# ECON361 Lecture Notes - Lecture 3: Discounting, Microsoft Excel, Social Discount Rate

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9 Aug 2016

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Module #3

-Most CBA studies, or projects, they tend to be investments over multiple years.

-These multi-period investments have costs and benefits occurring over different timelines.

-We need a method to separate the impacts from a quantitative and monetary point of view, uh,

and we usually put them in terms of cash flows.

-Now although we use the term “cash flows”, the dollar values might not be the same as the

actual cash amounts

-But in cash flow analysis, we separate the actual flow of funds out at a certain particular, or a

particular period of time. So for some, uh, for some instances, the actual market prices of any

particular input or output of a project will not reflect the true value of the project’s input or

output. In other instances, there may be no market price at all, and as we’ll introduce in the

course, we’ll often use shadow prices, or accounting price, when the, uh, when market prices

need to be adjusted to reflect the true values.

Here, we have a diagram of a typical conceptual cash flow where we start off initially early on in

the period of an, of a project with a negative cash flow, and as the project continues on, ideally,

those cash flows become positive.

The process to discounting cash flows, and it can be broken down into 3 components:

1. Identification of all cash flows: identifying what they are and when they’ll be.

2. Valuation of these impacts, or cash flows.

3. Comparison: we need to actually compare cash flows with alternative projects, alternative

impacts or projects to our stakeholders. We want to compare different cash flows of projects

and make decisions.

We’re going to focus on this last step of comparing cash flows of different projects

There are 3 possible methods to evaluate cash flows over a life cycle:

1. Future Value analysis - In future value analysis, we choose the project with the largest future

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value, quite naturally, where this future value is one year, or in one year of an amount x, invested at an

interest rate i, and this is denoted by the equation future value equals x times one plus i. Now we also

have future value analysis over multiple years, and this is a situation where interest is compound,

compounded year over year over the previous amount which has accrued.

2. Present Value analysis - Now, in present value

analysis, we choose the project with the largest present value,

PV, where naturally the present value of an amount y received in one year is equal to PV equals to y

over one plus i. Essentially, we’re taking a value in the future and bringing it back to the present.

Similar to future value analysis, present value analysis can have interest compounded annually as

well. The present value of an amount y received in n years, therefore, with interest compounded

annually at i is equal to the following: PV equals y over one plus i to the power of n. And, naturally, by

extension, the present value for a stream of benefits or costs over n years is equal to the present

value of those benefits, which is simply a function of the summation of all benefits, whatever they may

be, over each respective period over one plus i to the power of t, which is the timeline.

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3. Net Present Value analysis - In net present value

analysis, we choose the project with the largest net

present value, which is the sum of present values of all

benefits and costs. And these include all initial

investments at year zero, and usually these projects are

evaluated relative to the status quo. If there is only one new potential project, or one alternative, and

its impacts are calculated relative to the status quo, then the net present value provides us the

additional net benefits over doing nothing, or continuing business as usual. As a result, we have the

following equation for net present value of a particular project

or policy alternative. Now these equations are all covered in

your textbook, and you are encouraged to review them,

how they are derived.

Remember that costs and benefits realized at different timelines can be made comparable by

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