# Costs and Benefits.

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Costs and Benefits

Cost-Benefit analysis
Cost-Benefit analysis is a tool for evaluating alternative methods of achieving program results. The objective is to achieve economic efficiency, to find the alternative that produces the greatest benefit for the least cost. It is usually used before a program or project is undertaken to decide whether it should be undertaken, and if so, in what form or at what scale. It is most effective in assessing well defined projects, where the likely costs and benefits can be determined with some precision.

Cost-Benefit analysis
The concept can be useful even for programs whose costs and benefits are not easily quantified, by forcing decision-makers to at least consider the categories of costs and benefits, to define desired outcomes, and pay attention to the choices that are implicit in their decisions. The fundamental rule for cost benefit analysis is: “In any choice situation, select the alternative that produces the greatest net benefit.”

Procedure for Cost-Benefit Analysis
Identify the project or program to be analyzed Determine the impacts of the program, both favorable and unfavorable Assign values (usually monetary) to these impacts, with favorable impacts recorded as benefits and unfavorable impacts recorded as costs

Procedure for Cost-Benefit Analysis
Calculate the net benefit by subtracting the costs from the benefits Choose the alternative which results in the greatest net benefit

For Example….. New headquarters building for the Ministry of Transportation The initial cost of the building is estimated at \$175,000

Benefits are… benefits in form of net savings over the years on energy costs are calculated to be worth \$150,000 savings on maintenance costs that will result from more up-to-date headquarters are estimated to have the value of \$75,000

The net benefit is: 150, , ,000 = \$50,000

The Simple Case In this example the Authority must make a simple yes-no decision, between building the new headquarters with an estimated net benefit of \$50,000 or not building with a net benefit of \$0. Following the fundamental rule, net benefits are maximized if the Authority builds; \$50,000 is larger than \$0

The More Complex Case Suppose that rather than a single proposal for a new headquarters building, the Ministry has before it eight alternative proposals for its capital construction program, ranging from minimal storage facilities to a complete equipment repair facility with laboratories.

The 8 Project Scenario

Project B promises the largest net benefit, \$750,000, and should therefore be chosen.
Do you agree with that?

Project B

Funding is a big problem
Two possible choices Funding is no problem = B Funding is a big problem

Funding is a big problem
Your boss says “I want the project that gives the biggest benefit for the least amount of money” Which project is that? A or C?

Looking at the chart another way…
What do you see?

The 8 Projects Re-sorted in order of Cost

What about Project C? For an initial cost of 200, the net benefit is 600!

For an initial cost of 100, the net benefit is 500!
What about Project A? For an initial cost of 100, the net benefit is 500!

What’s the criteria? The eight alternatives posed were mutually exclusive and quite different alternatives

What’s the criteria? Sometimes alternatives are mutually exclusive because they involve alternative sizes or intensities of what is essentially the same proposal

Discounted cash flow Discounted cash flow valuation (sometimes also called Net Present Value Analysis) is based upon the notion that the value of an asset is: the present value of the expected cash flows of that asset, discounted at a rate that reflects the riskiness of those cash flows

Discounted Cash Flow Example
Money in the bank earns interest, right? If someone gives you a dollar now, you could put it aside (into the bank, etc.) and earn money for a year. At 5% interest, \$1.00 is worth \$1.05 in a year So, about \$0.95 now will be worth \$1.00 in a year, if invested the same way.

Discounted Cash Flow Example
If the one dollar is held for two years, it earns even more interest

Compounding In two years, \$1.00 becomes worth slightly more than \$1.10
In three years, \$1.00 becomes worth almost \$1.16 In four years, \$1.00 becomes worth almost \$1.22, if invested at 5%

Discounting, or compounding in reverse?
The present value of a future asset (like a capital project) is a function of its future cash flows. Future cash flows can be difficult to predict with accuracy, especially quantifying risk as a factor.

So, now what? How does this relate to capital projects?
By comparing the discounted value of the expected future cash flows to the total investment cost, a yes or no decision can be made.

Then investment in the capital project makes economic sense
If the value of the discounted future cash flow is positive (i.e.,net present value is greater than zero) Then investment in the capital project makes economic sense

What can go wrong? Choosing the appropriate discount rate is crucial to making the correct decision. Choosing a rate that is too low (one that values money at below market rates,) will lead to a bad decision. Overly optimistic assumptions about the future usage that will generate the expected revenues leads to bad initial valuation.

What more can go wrong? Failing to account for inflation in the estimates. Discounted cash flow valuation requires positive cash flows some time in the near term, so valuing big capital projects, which are likely to have negative cash flows in the foreseeable future, is likely to be difficult. Then consider trying to actually quantify risk, and the list starts to seem endless…

So, how do you do this stuff?
Really, this is a subject in itself, as is cost-benefit analysis. Look at “Principles of Corporate Finance” by Brealey and Meyers (any edition will do) for actual methods of discounting cash flows. Any finance textbook should cover the subject, or look on the internet. “Cost Benefit Analysis” by Boardman, et.al. is a typical book on the subject

The important point – money from the future is worth less today if you are planning on recovering costs

Quiz! A. As the discount rate increases, the value of an asset increases. True or False?

Answers A. As the discount rate increases, the value of an asset increases False. The reverse is generally true. There is an inverse relationship between interest rate and value, just like bonds.

Quiz! B. As the expected growth rate in cash flows increases, the value of an asset increases. True or False?

Answers B. As the expected growth rate in cash flows increases, the value of an asset increases True. The value of an asset is an increasing function of its cash flows.

Quiz! C. As the life of an asset is lengthened, the value of that asset increases. True or False?

Answers C. As the life of an asset is lengthened, the value of that asset increases (Usually) True. The value of an asset is an increasing function of its life.

Quiz! D. As the uncertainty about the expected cash flows increases, the value of an asset increases. True or False?

Answers D. As the uncertainty about the expected cash flows increases, the value of an asset increases False. Generally, the greater the uncertainty, the lower is the value of an asset.

Quiz! E. An asset with an infinite life (i.e., it is expected to last forever) will have an infinite value. True or False?

Answers E. An asset with an infinite life (i.e., it is expected to last forever) will have an infinite value. False. The present value effect will translate the value of an asset from infinite to finite terms.