ECON 2J03 Lecture Notes - Lecture 7: Sensitivity Analysis

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15 Mar 2018

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Project a: total benefits , total costs , project b: total benefits , total costs , compare net benefit and benefit cost ratio for each, project a: nb: bcr:2, project b: nb: bcr:1. 75, net benefit is what matters. Role of government budgets: the gov"t (cid:272)a(cid:374) pla(cid:455) a role i(cid:374) helpi(cid:374)g to (cid:373)a(cid:454)i(cid:373)ize (cid:374)et (cid:271)e(cid:374)efits, the principle is allocate resources so that the net benefit produced by the total budget are maximized. Sensitivity analysis: a sensitivity analysis that allows us to calculate the pv of the net benefits with a variety of different interest rates to see if changes in the discount rate affect the ranking of projects.

Related Questions

Assume that the costs and benefits associated with a proposed government project are as follows:

Year	Benefits (R millions)	Costs (R millions)
0 (Now)	200	500
End of Year 1	500	500
End of Year 2	1500	500
End of Year 3	800	200

(a) If the discount rate is 5 percent, calculate the present value of the net benefits for this project (show your work).
(b) Not all of the benefits associated with this project are easily quantifiable in Rand terms. What can be done to account for these factors?
(c) Detail the limitations associated with cost -benefit analysis.

bronzelouse754

1. Calculating the Net Present Value of Environmental Projects with Future Costs and Benefits

Bar-tailed godwits are birds that migrate between their (northern summer) nesting sites in Alaska non-stop all the way down to (southern summer) tidal estuaries in New Zealand . Ideal southern habitats are undisturbed muddy estuaries or lagoons.

Suppose that an estuary near Christchurch has seen a major drop in the number of migrating godwits, with the decline attributed to damage to the estuary caused by construction-related landfill after the earthquakes. A âBring Back the Godwitsâ group forms, and petitions the local council to restore the estuary to its pre-quake condition (clearing landfill, and restoring plantings.) The group is asked by the council to prepare an estimate of the costs of restoration, and the benefits to those people in Christchurch who enjoy observing the in- and out-migration of the birds. (Benefits to the godwits themselves are ignored, since if they do not migrate to the estuary, they will likely migrate to other more remote locations in New Zealand.) The council asks the group to consider a 20 year time horizon (from year 0, 1, 2, â¦19, 20), and use an annual time discount rate of delta (Î´) = .05 (i.e. 5%).

The group estimates that estuary restoration costs would be $30,000 in Year 0, $492,850 in Year 1, $300,000 in Year 2, and then an ongoing cost of $10,000 for each of Years 3-20. On the benefit side, based on a contingent valuation analysis of a representative sample of Christchurch residents, the group estimates aggregate benefits of restoration would be zero in Years 0 to 3, $40,000 in Years 4 to 5, and $100,000 for each of Years 6 to 20.

a. Based on the data collected by the group, calculate the net present value (NPV) of the estuary restoration to two decimal places. Would the estuary restoration be a potential Pareto improvement?

b. Given the timing of the costs and benefits of the project, would the estuary restoration be a potential Pareto improvement if the council required a higher discount rate be used? (You should not need to provide calculations to answer this question.)

1. What is the capitalized value of an infinite series of $1,000 biennial (every two years) payments? MARR = 10%

		$4,950
		$4,025
	.	$4,350
		$4,762

2. Frank West Enterpises would like to choose one of the following plans for expansion. Using present worth analysis, find the best alternative among the three alternatives and the Do-Nothing.

	Alt. A	Alt. B	Alt. C
Initial Cost	$10,000	$21,000	$8,000
EUAB	$6,000	$7,000	$4,000
EUAC	$1,500	$1,000	$2,000
Salvage Value	$2,000	$8,000	$3,000
Life	2 Years	3 Years	2 Years

Use a MARR of 10%.

	.	Do-Nothing
	.	Alt. C
	.	Alt. B
	.	Alt. A

U. S. Engineering is investigating the possibility of acquiring new automated packaging equipment at a cost of $12,000. It is expected that the equipment will have a salvage value of $1,000 at the end of its useful life of 10 years. It is determined by the plant engineering department at the company that the operation and maintenance cost will be $500 in the first year and will gradually increase every year starting year 2 at the rate of $50 until the equipment is retired. Determine the equivalent uniform annual cost (EUAC) if MARR for the company is 10%.

		$2,575.95
		$2,150.50
	.	$2,176.60
	.	$2,184.40

The cash flows given in table below are for two different alternatives. MARR =10%

Data	C	D
Initial Cost	$20,000	$80,000
Uniform Annual Benefits	$6,000	$10,000
Salvage Value	$5,000	$20,000
Useful Life in years	5	infinity

The equivalent uniform annual worth (EUAW) of alternative N is ______________.

Hint: Assume the Salvage Value is never realized since N is infinite.

		$2,000
		$1,920
		$1,762
		$2,476

Compare the following plans using a MARR of 6%.

Data	Plan X	Plan Y
Equipment First Cost	$50,000	$75,000
Annual Operation & Maintenance Cost	$3,000	$2,500
Salvage Value	$10,000	$0
Service Life, Years)	25	50

		$6,728; $7,255
		$7,255; $9,000
	.	$6,728; $7,728
	.	$6,728; $8,200

LAEP, Inc. wants to evaluate two methods of shipping their products. The following cash flows are associated with each alternative:

Data	Method
	A	B
Life (Years)	10	10
First Cost	$700,000	$1,512,000
M&O Cost	$18,000	$9,000
M&O Cost Gradient	$900	$775
Annual Benefit	$154,000	$303,000
Salvage Value	$142,000	$210,000

Annual profits are based on amount of products which can ordinarily be shipped each year as a function of the amount of vehicles or service purchased with the first cost and the M&O costs.

Using a MARR of 15%, calculate the equivalent uniform annual cash flow (EUAB - EUAC) for each alternative.

Determine the most desirable alternative based on the results.

		$389.57, $445.90; Method A
		$445.90, $389.57; Method A
	.	$445.90, $389.57; Method B
	.	$389.57, $445.90; Method B

For the cash flow diagram shown, which of the following equations properly calculates the uniform equivalent (A)?

n	0	3	6	9	12	15
Dollars	$100	$100	$100	$100	$100	$100

		A=100(A/P,i,15)+ 100(A/F,i,3)
		A=100(A/P,i,15)
		A=100(A/F,i,3) + 100(A/F,i,15)
		A=100(A/P,i,3) + 100(A/F,i,3)

Three different alternatives shown in table below are being considered by U. S. Engineering systems.

Assume that alternatives X and Z are replaced at the end of their lives.

Data	Alternative X	Alternative Y	Alternative Z
Initial Cost	$6,000	$1,000	$1,500
Uniform Annual Benefits	$810	$125	$ 230
Useful Life in Years	20	infinite	10
MARR	12%

The NPW for alternative

ECON 2J03 Lecture Notes - Lecture 7: Sensitivity Analysis

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