Question

1. Ying works for an private electricity utility that needs to decide between two options for a turbine that will be constructed in 2024. 2025 will be the first year of operation. She must decide which option will cost less to construct. Past capital cost estimates are available for both options. The cost of Option A, a Whirr Turbine, was estimated to be $9 million in 2012 dollars. The cost of Option B, a Zap Turbine, was estimated to be $13 million in 2014 dollars. She must project future costs for each option. A relevant Cost Index had a value of 115 in 2012, and 150 in 2019 (the latest year available).

a) What is the estimated inflation rate associated with the cost index between 2014 2012 and 2019, rounded to the tenths place?

b) The Whirr Turbine for which cost was originally estimated is now considered too small to meet the projected future need. The unit would need to be able to produce 60% more electricity. Using a power-sizing model to estimate this cost (to the nearest dollar), and assuming a power-sizing exponent of 0.69, estimate the revised cost for an appropriately sized Whirr Turbine in the year of construction.

c) The 2014 cost estimate for Option B, the Zap Turbine, was for the correct anticipated future size needed. What would the estimated cost of the Zap Turbine be in the year of construction, rounded to the nearest dollar? Is there any other data that you could use to improve the quality of your estimate?

d) On the basis of this analysis, which turbine should Ying recommend?

Answer 1

a) Estimated Inflation rate = (150/115) ^(1/7) -1 = 0.038687 or 3.87% p.a.

b) Cost of Whirr turbine in 2024 = cost in 2012* (1+inflation rate)^no of years till 2024

= $9 million * 1.038687^12

=$14.19253 million

To have a turbine producing 60% more , the power sizing model gives

Cost of required turbine

= cost of whirr turbine * (size of new turbine/size of whirr turbine)^power sizing exponent

= $14.19253 million * (1.6/1)^0.69

=$19.6292 million which is the required cost of appropriately sized whirr turbine in the year of construction 2024

c) The Zap turbine has the correct size

Cost of Zap turbine in 2024 = cost in 2014* (1+inflation rate)^no of years till 2024

= $13 million * 1.038687^10

=$19.00164 million

d) As the Zap turbine's cost is lesser in 2024, the Zap turbine is recommended