Question

The World Bank is considering an application from the country of Equatoria for a large dam project. In order to build this dam, villagers from an entire village will need to be relocated. In addition, there will be some watershed damage and ecological losses due to habitat destruction. Monetary costs and benefits for the dam project are given as follows:

Construction costs: $650 million at the beginning of the first year of the project. Construction costs for the start of the second year of the project will be 12% higher than the first year costs, and at the start of year 3 (the final year of construction) the costs will be 15% higher than the first year costs. Operating costs: $75 million/year (starting in year 3); and then increase to $80 million/year from year 8 onward Hydropower generated: 4 billion kilowatt hours/year (available from year 3) Price of electricity: $0.08/kilowatt hour Irrigation water available from the dam: 20 billion litres/year (available from year 3) Price of water: $0.008/litre Agricultural production lost from flooded lands: $54 million/year (loss from year 2)

Forestry production lost from flooded lands: $28 million/year (loss from year 2) Note: 1 billion = 1000 million  

You, as a consultant have been approached by the World Bank to carry out an analysis from which you will provide your recommendations.  

Your tasks: A. Calculate the NPV and the B/C using a real discount rate of 4.6%. Set up a basic template to complete your CBA. Put the variables in the clearly labeled cells above your Large Dam Project. Since we are given agricultural and forestry production losses, if we incorporate these we are automatically creating a ‘withwithout project’ analysis. Next complete your Large Dam Project with clearly labelled columns. Do this by creating formulae using your variables in the cells above. Always use formulae linked back to the data cells above so that if you wish to change a data cell value (for a sensitivity analysis) then all your calculations will automatically

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change. Once you have created a formula in one cell of a column you should be able to drag down so that it accurately duplicates the formula right down the column. To do the analysis I want you to complete the columns initially for 10 years of the project. However, we can assume that once built this dam will remain in place indefinitely. So to extend the analysis to cover the long term, follow these instructions:  

i) Underneath Yr 10 put Yr 11 to infinity (11 – infinity).

ii) Since the last few years have the same Net Cash Flow (NCF) and we do not have any further information, we can assume that the future NCFs will remain the same. This means that we can calculate the future NCFs based on these last NCFs and use the formula for a perpetuity that states: PV of all future expected cashflows = NCF/discount rate, (this effectively capitalizes the future NCFs)

iii) To create the formula for this in the NCF cell for yrs 11 – infinity (in your NCF column), use the NCF cell in year 9 and divide this value by the discount rate cell. (Use the year 9 NCF rather than the one in year 10, because you will shortly be changing the NCF entry in year 10). You have now calculated the PV of all future NCFs, to the beginning of year 11 (as this is the beginning point of yrs11-infinity).

iv) But you want your final PV to be today (year 0) not year 11. Remember that the beginning of year 11 is the same as the end of year 10, so now you can add this cell containing the large value for (NCF/disc. rate) into your calculation for the year 10 NCF. v) Your final column is where you calculate the PV(NCF)s – i.e. the PV of each entry in your NCF column.  

vi) Finally, sum your PV(NCF) column and this sum will give you your NPV. vii) Similarly, for your B/C you will need to calculate the PV(future Costs) and PV(future Bens) in a similar manner (as you did for the NCF) for years 11 – infinity. This is so that you capture all future streams of costs and also of benefits. Then finally calculate the NPV(Costs) and NPV(Benefits) so that you can use these to calculate your B/C.  

Also begin a Word doc. and for Part A. give the NPV(Large Dam) and also the B/C(Large Dam).

B. Now consider an alternative project: several smaller dams constructed to avoid flooding significant agricultural land or forested areas. For this project, total construction costs are exactly half the costs of the large dam project, while operating costs are two-thirds those of the large dam. Power and irrigation benefits are also half as much as those for the large dam. Agricultural land and forests are not affected and the project incurs no ecological or resettlement costs.  

(i) Calculate the NPV of this Smaller Dams Project using the discount rate of 4.6%. You already have all the variables set up (for the Large Dam project) so do not create new cells but work from the original cells. Conduct your analysis for the Smaller Dams Project on a new table beneath that for the Large Dam Project (using some or all the same columns). Label the Small Dams Project clearly (all on the one sheet of your spreadsheet file – this makes marking easier). Include the years 11 – infinity in your Small Dams analysis in exactly the same way as you did for the Large Dam project.

On your Word doc. for B.

(i) give the NPV(Smaller Dams).

(ii) Now you are to compare both projects under different discount rates. Set up a table with a column containing various discount rates, another column for the NPV for the Large Dam Project and a third column for the NPV for the Small Dams Project. Complete the table and use it to draw a graph that shows the changing NPVs plotted against the discount rate, for both projects on the one graph. Make sure your graph is properly labelled and has an appropriate title that contains your name. On your Word doc. for B (ii) if your decision regarding the two different dam projects were to be based solely on the CBAs calculated thus far, give the range of discount rates for which you would choose the Large Dam Project over the Smaller Dams Project, and vice versa.

(iii) For just the Large Dam Project, carry out this sensitivity analysis: Suppose the amount of hydropower generated was overestimated, and instead 3.2 billion kilowatt hours/year were generated and in addition, the price of electricity was $0.06/kilowatt hour and the price of water was $0.005/litre. Make these changes and make a note of the new NPV and B/C, and then return your analysis to its original numbers for handing in.

On your Word doc. for B

(iii), for the Large Dam Project give the NPV and B/C under this sensitivity analysis. In a sentence what would you say about this? Also explain what the B/C is predicting regarding our investment

C. Finally, in your Word document you are to evaluate the two projects, the Large Dam project (originally, before the sensitivity analysis) and the Smaller Dams project individually and then make comparison between the two. Your evaluation should include a discussion on the costs and benefits not quantified in your spreadsheet analyses. In this discussion make recommendations as to how you could incorporate these costs and benefits into your spreadsheet analysis. Conclude this analysis by giving your final recommendations to the World Bank. 600words

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.