Economics 290 Assignment 4

Consider the following stream of payments:

Current -100,000

One year from now - 50,000

Two years from now + 3,000

Three years from now + 50,000

Four years from now + 50,000

a) Compute the net present value of this stream of payments, using the exponential discount rate of 4%.

Using an exponential discounting method, each payment is multiplied by 1/(1+r)^t, where "^"means "raised to the power of", and t is the number of periods of delay. For a rate of 4%, the discount factors are 1, 0.9615, 0.9246, 0.8890, and 0.8548. The present value of each payment is -100,000; -48,077; 2,774; 44,450; and 42,740. Thus the NPV is -58,113.

b) Compute the net present value of this stream of payments using a hyperbolic discount rate which is a function of the 4% and time.

There are various ways of discounting hyperbolically. One of the simplest is multiplying each period by 1/(1+r*t). If we use this method, the discount ractors are: 1, 0.9615, 0.9259, 0.8929, and 0.8621. Note that these factors are all higher than the exponential discount factors, as they should be. Note also that whatever complicated hyperbolic discount factor formula you might be using, the discount factor for the present period should always be set to 1. Continuing on with our hyperbolic discounting, the present value of each payment is -100,000; -48,077; 2,778; 44,6423; and 43,103 for a grand NPV total of -57,553.

2. Consider a payment of $25,000 every year forever, beginning today. Using an exponential discount rate of 4%, and the given mathematical formula, calculate the present value of this stream. (Formula: the present value of an infinite stream of x, beginning one period from now, is quite simply x/r, where r is the discount rate expressed as a fraction of 100. eg. 4% means r =0.04.)

A payment of $25,000 beginning today and continuing forever can be separated into the payment today valued at $25,000, and the payment stream beginning next year and continuing forever, valued at $25,000/r. Since r = .04, the total is $25,000 + $625,000 = $650,000.

3. Let’s imagine that Ducks Unlimited is considering which of three wetland restoration projects to adopt.

	Project 1: Hill View Site	Project 2: Old Walmart site	Project 3: Old Farm site
Present value of costs	80,000	120,000	120,000
# ducks affected	80 breeding pairs	50 breeding pairs	100 breeding pairs
Present value of birdwatching benefits	50,000	30,000	50,000
Present value of hunting benefits	40,000	0	50,000

a) Calculate the net present value of each project using only the available information. Which project (if any) should be chosen according to CBA?

Without being able to put a value on ducks, we can only conclude that Project 1 should be adopted, since it has the highest NPV. In fact, it is the only project where the present value of benefits exceeds the present value of costs.

b) Let’s say an “existence value” was estimated. What existence value per breeding pair of ducks would be needed to give Project 2 a NPV = 0?

Currently, Project 2 has an NPV of -90,000. To get this up to zero, an additional $90,000 of benefits would have to be found. This could come from the existence value on ducks. With 50 breeding pairs, an existence value of $1,800 per pair in present value terms would do the job of making this project's benefits balance with its costs.

c) Let’s say Ducks Unlimited has the simple goal of maximizing the # ducks affected. Which project should be chosen according to the criterion of cost-effectiveness analysis?

Project 1 has the lowest cost per pair of ducks. It also has the lowest cost net of hunting and birdwatching benefits per pair of ducks. It would be chosen by cost-effectiveness analysis.

d) Describe in detail 5 methods of estimating birdwatching benefits.

The 5 methods are direct measurement of birdwatching prices (perhaps there are such services on the market), preventive/mitigating expenses hedonic estimation, surrogate markets, and contingent valuation. On the exam, the detail with which you describe these methods' application to birdwatching depends on how much the question is worth as a percentage of the exam. You should at least: list the method, describe the principle, and then suggest one application of the method to the particular case of birdwatching.

4. Returning to the Ducks Unlimited example, which of the following are relevant costs to society and briefly, how should they be estimated?

a) Cost of the site if it is donated by government.

If the land is freely given to Ducks Unlimited, it is not a cost to Ducks Unlimited, but it is still a cost to society, because the land has alternative uses. Estimate the shadow value of the land. The market value of the land may suffice.

b) Cost to monitor the site for dumping or poaching.

This is a cost both to Ducks Unlimited and to society. Labour and equipment are diverted from other uses to be applied to the project. The market value of labour and equipment will suffice if markets are not distorted.

c) Cost of ducks fouling nearby parking lots.

This is not a cost to Ducks Unlimited but it is a cost to society. Some people will pay carwash fees; some people will give up their leisure time to wash their cars by hand; and businesses around the parking lot may lose consumer surplus as some people avoid the shopping centre. Estimate the willingness to pay of shoppers and businesses to have a bird poop-free parking lot.

d) Noise pollution from hunting experienced by nearby residents.

This is not a cost to Ducks Unlimited but it may be a cost to society. If hunting noise is simply diverted from one bunch of people to another of equal size, there is no net cost to society; but if hunting is diverted from a rural region where there are few residents to the city where there are more, there is a net cost to society in terms of noise damage. Similarly, if restoring the wetland leads to an overall increase in hunting, so that the total number of people affected by noise increases, there is a net cost to society. Describe one or more ways to estimate the shadow value of noise i.e. people's willingness to pay to avoid it.

e) Lowered valuation of nearby residential property.

This is not a cost to Ducks Unlimited, but it is a cost to the owners. However, we have to be careful not to double-count damages. We have "already" measured damages from noise, say; now we want to measure reduced house prices, but some of that reduced house price may be because of the noise, which we have already counted. In fact, we may have used house prices in our hedonic estimation to estimate the willingness to pay to avoid noise and other negative externalities due to proximity to the wetland.

f) Reduced contributions to other local land conservancy projects.

If we are talking about donations to Ducks Unlimited competing with donations to the Nature Conservancy of Canada, that's just a redistribution of spending from one category to another, and not counted as a net cost to society.

You might ask, "But what if the Nature Conservancy's projects are better than Ducks Unlimited's projects? We don't usually ask whether it's better for people to spend on basketballs or pingpong balls or one charity or another. If Ducks Unlimited's project is not too hot for society compared to other projects, that will show up as we value the resources DU uses at their social opportunity costs; that will show up in a lower NPV for the Ducks Unlimited project.