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.

CED 201: Introductory Environmental and Resource Economics

2. Assume that all costs and benefits are paid and received at the end of each year. (It will be easiest to do this using Excel. Help with this can be found in the book as well as using the Excel spreadsheet from the first homework assignment. I will also post another example on CANVAS.) For this part, do the discounting for the CBA using a 7% interest rate. Do your results indicate a definiteyes or no answer for the project?

3. 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?

4. (Return to the setup from part (a.) with a 7% discount rate.) In addition to the components of the project listed above, what other costs and/or benefits do you think are missing that should be included? How do you think they will impact the overall conclusion regarding the profitability of the project? (Hint: I would suggest thinking about this in terms of existence values – i.e., based on our discussion in class surrounding the development of ANWR what values may need to be built into this analysis and how would you go about getting them. There isn’t one right answer – you just need to defend your reasoning for what you come up with. I would suggest starting by thinking about how many households there are in the US and how much each would pay per year to protect the ecosystems associated with the dam.)

5. 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

LARGE DAM PROJECT
Year	0	1	2	3	4	5	6	7	8	9	10
Construction costs	-650	-728	-747.5
Operating costs				-75	-75	-75	-75	-75	-80	-80	-80
Price of Hydropower(4000 mlns. *0.08)				320	320	320	320	320	320	320	320
Price of Water(20000 mlns.*0.008)				160	160	160	160	160	160	160	160
Agricultural prodn.lost			-54	-54	-54	-54	-54	-54	-54	-54	-54
Forestry prodn.lost			-28	-28	-28	-28	-28	-28	-28	-28	-28
PV of Yr.11-Infinity NCFs(318/4.6%)											6913.043
Net cash flows	-650	-728	-829.5	323	323	323	323	323	318	318	7231.043
PV F at 4.6%	1	0.95602	0.91398	0.87379	0.83536	0.79862	0.76350	0.72992	0.69782	0.66714	0.63780
PV at 4.6%	-650	-695.985	-758.146	282.23279	269.821	257.955	246.611	235.7658	221.9083	212.1495	4611.945
NPV	4234.258
Benefits
Price of Hydropower(4000 mlns. *0.08)				320	320	320	320	320	320	320	320
Price of Water(20000 mlns.*0.008)				160	160	160	160	160	160	160	160
PV of total price(320+160)for yrs. 11-to Infinity(480/4.6%)											10434.78
Total benefits	0	0	0	480	480	480	480	480	480	480	10914.78
PV F at 4.6%	1	0.956023	0.91398	0.8737857	0.835359	0.79862	0.763501	0.729925	0.697825	0.667137	0.637798
PV at 4.6%	0	0	0	419.41715	400.9724	383.339	366.4807	350.364	334.956	320.2256	6961.427
NPV of Benefits	9537.181
Costs
Construction costs	-650	-728	-747.5
Operating costs				-75	-75	-75	-75	-75	-80	-80	-80
Agricultural prodn.lost			-54	-54	-54	-54	-54	-54	-54	-54	-54
Forestry prodn.lost			-28	-28	-28	-28	-28	-28	-28	-28	-28
PV of total costs(80+54+28)for yrs. 11-to Infinity(162/4.6%)											-3521.74
Total costs	-650	-728	-829.5	-157	-157	-157	-157	-157	-162	-162	-3683.74
ie.	650	728	829.5	157	157	157	157	157	162	162	3683.739
PV F at 4.6%	1	0.956023	0.91398	0.8737857	0.835359	0.79862	0.763501	0.729925	0.697825	0.667137	0.637798
PV at 4.6%	650	695.9847	758.1463	137.18436	131.1514	125.384	119.8697	114.5982	113.0476	108.0761	2349.481
NPV of Costs	5302.924
B/C= NPV Benefits/ NPV Costs=	1.80

SMALLER DAMS PROJECT
Year	0	1	2	3	4	5	6	7	8	9	10
Construction costs	-325	-364	-373.75
Operating costs				-50	-50	-50	-50	-50	-53	-53	-53
Price of Hydropower(4000 mlns. *0.08/2)				160	160	160	160	160	160	160	160
Price of Water(20000 mlns.*0.008/2)				80	80	80	80	80	80	80	80
PV of Yr.11-Infinity NCFs(187/4.6%)											4065.217
Net cash flows	-325	-364	-373.75	190	190	190	190	190	186.6667	186.6667	4251.884
PV F at 4.6%	1	0.95602	0.91398	0.87379	0.83536	0.79862	0.76350	0.72992	0.69782	0.66714	0.63780
PV at 4.6%	-325	-347.992	-341.6	166.01929	158.7182	151.738	145.0653	138.6857	130.2607	124.5322	2711.843
NPV	2712.271
Benefits
Price of Hydropower(4000 mlns. *0.08/2)				160	160	160	160	160	160	160	160
Price of Water(20000 mlns.*0.008/2)				80	80	80	80	80	80	80	80
PV of total price(160+80)for yrs. 11-to Infinity(240/4.6%)											5217.391
Total benefits	0	0	0	240	240	240	240	240	240	240	5457.391
PV F at 4.6%	1	0.956023	0.91398	0.8737857	0.835359	0.79862	0.763501	0.729925	0.697825	0.667137	0.637798
PV at 4.6%	0	0	0	209.70857	200.4862	191.669	183.2404	175.182	167.478	160.1128	3480.713
NPV of Benefits	4768.591
Costs
Construction costs	-325	-364	-373.75
Operating costs				-50	-50	-50	-50	-50	-53	-53	-53
PV of total opg.costs 53 for yrs. 11-to Infinity(53/4.6%)											-1152.17
Total costs	-325	-364	-373.75	-50	-50	-50	-50	-50	-53.3333	-53.3333	-1205.51
ie.	325	364	373.75	50	50	50	50	50	53.33333	53.33333	1205.507
PV F at 4.6%	1	0.956023	0.91398	0.8737857	0.835359	0.79862	0.763501	0.729925	0.697825	0.667137	0.637798
PV at 4.6%	325	347.9924	341.6	43.689286	41.76796	39.9311	38.17507	36.49625	37.21733	35.58062	768.8701
NPV of costs	2056.32
B/C= NPV Benefits/ NPV Costs=	2.32

Diffferent discount rates--6%,8%,3.5%. 15%
LARGE DAM PROJECT
Net cash flows	-650	-728	-829.5	323	323	323	323	323	318	318	7231.043
PV F at 6%	1	0.94340	0.89000	0.83962	0.79209	0.74726	0.70496	0.66506	0.62741	0.59190	0.55839
PV at 6%	-650	-686.792	-738.252	271.19703	255.8463	241.364	227.7023	214.8134	199.5171	188.2237	4037.777
NPV of cash flow	3561.397
Total benefits	0	0	0	480	480	480	480	480	480	480	10914.78
PV F at 6%	1	0.94340	0.89000	0.83962	0.79209	0.74726	0.70496	0.66506	0.62741	0.59190	0.55839
PV at 6%	0	0	0	403.01726	380.205	358.684	338.3811	319.2274	301.1579	284.1113	6094.758
NPV of Benefits	8479.541
Total costs	650	728	829.5	157	157	157	157	157	162	162	3683.739
PV F at 6%	1	0.94340	0.89000	0.83962	0.79209	0.74726	0.70496	0.66506	0.62741	0.59190	0.55839
PV at 6%	650	686.7925	738.252	131.82023	124.3587	117.32	110.6788	104.414	101.6408	95.88755	2056.981
NPV of Costs	4918.145
NPV Benefits/NPV Costs(B/C)	1.72
SMALLER DAMS PROJECT
Net cash flows	-325	-364	-373.75	190	190	190	190	190	186.6667	186.6667	4251.884
PV F at 6%	1	0.94340	0.89000	0.83962	0.79209	0.74726	0.70496	0.66506	0.62741	0.59190	0.55839
PV at 6%	-325	-343.396	-332.636	159.52766	150.4978	141.979	133.9425	126.3609	117.117	110.4877	2374.23
NPV of cash flow	2313.11
Total benefits	0	0	0	240	240	240	240	240	240	240	5457.391
PV F at 6%	1	0.94340	0.89000	0.83962	0.79209	0.74726	0.70496	0.66506	0.62741	0.59190	0.55839
PV at 6%	0	0	0	201.50863	190.1025	179.342	169.1905	159.6137	150.579	142.0556	3047.379
NPV of Benefits	4239.771
Total costs	-325	-364	-373.75	-50	-50	-50	-50	-50	-53.3333	-53.3333	-1205.51
PV F at 6%	1	0.94340	0.89000	0.83962	0.79209	0.74726	0.70496	0.66506	0.62741	0.59190	0.55839
PV at 6%	-325	-343.396	-332.636	-41.98096	-39.6047	-37.3629	-35.248	-33.2529	-33.462	-31.5679	-673.149
NPV of   Costs	-1926.66
NPV Benefits/NPV Costs(B/C)	2.20

Summary:
Discount Rates	NPV		B/C
	Larger	Smaller	Larger	Smaller
3.50%	4834.71	3068.19	1.86	2.41
4.60%	4234.26	2712.27	1.80	2.32
6%	3561.40	2313.11	1.72	2.20
8%	2750.68	1831.60	1.62	2.04
15%	890.20	722.55	1.27	1.52

iii.Sensitivity Analysis:
LARGE DAM PROJECT
Year	0	1	2	3	4	5	6	7	8	9	10
Construction costs	-650	-728	-747.5
Operating costs				-75	-75	-75	-75	-75	-80	-80	-80
Price of Hydropower(3200 mlns. *0.06)				192	192	192	192	192	192	192	192
Price of Water(20000 mlns.*0.005)				100	100	100	100	100	100	100	100
Agricultural prodn.lost			-54	-54	-54	-54	-54	-54	-54	-54	-54
Forestry prodn.lost			-28	-28	-28	-28	-28	-28	-28	-28	-28
PV of Yr.11-Infinity NCFs(130/4.6%)											2826.087
Net cash flows	-650	-728	-829.5	135	135	135	135	135	130	130	2956.087
PV F at 4.6%	1	0.95602	0.91398	0.87379	0.83536	0.79862	0.76350	0.72992	0.69782	0.66714	0.63780
PV at 4.6%	-650	-695.985	-758.146	117.96107	112.7735	107.814	103.0727	98.53987	90.71725	86.72777	1885.386
NPV	498.8616
Benefits
Price of Hydropower(4000 mlns. *0.08)				192	192	192	192	192	192	192	192
Price of Water(20000 mlns.*0.008)				100	100	100	100	100	100	100	100
PV of total price(320+160)for yrs. 11-to Infinity(292/4.6%)											6347.826
Total benefits	0	0	0	292	292	292	292	292	292	292	6639.826
PV F at 4.6%	1	0.956023	0.91398	0.8737857	0.835359	0.79862	0.763501	0.729925	0.697825	0.667137	0.637798
PV at 4.6%	0	0	0	255.14543	243.9249	233.198	222.9424	213.1381	203.7649	194.8039	4234.868
NPV of Benefits	5801.785
Costs
Construction costs	-650	-728	-747.5
Operating costs				-75	-75	-75	-75	-75	-80	-80	-80
Agricultural prodn.lost			-54	-54	-54	-54	-54	-54	-54	-54	-54
Forestry prodn.lost			-28	-28	-28	-28	-28	-28	-28	-28	-28
PV of total costs(80+54+28)for yrs. 11-to Infinity(162/4.6%)											-3521.74
Total costs	-650	-728	-829.5	-157	-157	-157	-157	-157	-162	-162	-3683.74
ie.	650	728	829.5	157	157	157	157	157	162	162	3683.739
PV F at 4.6%	1	0.956023	0.91398	0.8737857	0.835359	0.79862	0.763501	0.729925	0.697825	0.667137	0.637798
PV at 4.6%	650	695.9847	758.1463	137.18436	131.1514	125.384	119.8697	114.5982	113.0476	108.0761	2349.481
NPV of Costs	5302.924
B/C= NPV Benefits/ NPV Costs=	1.09

After sensitivity analysis as in iii.
NPV=	498.8616
B/C=	1.09
Both NPV & B/C Ratio predictions depend on the price of electricity & water

C..Decision:

At diff. discount rates , NPV is greater for larger dam alternative--but B/C ratio is higher for the smaller dams alternative.

Naturally ,as per mathematics, lower discount rates give higher NPVs & higher B/C ratio (the latter is derived from NPVs of benefits & costs--so naturally the discount rates will influence the final number.)

If the decision is to be based solely on NPV criteria, then larger dams are recommended.

If the decision is to be based solely on B/C ratio criteria, then smaller dams are recommended .

NPV gives the absolute $ value,whereas, B/C ratio, is all said, a relative figure & as seen above the NPV relevant to that alternative is always less than that of the larger-dam alternative.

When both NPV & B/C ratio, are combined to take a decision, the LARGER DAM alternative is RECOMMENDED irrespective of discount rates.