# Posts for Tag: calculator

### Greenhouse gas emissions from airplane flights

Posted In: Environment | Transportation

#### Traveling by airplane produces significant greenhouse gas emissions

Flying in an airplane is likely the most greenhouse gas intensive activity you can do.  In a few short hours, you can can travel thousands of miles across the country or ocean.  It takes a large amount of fossil-fuel energy (oil) to lift an 80+ ton airplane off the ground and propel it at 600 miles per hour through the air.  Every hour of travel (in a Boeing 737) consumes around 750 gallons of jet fuel.

Even when dividing the fuel usage across all of the passengers (and cargo) of an aircraft, airplane travel consumes a significant amount of fuel per passenger.  The fuel economy is estimated to be about the same as a fairly efficient hybrid car driven by one person (60-70 passenger miles per gallon).  However, because you can go 10 times faster and much further more easily than you would in a car, airline travel can, on an absolute basis, emit larger amounts of greenhouse gases. In fact, an individual passenger’s share of emissions from a single airplane flight can exceed the annual average greenhouse gas emissions per capita from a number of countries (and the global average).

The following flight calculator and data visualization shows the miles and emissions produced per passenger by a airplane trip that you can specify.  Choose two airports that you are interested in and click the “Calculate Flight Emissions” button to see the emissions associated with a round-trip flight between these two cities.  The map will show you the flight route and also shows you the countries in the world where this one single round-trip flight produces more emissions per passenger than the average resident does in one year from all sources (annual per capita emissions).

In addition to individual countries, the tool also compares the flight’s per passenger emissions to the global average emissions per capita in 2017 (4.91 tonnes) and the emissions required to achieve a 22℃ climate stabilization in 2030 (3.08 tonnes) and in 2050 (1.37 tonnes). These 2030 and 2050 numbers are based on an International Energy Agency scenario.

#### Calculations of Airplane Emissions

The emissions calculated by this calculator are based on calculations from myclimate.org, a non-profit environmental organization.
The fuel consumption of a jet depends on the size of the aircraft and distance traveled, but takeoff and climbing to cruising altitude are particularly fuel-intensive. On shorter flights, the takeoff and initial climb will constitute a greater proportion of the total flight time so fuel consumption per mile will be higher than on longer (e.g. international) flights.

The detailed methodology is described in more detail in this document.

In addition to emissions of CO2 from the burning of jet fuel, jets also emit other gases (including methane, NOx, and water vapor) which can also contribute to warming (also known as “radiative forcing”). Because the emissions are occurring at high altitude, these gases can have different impacts than those at lower altitude. A number of studies have estimated the impact of these other gases can significantly contribute to the overall radiative forcing and have somewhere between 1.5 and 3 times the impact that the CO2 alone would. A number of studies, including the myclimate calculator use a factor of 2 to account for these non-CO2 gases and their warming impact, and that is what is used in this calculator as well.

Unlike cars, trucks and trains, it is much harder to power airplanes with batteries and electricity and producing low-carbon jet fuels from biomass is proving very challenging.

In order to achieve climate stabilization at 2 degrees C, global emissions need to basically go to zero over the next 40 years. With a growing global population, this means that the allowable emissions per person will shrink rapidly over these coming decades.

Ultimately, while aviation is a small part of global greenhouse gas emissions, it is a larger part of emissions in richer countries (i.e. if you are reading/viewing this post). And there are many in these richer countries who fly a disproportionate amount and therefore contribute a disproportionate amount of emissions. Hopefully, putting airplane travel in this context can help us better understand the impact of our actions and choices and maybe even change behavior for some.

Tools and Data Sources
The calculator estimates flight emissions based on the myclimate carbon footprint calculator. Data for CO2 emissions by country was downloaded from the European Commissions’s Emissions Database for Global Atmospheric Research. The map was built using the leaflet open-source mapping library in javascript.

### Visualizing the 4% Rule, Trinity Study and Safe Withdrawal Rates

Posted In: Financial Independence | Money

#### Instructions for using the calculator:

This calculator is designed to let you learn as you play with it. Tweaking inputs and assumptions and hovering and clicking on results will help you to really gain a feel for how withdrawal rates and market returns affect your chance of retirement success (i.e. making it through without running out of money).

• Spending and initial balance – This will affect your withdrawal rate.  The withdrawal rate is really the only thing that is important (doubling spending and retirement savings will still yield the same success rate).
• Asset allocation – Raise or lower your risk tolerance by holding more or less stock vs bonds
• Adjust retirement length – This affects the number of historical cycles that are used in the simulation, but also increases risk of failure.
• Add tax rates and investment fees – these will put a drag (i.e. lower) market returns and lower success rates

Options for Visualization:

• Display all cycles – this is the mess of spaghetti like curves that show all historical cycle simulations
• Display percentiles – this aggregates the simulations into percentiles to show most likely outcomes
• Hover/Click on legend years – this will allow you to highlight a single historical cycle (you can also use the arrow keys to step through historical cycles)
• Bottom graph can show either the sequence of returns (with average returns in 5 year periods) for a single historical cycle or distributions of returns in our historical data (1871 to 2016) and a single historical cycle.  You can choose to look at returns for stocks, bonds or your specific asset allocation.
• The graph on the right shows a histogram of the ending balance of each historical cycle and color codes them to show percentiles.

#### What is the 4% Rule?

The 4% rule is a “rule of thumb” relating to safe retirement withdrawals.  It states that if 4% of your retirement savings can cover one years worth of retirement spending (an alternative way to phrase it is if you have saved up 25 times your annual retirement spending), you have a high likelihood of having enough money to last a 30+ year retirement. A key point is that the probabilities shown here are just historical frequencies and not a guarantee of the future. However, if your plan has a high success rate (95+%) in these simulations, this implies that retirement plan should be okay unless future returns are on par with some of the worst in history.

The overall goal of this rule and analysis is identifying a “safe withdrawal rate” or SWR for retirement.  A withdrawal rate is the percentage of your money that you withdraw from your retirement savings each year.  If you’ve saved up $1 million and withdraw$100,000 each year, that is a 10% withdrawal rate.

The “safe” part of the withdrawal rate relates to the fact that if your investments generally grow by more than your annual spending, then your retirement savings should last over the length of your retirement.  But average returns do not tell the whole story as the sequence of returns also plays a very important role, as will be discussed later.

One way to test this is through a backtesting simulation which forms the basis for the “Trinity Study”.

#### What is the Trinity Study?

The “Trinity Study” is a paper and analysis of this topic entitled “Retirement Spending: Choosing a Sustainable Withdrawal Rate,” by Philip L. Cooley, Carl M. Hubbard, and Daniel T. Walz, three professors at Trinity University. This study is a backtesting simulation that uses historical data to see if a retirement plan (i.e. a withdrawal rate) would have survived under past economic conditions.  The approach is to take a “historical cycle”, i.e. a series of years from the past and test your retirement plan and see if it runs out of money (“fails”) or not (“survives”).

#### How do you test withdrawal rate?

Given modern equity and bond market data only stretches back about 150 years, there is some, but not a huge amount of data to use in this simulation.  One example of a 30 year historical cycle would be 1900 to 1930, and another is 1970 to 2000.  The Trinity study and this calculator tests withdrawal rates against all historical periods from 1871 until the present (e.g. 1871 to 1901, 1872 to 1902, 1873 to 1903, . . . . 1986 to 2016).  Then across this 115 different historical cycles, it determines how many of these survived and how many failed.

The thinking is that if your retirement plan can survive periods that include recessions, depressions, world wars, and periods of high inflation, then perhaps it can survive the next 30-50 years.

The 4% rule that comes out of these studies basically states that a 4% withdrawal rate (e.g. $40,000 annual spending on a$1,000,000 retirement portfolio) will survive the vast majority of historical cycles (~96%).  If you raise your withdrawal rate, the rate of failure increases, while if you lower your withdrawal rate, your rate of failure decreases.

The goal of this tool is to help you understand the mechanics of the a historical cycle simulation like was used in the Trinity Study and how the 4% rule came to be. This understanding can help you better plan for retirement with the uncertainty that goes along with planning 30+ years into the future. If you want to also see how longevity and life expectancy play a role in retirement planning, you can take a look at the Rich, Broke and Dead calculator.

This post and tool is a work in progress. I have a number of ideas that I will implement and add to it to help improve the visualization and clarity of these concepts.

#### If 4% is a conservative rate, what is the maximum withdrawal rate?

The future is unlikely to be identical to any of the set of historical cycles that are used in this simulation. And yet, there are enough years of data that there are a fairly large set of possible outcomes from running a simulation with this input data. One way to understand this variation is to see in the main graph above that the ending balance can potentially vary by more than $5 million dollars on an inflation adjusted basis on a starting balance of$1 million.

Another way to see this same variation in market returns is by looking at maximum withdrawal rate. This is the highest amount that you could withdraw annually over your retirement and (just barely) not run out of money by the end of your retirement.

This graph shows the maximum withdrawal rate for a given historical cycle (i.e. 1871 to 1901). For example, in the 1871 to 1901 30 year historical cycle, you could have used an 8.8% withdrawal rate (inflation adjusted $80,000 withdrawal annually on a$1 million initial investment balance) and not run out of money. This is because the sequence of market (stock and bond) returns in this historical cycle were able to (barely) outpace the rate of withdrawals at the end of the 30 year retirement period. Many other cycles show lower successful withdrawal rates, because those cycles had poorer sequences of returns, while some had higher maximum withdrawal rates.
The graph also highlights those cycles that show a maximum withdrawal rate below 4% in red, while all others are shown in green. Most of these withdrawal rates are well over 4%, with some quite a bit higher. This again shows that if the future is somewhat like one of these historical cycles, most likely a 4% withdrawal rate will be enough for you to retire without running out of money and that it is likely that you could end up with more money than you started.

Data source and Tools Historical Stock/Bond and Inflation data comes from Prof. Robert Shiller. Javascript is used to create the interactive calculator tool and the create the code in the simulations to test each historical cycle and aggregate the results, and graphed using Plot.ly open-source, javascript graphing library.

### Visual Guide to Understanding Marginal Tax Rates

Posted In: Money

##### What is a marginal tax rate?

There is a fair amount of confusion about what a marginal tax rate is and how it affects how much tax you would owe the government on a certain amount of income. These graphs are here to help you better understand the difference between a marginal and average tax rate and to easily calculate these rates for specific examples in the US context. This tool only looks at US Federal Income taxes and ignores state, local and Social Security/Medicare taxes.

Marginal tax rates are the rate at which an additional dollar of income will be taxed at. There are different tax brackets (each with its own marginal rate) depending on which dollar of income you are looking at. This is very different from the Average (or effective) tax rate that is the result of applying these marginal tax rates across all of your income.

#### **Click Here to view other financial-related tools and data visualizations from engaging-data**

Instructions for using the visual tax calculator:

• Select filing status: Single, Married Filing Jointly or Head of Household. For more info on these filing categories see the IRS website
• Select percentage of regular income vs capital gains income. Regular income is wage or employment income and is taxed at a higher rate than capital gains income. Capital gains income is typically investment income from the sale of stocks or dividends and taxed at a lower rate than regular income.
• Move your cursor or click on the graph to select a specific income Make sure you note that the x-axis is a logarithmic-scale, meaning that income grows exponentially as you move to the right.
• Choose your graph preference One graph (Individual Tax Brackets) shows the individual tax brackets and how much of your income is taxed at the different marginal rates. The other graph (Aggregate Rates) shows the net result of applying the different rates to get your effective rate.
One of the most interesting things is to vary the proportion of regular income vs capital gains taxes. Generally, wealthier households earn a greater fraction of their income from capital gains and as a result of the lower tax rates on capital gains, these household pay a lower effective tax rate than those making an order of magnitude less in overall income.

Here are two tables that lists the marginal tax brackets in the United States in 2019 that form the basis of the calculations in the calculator. 2018’s numbers are pretty similar.

US Tax Brackets and Rates for 2019
Rate Single
Taxable Income Over
Married Filing Joint
Taxable Income Over
10% $0$0 $0 12%$9,700 $19,400$13,850
22% $39,475$78,950 $52,850 24%$84,200 $168,400$84,200
32% $160,725$321,450 $160,700 35%$204,100 $408,200$204,100
37% $510,300$612,350 $510,300 You can see that tax rates are much lower for capital gains in the table below than for regular income (table above). Capital Gains Brackets for 2019 Single Capital Gains Over Married Filing Jointly Capital Gains Over Heads of Households Capital Gains Over 0%$0 $0$0
15% $39,375$78,750 $52,750 20%$434,550 $488,850$461,700
For those not visually inclined, here is a written description of how to apply marginal tax rates. The first thing to note is that the income shown here in the graphs is taxable income, which simply speaking is your gross income with deductions removed. The standard deduction for 2019 range from $12,200 for Single filers to$24,400 for Married filers.
• If you are single, all of your regular taxable income between 0 and $9,700 is taxed at a 10% rate. This means that your all of your gross income below$12,200 is not taxed and your gross income between $12,200 and$21,900 is taxed at 10%.
• If you have more income, you move up a marginal tax bracket. Any taxable income in excess of $9,700 but below$39,475 will be taxed at the 12% rate. It is important to note that not all of your income is taxed at the marginal rate, just the income between these amounts.