Question

Solar Collector Field: This design uses a series of Fresnel lenses and concave mirrors to concentrate solar radiation onto a boiler mounted on a tower. The boiler then produces steam, which then is used to generate electricity. This system is expected to yield a power of 3.3 MW and will cost $91 million initially with first-year operating costs of $3 million, growing 350,000 annually. It will produce electricity worth $9.7 million the first year; this revenue stream is expected to increase at a simple interest rate of 8%, every year from there on (that is, 112% of 9.7 Mil in year 2, 124% of 9.7 Mil in Year 3, etc.).

Use an interest rate of 10% and a 20-year planning horizon to find the net present value of this project using economic logic equations.

Answer 1

Initial investment = $91 Million

O&M cost in year 1= $3 M

Arithmetic gradient of O&M cost = $.35 Million

Revenue in year 1 = $9.7 Million

Arithmetic gradient = 9.7*8% = .776 Million

time period = 20 years

R = 10%

So,

Net present value of the project = - initial investment - PV of the O&M cost + PV of the revenues

Net present value of the project = -91 - 3*(P/A, 10%, 20) - .35*(P/G, 10%, 20) + 9.7*(P/A, 10%, 20) + .776 *(P/G, 10%, 20)

Net present value of the project = -91 - 3*8.5136 - .35*55.407  + 9.7*8.5136  + .776 *55.407

Net present value of the project = -$10.36 Million

So, net present value of the project is -$10.36 Million.

Due to the negative value of NPV, the project should not be accepted.