Question

A power company is planning to replace a 39 years old thermal power generator with a capacity of 370 MW, with a new generator with a capacity of 740 MW. 39 years ago the cost index was 156 and it is 394 now. If the cost of 370 MW generator was $411 million 39 years ago and the cost of 740 MW generator is $1549 million today, what is the cost capacity factor?

Answer 1

Cost of 370 MW generator = $411 million

Cost of 740 MW generator = $1549 million

Cost index 39 years ago = 156

Cost index now = 394

Let cost capacity factor be x

Calculate cost capacity factor -

Cost of 740 MW generator = Cost of 370 MW generator * [Capacity of new generator/Capacity of old generator]^{cost-capacity factor} * [Cost index now/Cost index 39 years ago]

$1549 million = $411 million * [740/370]^x * [394/156]

$1549 million/$411 million = [2]^x * [349/156]

3.77 = 2^x * 2.24

2^x = 3.77/2.24

2^x = 1.68

Taking log both sides

x log 2 = log 1.68

x * 0.30 = 0.22

x = 0.22/0.30

x = 0.73

The cost capacity factor is 0.73