As with pro-con lists, it is still hard to account for every cost and benefit in a cost-benefit analysis. However, it is important to note that this model works well only if you are thorough, because you will use that final number to make decisions. One useful tactic is to talk to people who have made similar decisions and ask them to point out costs or benefits that you may have missed. For instance, by talking to other homeowners, you might learn about maintenance costs you didn’t fully consider (like how often things break, removing dead trees, etc.). Longtime homeowners can easily rattle off this hidden litany of costs (said with experience!).
When writing down costs and benefits, you will find that some are intangible. Continuing the house example, when you buy a house, you might have some anxiety around keeping it up to date, and that anxiety can be an additional “cost.” Conversely, there may be intangible benefits to owning a home, such as not having to deal with a landlord. In a cost-benefit analysis, when faced with intangibles like these, you still want to assign dollar values to them, even if they are just rough estimates of how much they are worth to you. Doing so will help you create a fair quantitative comparison between the courses of action you are considering.
Writing down dollar values for intangible costs and benefits can seem strange—how do you know what it’s worth to you to not have to deal with a landlord? But if you think about it, this is no different than scoring a pro-con list. In the scoring method, if the extra amount you’d have to pay monthly rated a −10 (out of 10) and landlord avoidance rated a +1 (out of 10), then you have a quick way to start an estimate: just take the extra payment amount and divide it by 10. Say the excess monthly payments are expected to be $1,000 per month; then you could estimate it is worth $100 per month to avoid a landlord. Of course, you can pick any numbers that make sense to you.
You can get hung up here because it can feel arbitrary to write down specific values for things that you don’t know exactly. However, you should know that doing so truly helps your analysis. The reason is that you really do have some sense for how valuable things are and putting that (even inexact) sense into your analysis will improve your results. And, as we will see in a moment, there is a method for testing how much these values are influencing your results.
So far, you’ve moved from scoring to dollar values. Next, you graduate to a spreadsheet! Instead of a column of costs and a column of benefits, now you want to arrange the costs and benefits on a timeline. Give each item its own row, and each column in the timeline will now list the cost or benefit created by that item in a given year. So, the first column holds all the costs and benefits you expect this year (in year 0), the next column in year 1, then year 2, and so on. The row for a $2,000-per-month mortgage payment would look like −$24,000, −$24,000, −$24,000, for as many years as the life of the mortgage.
The reason it is important to lay out the costs and benefits over time in this manner (in addition to increased clarity) is that benefits you get today are worth more than those same benefits later. There are three reasons for this that are important to appreciate, so please excuse the tangent; back to the cost-benefit analysis in a minute.
First, if you receive money (or another benefit) today, you can use it immediately. This opens up opportunities for you that you wouldn’t otherwise have. For instance, you could invest those funds right now and be receiving a return on that money via a different investment, or you could use the funds for additional education, investing in yourself. (See opportunity cost of capital in Chapter 3.)
Second, most economies have some level of inflation, which describes how, over time, prices tend to increase, or inflate. As a result, your money will have less purchasing power in the future than it does today. When we were younger, the standard price for a slice of pizza was one dollar; now a slice will run you upward of three dollars! That’s inflation.
Because of inflation, if you get one hundred dollars ten years from now, you won’t be able to buy as much as you could if you had the same amount of money today. Consequently, you don’t want to regard an amount of money in ten years as the equivalent amount of money available today.
Third, the future is uncertain, and so there is risk that your predicted benefits and costs will change. For instance, benefits that depend on currencies, stock markets, and interest rates will fluctuate in value, and the further you go into the future, the harder they are to predict.
Now back to cost-benefit analysis. As you recall, you have a spreadsheet that lays out current and future costs and benefits across time. To account for the differences in value between current and future benefits, you use a mental model we introduced back in Chapter 3: the discount rate. You simply discount future benefits (and costs) when comparing them to today. Let’s walk through an example to show you how it works.
Cost-benefit analysis is arguably most straightforward with simple investments, so let’s use one. Bonds are a common investment option, which operate like a loan: you invest (loan) money today and expect to get back more money in the future when the bond matures (is due). Suppose you invest $50,000 in a bond, which you expect to return $100,000 in ten years. Feel free to make a spreadsheet and follow along.
Cost-Benefit Analysis
Time line
Year 0
Year 1
Year 2
Year 3
Year 4
...
Year 10
Costs
$(50,000)
—
—
—
—
...
—
Benefits
—
—
—
—
—
...
$100,000
Discounted (6%)
$55,859
...
Net benefit
$5,839
...
The only cost today (year 0) is $50,000, to purchase the bond. The only benefit in the future (year 10) is $100,000, what you get back when the bond matures. However, as noted, that benefit is not actually worth $100,000 in today’s dollars. You need to discount this future benefit back to what it is worth today.
Using a discount rate of 6 percent (relatively appropriate for this situation—more on that in a bit), you can use a net present value calculation (again see Chapter 3 if you need a refresher) to translate the benefit of $100,000 in ten years into today’s dollars given the 6 percent discount rate. The formula is $100,000/1.0610 and you get the result of $55,839.
That’s all you need for a relatively sophisticated cost-benefit analysis right there! To finish the analysis, just add up all the discounted costs and benefits in today’s dollars. You have the discounted benefit of $55,839 minus the initial cost of $50,000, netting you $5,839.
You want the net benefit to be positive or else the deal isn’t worth doing, since you’d end up worse off (in today’s dollars). In this case, the net benefit is positive, so the investment is worth considering among your other options.
A central challenge with cost-benefit analysis is that this end result is sensitive to the chosen discount rate. One way to show this sensitivity is through a sensitivity analysis, which is a useful method to analyze how sensitive a model is to its input parameters. Using the $50,000 bond example, let’s run a sensitivity analysis on the discount rate. To do so, you just vary the discount rate and calculate the net benefit for each variation.
Sensitivity Analysis
Discount rate
Net benefit
0%
$50,000
2%
$32,033
4%
$17,556
6%
$5,839
8%
-$3,680
10%
-$11,446
12%
-$17,803
14%
-$23,026
16%
-$27,332
Notice how a seemingly small difference in the di
scount rate can represent a huge difference in the net benefit. That is, the net benefit is very sensitive to the discount rate. While the net benefit is positive at a 6 percent discount rate, it is three times more positive at 4 percent, and it is negative at 8 percent. That’s because at higher discount rates, the future benefit is discounted more. Eventually, it is discounted so much that the net benefit drops into negative territory.
Running a sensitivity analysis like this can give you an idea of a range of net benefits you can expect under reasonable discount rates. You should similarly run a sensitivity analysis on any input parameter about which you are uncertain so that you can tell how much it influences the outcome.
Recall how earlier we discussed the difficulties around putting dollar values to intangible costs and benefits, such as how much not having a landlord is worth. You could use sensitivity analysis to test how much that input parameter matters to the outcome, and how a range of reasonable values would directly influence the outcome.
In general, sensitivity analysis can help you quickly uncover the key drivers in your spreadsheet inputs and show you where you may need to spend more time to develop higher accuracy in your assumptions. Sensitivity analysis is also common in statistics, and we actually already presented another one in Chapter 5 when we showcased how sample size is sensitive to alpha and beta when designing experiments.
Given that the discount rate is always a key driver in cost-benefit analyses, figuring out a reasonable range for the discount rate is paramount. To do so, consider again the factors that underlie the discount rate: inflation (that the purchasing power of money can change over time), uncertainty (that benefits may or may not actually occur), and opportunity cost of capital (that you could do other things with your money). Since these factors are situationally dependent, there is unfortunately no standard answer for what discount rate to use for any given situation.
Governments typically use rates close to their interest rates, which normally move with inflation rates. Large corporations use sophisticated methods that account for their rates of borrowing money and the return on investment seen from previous projects, together resulting in a rate that is usually significantly higher than government interest rates. New businesses, which are highly speculative, should be using much higher discount rates still, since it costs them a lot to borrow money and they are often in a race against time before they run out of money or get eaten by competitors. Thus, the range of acceptable rates can vary widely, from close to the inflation rate all the way up to 50 percent or higher in an extremely high-risk/high-reward situation.
One decent approach is to use the rate at which you can borrow money. You would want your investment returns to be higher than this rate or else you shouldn’t be borrowing money to invest. Note that this rate would typically have the inflation rate already built into it, since credit rates move with interest rates, which typically move with inflation. That is, people loaning you money also want to be protected from inflation, and so they usually build an expected inflation rate into their lending rates.
As investments can look very different based on different discount rates, there are many open debates about which discount rates are most appropriate to use in differing situations, especially when it comes to government programs. Different discount rates can favor one program over another, and so there can be a lot of pressure from different lobbying groups to choose a particular rate.
Another problem occurs in situations where the costs or benefits are expected to persist far into the future, such as with climate change mitigation. Because the effects of the discount rate compound over time, even rather small rates discount far-future effects close to zero. This has the effect of not valuing the consequences to future generations, and some economists think that is unfair and potentially immoral.
Even with this central issue around discount rate, cost-benefit analysis is an incredibly valuable model to frame a more quantitative discussion around how to proceed with a decision. As such, many governments mandate its use when evaluating policy options. In 1981, U.S. President Ronald Reagan signed Executive Order 12291, which mandated that “regulatory action shall not be undertaken unless the potential benefits to society from the regulation outweigh the potential costs to society.’’ This language has been tweaked by subsequent U.S. presidents, though the central idea of it continues to drive policy, with the U.S. federal government conducting cost-benefit analyses for most significant proposed regulatory actions.
One final issue with cost-benefit analysis to keep in mind is the trickiness of comparing two options that have different time horizons. To illustrate this trap, let’s compare our theoretical bond investment from earlier to another bond investment. Our bond investment from before cost $50,000 and returned $100,000 in ten years, which at a 6 percent discount rate resulted in a net benefit in today’s dollars of $5,839.
Our new investment will also be a $50,000 bond investment, though instead of returning $100,000 in ten years, it pays back $75,000 in just six years. The cost today (year 0) for this second bond is again −$50,000. Using the same 6 percent discount rate, the $75,000 benefit six years from now discounted back to today’s dollars would be worth $52,872, for a net benefit of $2,872 ($52,872 − $50,000). This net benefit is less than the net benefit of the first bond investment opportunity of $5,839 and so it seems the first bond is a better investment.
However, if you purchased the second bond, your $75,000 would be freed up after six years, leaving you four more years to invest that money in another way. If you were able to invest that money in a new investment at a high enough rate, this second bond is potentially more attractive in the end. When making a comparison, you therefore must consider what could happen over the same time frame.
In other words, cost-benefit analysis is only as good as the numbers you put into it. In computer science, there is a model describing this phenomenon: garbage in, garbage out. If your estimates of costs and benefits are highly inaccurate, your timelines don’t line up, or your discount rate is poorly reasoned (garbage in), then your net result will be similarly flawed (garbage out).
On the other hand, if you take great care to make accurate estimates and perform relevant sensitivity analyses, then cost-benefit analysis can be a first-rate model for framing a decision-making process, and is in most cases a desirable replacement for a pro-con list. Next time you make a pro-con list, at least consider the scoring method to turn it into a simple cost-benefit analysis.
TAMING COMPLEXITY
When you can list out your options for a decision, and their costs and benefits are relatively clear, then cost-benefit analysis is a good starting point for approaching the decision. However, in many cases, your options and their associated costs and benefits are not very clear. Sometimes there is too much uncertainty in potential outcomes; other times, the situation can be so complex that it becomes difficult even to understand your options in the first place. In either case, you’ll need to use some other mental models to navigate such complexity.
Consider a relatively common situation that homeowners face: the expensive repair. Suppose you want to repair your pool equipment before the summer swimming season. You get bids from two contractors. One bid is from your usual dependable pool service, but it seems high at $2,500. The second bid comes in at a lower cost of $2,000, though this contractor is a team of one, you don’t have a history with them, and they also seem like they might be a little out of their depth.
As such, you get the impression that there is only a 50 percent chance that this contractor will finish at the quoted cost in a timely manner (in one week). If not, you estimate the following scenarios:
A 25 percent chance that they will be one week late at an extra cost of $250 for the extra labor
A 20 percent chance that they will be two weeks late at an extra cost of $500
A 5 percent chance that they will not only take longer than three weeks to complete the job, but also that some of their work will need to be r
edone, totaling extra costs of $1,000
This situation (multiple bids with timing/quality concerns) is very common, but because of the uncertainty introduced in the outcome, it’s a bit too complex to analyze easily with just cost-benefit analysis. Luckily, there is another straightforward mental model you can use to make sense of all these potential outcomes: the decision tree. It’s a diagram that looks like a tree (drawn on its side), and helps you analyze decisions with uncertain outcomes. The branches (often denoted by squares) are decision points and the leaves represent different possible outcomes (often using open circles to denote chance points). A decision tree that represents this pool situation could look like the figure below.
Decision Tree
The first square represents your choice between the two contractors, and then the open circles further branch out to the different possible outcomes for each of those choices. The leaves with the closed circles list the resulting costs for each outcome, and their probabilities are listed on each line. (This is a simple probability distribution [see Chapter 5], which describes how all the probabilities are distributed across the possible outcomes. Each group of probabilities sums to 100 percent, representing all the possible outcomes for that choice.)
You can now use your probability estimates to get an expected value for each contractor, by multiplying through each potential outcome’s probability with its cost, and then summing them all up. This resulting summed value is what you would expect to pay on average for each contractor, given all the potential outcomes.
Super Thinking Page 21
