Question

The installation cost (IC) of a solar power plant is INR 89,000. The plant shall be operational for 5 years. The recurring costs for maintenance of the solar plant per year is INR 5,000 but the benefits it creates including reduction in emissions amounts to INR 25,000 per year. These are the only costs and benefits associated with this project. The social discount rate (r) considered is 4% per year. The yearwise information is presented below.

 

Hint:

When calculating the net present value (NPV), remember that it is the difference between the present value of benefits and the present value of costs. A negative NPV indicates that the project is not financially viable given the social discount rate.

Answer 1

Step 1: Calculate the Present Value of Benefits and Costs for each year.
\[ {PV of Benefits}_t = {Benefits}_t \times {Discount Factor}_t \]
\[ {PV of Costs}_t = {Costs}_t \times {Discount Factor}_t \]
For each year:
- Year 0:
\[ {PV of Costs} = 89 \times 1.00 = 89,000, \quad {PV of Benefits} = 0 \]
- Year 1:
\[ {PV of Benefits} = 25 \times 0.96 = 24,000, \quad {PV of Costs} = 5 \times 0.96 = 4,800 \]
- Year 2:
\[ {PV of Benefits} = 25 \times 0.92 = 23,000, \quad {PV of Costs} = 5 \times 0.92 = 4,600 \]
- Year 3:
\[ {PV of Benefits} = 25 \times 0.89 = 22,250, \quad {PV of Costs} = 5 \times 0.89 = 4,450 \]
- Year 4:
\[ {PV of Benefits} = 25 \times 0.85 = 21,250, \quad {PV of Costs} = 5 \times 0.85 = 4,250 \]
- Year 5:
\[ {PV of Benefits} = 25 \times 0.82 = 20,500, \quad {PV of Costs} = 5 \times 0.82 = 4,100 \]
Step 2: Calculate the Total Present Value of Benefits and Costs.
\[ {Total PV of Benefits} = 0 + 24,000 + 23,000 + 22,250 + 21,250 + 20,500 = 110,000 \]
\[ {Total PV of Costs} = 89,000 + 4,800 + 4,600 + 4,450 + 4,250 + 4,100 = 111,200 \]
Step 3: Calculate the Net Present Value (NPV).
\[ {NPV} = {Total PV of Benefits} - {Total PV of Costs} \]
\[ {NPV} = 110,000 - 111,200 = -1,200 \]
Final Answer: The net present value (NPV) of the plant is \(\boxed{-200}\).