisoon is made on a 35 years period which is the minimum common multiple of the lives of alternative 1 and 2


## Example 10.4 Page 141¶

In :
#initiation of variable
#cost of the state
n=20.0;#in years
P=2500000000.0;#in Rs.
Agt=10000000.0;#in Rs.
Ai=1000000.0;#in Rs.
Com=48000.0;#in Rs./year/employee
C1=Com*300;#in Rs.
i=10.0;#in % per annum

#calculation
C2=P*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);#in Rs
CA=C2+C1;#in Rs

#result
print "Annual equivalent initial cost in Rs. : ",round(C2,3);
print "Total Annual equivalent cost of the project in Rs. : ",round(CA,3);

#Benefit to the state :
W=30000000.0;#in Rs.
A1=W*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);#in Rs.
Agpy=10000000.0;#in ton/year
A2=Agpy*(30-10);#in Rs.
AvgAI=1000000.0;#in tons Km.
G=20000000.0;#in Rs.

#calculation
A3=A2+G*(((1+i/100)**n)-i*n/100-1)/(((i/100)*(1+i/100)**n)-i/100) ;#in Rs.
BA=A1+A3;#in Rs
BCratio=BA/CA;#unitless
print "Annual equivalent average of transport cost saving in Rs. : ",round(A3,3);
print "Total annual equivalent benefits to the state : ",round(BA,3);
print "BCratio : ",round(BCratio,3);
print "The benefit cost ratio is more than 1,the project is justified.";

Annual equivalent initial cost in Rs. :  293649061.931
Total Annual equivalent cost of the project in Rs. :  308049061.931
Annual equivalent average of transport cost saving in Rs. :  330161500.91
Total annual equivalent benefits to the state :  333685289.653
BCratio :  1.083
The benefit cost ratio is more than 1,the project is justified.


## Example 10.5 Page 143¶

In :
#initiation of variable
#project A
i=9.0;#% per annum
n=50.0;#in years
P_A=150000000.0;#in RS.
Fcs_A=2500000;#in Rs.
Ib_A=3500000;#in Rs.
Rb_A=1000000;#in RS.
OMC_A=2000000.0;#in Rs.
Psy_A=10000000.0;#in Rs.

#calculation
AE_A=P_A*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);
Cpy_A=AE_A+OMC_A-Psy_A;#in Rs.
Bpy_A=Fcs_A+Ib_A+Rb_A;#in Rs.
BCratio_A=Bpy_A/Cpy_A;#unitless

#result
print "Costs/year : ",round(Cpy_A,3);
print "Benefits/year : ",round(Bpy_A,3);
print "BC Ratio of project A : ",round(BCratio_A,3)

#Project B :
P_B=250000000.0;#in Rs.

OMC_B=2500000.0;#in Rs.
Psy_B=12000000.0;#in Rs.
Fcs_B=3500000.0;#in Rs.
Ib_B=4500000.0;#in Rs.
Rb_B=2000000.0;#in RS.
AE_B=P_B*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);
Cpy_B=AE_B+OMC_B-Psy_B;#in Rs.
Bpy_B=Fcs_B+Ib_B+Rb_B;#in Rs.
BCratio_B=Bpy_B/Cpy_B;#unitless

#result
print "Costs/year : ",round(Cpy_B,3);
print "Benefits/year : ",round(Bpy_B,3);
print "BC Ratio of project B : ",round(BCratio_B,3)

#Project C :
P_C=400000000.0;#in Rs.
OMC_C=3500000.0;#in Rs.
Psy_C=18000000.0;#in Rs.
Fcs_C=5000000.0;#in Rs.
Ib_C=6000000.0;#in Rs.
Rb_C=3500000.0;#in RS.
AE_C=P_C*((i/100)*(1+i/100)**n)/(((1+i/100)**n)-1);
Bpy_C=Fcs_C+Ib_C+Rb_C;#in Rs.
Cpy_C=AE_C+OMC_C-Psy_C;#in Rs.
BCratio_C=Bpy_C/Cpy_C;#unitless

#result
print "Costs/year : ",round(Cpy_C,3);
print "Benefits/year : ",round(Bpy_C,3);
print "BC Ratio of project C : ",round(BCratio_C,3)
print"From the computations it is clear that only alternative A is eligible because other two alternatives have BC ratio less than one."

Costs/year :  5684030.212
Benefits/year :  7000000.0
BC Ratio of project A :  1.232
Costs/year :  13306717.021
Benefits/year :  10000000.0
BC Ratio of project B :  0.752
Costs/year :  21990747.233
Benefits/year :  14500000.0
BC Ratio of project C :  0.659
From the computations it is clear that only alternative A is eligible because other two alternatives have BC ratio less than one.