Cost-Benefit Analysis

A cost-benefit analysis is a process of pricing tangible and intangible features of an option or investment and analyzing decisions. The decision-maker sums the benefits of an option and then subtracts the costs associated with taking that action.

Money is a universal medium of exchange. Apart from some extreme emotional context, a price can be assigned to almost anything. Therefore, we can use the money to price out a benefit and a problem and perform better numerical analysis for a decision problem.

Finally, when you have priced out all the benefits and problems in terms of money, you can subtract the problem costs from the benefit price value. If the result value > 0, then you can choose that option. This metric is called Profitability.

Profitability = Sum of Benefits - Sum of Costs.

There are also other metrics used in cost-benefit analysis, called "Benefit to Cost Ratio".

The Benefit to Cost ratio = Benefit values / Costs.

How to price a benefit?

The idea is that, when you consider a benefit, think that, if the benefit were not available, 'How much money you are willing to pay, just to get this benefit in an option'.

Let's give an example: So, you have 2 choices for selecting an apartment for rent. Location A and Location B. There is a good school around location A, but there is not a good school around location B.

Now, when evaluating location A, think that there were no good schools around the location A. Someone comes up and asks you "Hey, if you pay me some X dollar amount, I can bring a good school around Location A, (like a Magic).". How much money are you willing to Pay to that magician to get that good school around location A.? Maybe you care too much for your kid's education, over anything. You may say, well, I can pay 20000$ to you, give me the school in Location A. If that will be your priority, you can use 20000$ as the value (or importance) of the benefit "Good school".

There is another way you can price out a benefit. Think that you have chosen an option that comes with the benefit. Now, you can sell that specific benefit to someone. After you sell out, you will not have that benefit in your option. How much money will you take to sell out that benefit?

How to price a problem or a missing feature?

Same as a benefit, when you evaluate a problem or a missing feature, ask yourself a question "How much money you are willing to pay, Just to get rid of this problem?". If it is a missing feature, then, ask yourself "How much money you are willing to pay to bring that feature into the option?"

Think about the same Location as a choice problem for your apartment. Say, Location A has an Ice Cream truck sticking around all the time, that you do not like. Because, the Ice Cream truck makes annoying notice, play loud Jingles all the time which can drive you crazy when you plan to sleep.

Now, say, someone shows up and offers you a deal, "Hey, I can convince the ice cream truck owner to move out from your place to another location. But you need to give me some money for that." - How much money are you willing to pay to that agent to get rid of that ice cream truck? This amount will vary for different persons. For example, some people have a high level of annoyance tolerance. They think, well, I can pay at most 500$ to get rid of that noisy ice cream truck. Nothing more. Maybe, someone else who is writing a book, or doing scientific research, may like to avoid all kinds of noise and stay in peace all the time. He may say, "I can pay 10,000$ just to get rid of that truck.". So, you can use that monetary value when evaluating the problem 'Noisy Ice Cream Truck'.

A worked-out example model

Lets model a dilemma about taking a vacation or not.

Start the SpiceLogic Rational Will and click the "Pros and Cons" button.

rational-will-dashboard

The following screen will appear.

pros-cons-start-page

Create some benefits and costs as shown below.

Money In Options Page

Now, it is pricing time.

For the benefits section, the only benefit you listed is "Feel Good". How much money are you willing to pay for getting this good feeling? It should be easy to price out depending on your mood. Say, you did not take a vacation for a long time, and you are exhausted with your stress, then, this price can be a very high number. But, if you are okay to continue work, then, this price may be a small number. Let's assume, for you, this price is 1200$. Enter this amount in the box beside "Feel good".

For Costs section, the first problem we see is "Waste of money". Well, it sounds very easy to price out. Just predict and sum up all possible expenditures associated with that vacation, like plane tickets, hotel costs, meals, etc. Also if you are paid hourly as a contractor, then you can also include how much money you will not be paid when you won't work. This kind of cost is called "Opportunity Cost". Say, you figured, this amount would be 500$.

The next problem is "Waste of time". Hmm, this item may be redundant if you have priced out the opportunity cost already in the "waste of money" section. But, if you did not include the opportunity cost for the time you will be absent, then you can price out the opportunity cost and place it there. Say, that amount will be 800$.

The last item is the "Risk of an accident" or getting sick etc. Of course, you do not want to get sick on a vacation, especially, if your place of vacation is a foreign country. Say, if you get sick (which is also kind of an accident), how much money you think, you will lose (possibly on medical cost or some other opportunity costs). Say, that amount will be 1500$.

Once these numbers are entered, you get a metric "Profitability = Sum of Benefits - Sum of Costs = -1300. This is a negative number, and so, the software is recommending against taking the vacation, as you can see in the screenshot.

model-created-and-analyzed

Uncertainty

But, wait a minute. Should you simply include that 1500$ into the price box of "Risk of an accident"? I think no. Because, it is a risk, which is uncertain. It is not that, every time you go for a vacation, you encounter an accident or get sick. Say, you are predicting that there is a 10% chance of getting sick or an accident.

Check the "Uncertain" checkbox beside the "Risk of accident" item. Then, a probability box will appear. Enter the probability of 10%. Once you do that, an expected value will be calculated and this time, the probability will be higher enough so that, the software will recommend you to take the vacation.

result-with-probability

Last updated on May 28, 2020