Example problem on evaluation of public alternative -2
Example problem on evaluation of public alternative -2
In a particular locality of a state, the vehicle users take a roundabout route to reach certain places because of presence of a river. This results in excessive travel time and increased fuel cost. So, the state government is planning to construct a bridge across the river. The estimated initial investment for constructing the bridge is Rs.40,00,000. The estimated life of the bridge is 15 years. The annual operation and maintenance cost is Rs.2,50,000. The value of the fuel savings due to the construction of the bridge is Rs.6,00,000 in the first year and it increases by Rs.50,000 every year thereafter till the end of the life of the bridge. Check whether the project is justified based on BC ratio by assuming an interest rate of 20% compounded annually.
Given data
Initial
investment, P = ₹. 40,00,000
Annual
operation and maintenance cost =
₹. 2,50,000
Annual
fuel savings during the first year = ₹. 6,00,000
Annual
fuel savings increment after first year, G = ₹. 50,000
Life
of the project, n = 15 years
Interest
rate = 20%
Cash flow diagram
For
bridge construction
For fuel savings
Formula used
BC
ratio = BP / (P+ CP)
Present
worth of annual operating and maintenance cost (CP) = A (P/ A, i, n)
Present
worth of fuel savings BP = A (P/A, i, n)
here, A = A1 + G A (A/G, i, n)
Solution
Present
worth of annual operating and maintenance cost (CP) = A (P/ A, i, n)
=
2,50,000 (P/A, 20%,15)
=
2,50,000 (4.6755)
CP =
₹. 11,68,875
Fuel Savings:
A =
A1 + G (A/G, i, n)
=
6,00,000 + 50,000 (A/G, 20%, 15)
A =
₹. 7,97,940
Present
worth of fuel savings BP = A
(P/A, i, n)
=
7,97,940 (P/A, 20%, 15)
= 7,97,940 (4.6755)
BP = ₹. 37,30,768.47
BC
ratio = BP / (P+ CP)
= 37,30,768.47 /
(40,00,000 + 11,68,875)
BC
ratio =0.7217
