the invanpah solar power plant cost $2.2 billion to build. it was expected to ge

Question

the invanpah solar power plant cost $2.2 billion to build. it was expected to generate one million megawatt hours of electricity a year at a price of $0.12 per kilowatt hours. (a megawatt is 1000 kilowatts). it has only produced 40% of that over the last year. if it maintains the same generation rate (40% of what was expected) for the next 30 years and the price of electricity rises to $0.15 per kilowatt hours after the 15th year, what will be it's payback, IRR, and NPV? the discount rate is 4% a year the invanpah solar power plant cost $2.2 billion to build. it was expected to generate one million megawatt hours of electricity a year at a price of $0.12 per kilowatt hours. (a megawatt is 1000 kilowatts). it has only produced 40% of that over the last year. if it maintains the same generation rate (40% of what was expected) for the next 30 years and the price of electricity rises to $0.15 per kilowatt hours after the 15th year, what will be it's payback, IRR, and NPV? the discount rate is 4% a year the invanpah solar power plant cost $2.2 billion to build. it was expected to generate one million megawatt hours of electricity a year at a price of $0.12 per kilowatt hours. (a megawatt is 1000 kilowatts). it has only produced 40% of that over the last year. if it maintains the same generation rate (40% of what was expected) for the next 30 years and the price of electricity rises to $0.15 per kilowatt hours after the 15th year, what will be it's payback, IRR, and NPV? the discount rate is 4% a year

Explanation / Answer

Initial outflow = $2.2 billion or (2.2*10^9)

Inflow per year(1st 15 years) = electricity generated*rate = 40% of 1 million *1,000 kilowatt * $0.12

= 10^6*10*3*0.12 = $12*10^7 per year

Inflow per year (next 15 years) = electricity generated*rate = 40% of 1 million *1,000 kilowatt * $0.15

= 10^6*10*3*0.15 = $15*10^7 per year

For all calculations below the PV formula has been used = amount/(1+rate)^time period

1. Payback -

So, payback occurs between 28th and 29th year, as it is during this time that the cumulative cash flows become positive.

IRR - Creating the same table on excel, and leaving the rate cell as blank. Then use solver with the condition that sum of all PVs should be 0 i.e. NPV should be 0. Solving we get:

Thus IRR is 4.2108%

NPV at 4%:

If in the above table of IRR, we make the discount factor as (1+4%) = 1.04, we get the NPV as $60,253,372

Year Cash flows PV @ 4% Cumulative PV 0 -2,200,000,000 -2,200,000,000 -2,200,000,000 1 120,000,000 115,384,615 -2,084,615,385 2 120,000,000 110,946,746 -1,973,668,639 3 120,000,000 106,679,563 -1,866,989,076 4 120,000,000 102,576,503 -1,764,412,573 5 120,000,000 98,631,253 -1,665,781,320 6 120,000,000 94,837,743 -1,570,943,577 7 120,000,000 91,190,138 -1,479,753,440 8 120,000,000 87,682,825 -1,392,070,615 9 120,000,000 84,310,408 -1,307,760,207 10 120,000,000 81,067,700 -1,226,692,506 11 120,000,000 77,949,712 -1,148,742,795 12 120,000,000 74,951,646 -1,073,791,149 13 120,000,000 72,068,890 -1,001,722,258 14 120,000,000 69,297,010 -932,425,248 15 120,000,000 66,631,740 -865,793,508 16 150,000,000 80,086,226 -785,707,282 17 150,000,000 77,005,987 -708,701,295 18 150,000,000 74,044,218 -634,657,077 19 150,000,000 71,196,364 -563,460,713 20 150,000,000 68,458,042 -495,002,671 21 150,000,000 65,825,040 -429,177,631 22 150,000,000 63,293,308 -365,884,323 23 150,000,000 60,858,950 -305,025,373 24 150,000,000 58,518,221 -246,507,152 25 150,000,000 56,267,520 -190,239,631 26 150,000,000 54,103,385 -136,136,246 27 150,000,000 52,022,486 -84,113,761 28 150,000,000 50,021,621 -34,092,140 29 150,000,000 48,097,712 14,005,572 30 150,000,000 46,247,800

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