Question

1. The EPA is considering an application from the state of Colorado for a large dam project on the Colorado River. The basic costs and benefits of the project (in inflation-adjusted dollar values) are as follows:

Costs			$900 million/year first three years
Construction costs:
Operating costs:			$80 million/year
Agricultural product lost from flooded lands:			$65 million/year
Forest products lost from flooded lands:			$40 million/year
Benefits
Revenues from Power Generation
	Hydropower generated:		4 billion Kilowatt hours/year
	Price of electricity:		$0.125/Kilowatt hour
Revenues from Irrigation Services
	Irrigation water available from the dam:		200K Acre-Feet
	Price of water:		$700/Acre-Foot

1. Do a formal Cost-Benefit Analysis (CBA) using the quantifiable factors listed above. Assume that the operating lifespan of the dam is 30 years. Assume construction begins in year 1. All other impacts start when the dam is completed (at the beginning of Year 4) and continue for 30 years, which implies the full lifespan for the project is 33 years.
2. Using the same parameters and results from part (a.), adjust the interest rate to determine the level of discounting necessary to just break even. (Hint: I would start by changing the interest rate in 1% increments and then refine the changes as you get close to the break-even point.) What does this increase or decrease in interest rate imply about the relationship between costs and benefits over time?
3. Finally, holding constant the analysis you did in part (c.) what happens when you increase the acre-foot price of irrigation water from $700 to $1500 and/or the price per kilowatt hour of electricity from $0.125 to $0.15?

Answer 1

		ANNUAL BENEFITS: Year4-33	($ million)
		Revenue from power generation	$500	(4000*0.125)
		Revenue from irrigation services	$140	(200/1000)*700
		Total annual benefit Year4-33	$640
		ANNUAL COSTS : YEAR4-33
		Operating Cost	$80
		Agricultural Product Lost	$65
		Forest Product Lost	$40
		Total annual costs Year4-33	$185
		Net Annual Benefit (Year4-33)	$455
		Year	1	2	3
		Construction Cost	$900	$900	$900
	b	Break Even Interest Rate
		Future Value of Construction Cost at end of Year 3 =Present Value of Net Annual Benefit at end of year 3
		Future value of Construction Cost:
	Pmt	Annual Cost	$900
	Nper	Number of years of costs	3
	Rate	Interest Rate=r
		Future value of Construction Cost can be determined by using FV function of excel with Rate=r, Nper =3, Pmt=-900
		Present Value of Net annual benefit:
	Pmt	Annual Benefit	$455
	Nper	Number of years of benefits	30
	Rate	Interest rate=r
		Present value of Net Benefits can be determined by using PV function of excel with Rate=r, Nper =30, Pmt=-455
		Rate	FV of costs at year3	PV of benefits at year3
		5%	$2,837.25	$6,994.47
		6%	$2,865.24	$6,263.00
		7%	$2,893.41	$5,646.11
		8%	$2,921.76	$5,122.29
		9%	$2,950.29	$4,674.51
		10%	$2,979.00	$4,289.25
		11%	$3,007.89	$3,955.68
		12%	$3,036.96	$3,665.11
		13%	$3,066.21	$3,410.52
		14%	$3,095.64	$3,186.21
		14.3843%	$3,107.00	$3,107.05
		15%	$3,125.25	$2,987.52
		16%	$3,155.04	$2,810.63
		17%	$3,185.01	$2,652.37
		18%	$3,215.16	$2,510.15
		LEVEL OF DISCOUNTING NECESSARY TO BREAK EVEN
		Level of discounting	14.38%	(rounded to two decimal)