Half of Police Homicides are Justified – A Data Analysis

Analysis of all 2019 US police homicides indicates that half are not justified – over 500 individuals per year die unnecessarily at the hands of police.

In 2019, police in the United States killed 1,099 people – and US police are tracking toward 1150 for all of 2020 [1]. While there is no uniform government database for police homicides in the United States, non-profit efforts like Mapping Police Violence have emerged to track the issue. While great work has been done collecting data, I’ve seen no analysis as to whether the homicides are justified. At one extreme, police unions argue that the police are always right – they believe that police homicides have a nearly 100% justified rate. BLM protesters and others argue the opposite – but where does the truth lie? If all police violence were justified, then there’s no reason for concern. As hundreds of videos and photos now show, it appears that the fraction is much lower – necessitating this analysis.

I analyzed fifty 2019 police homicides by hand, reading media reports, reviewing video evidence, and reading police reports. All 1,099 police homicides in 2019 were then analyzed using an automated approach – see the spreadsheet at bottom for the full details [2]. I used calendar year 2019 data, and manually scored 50 homicides using a list of rules as follows:

Rules Used in Manual Scoring: (51% of police homicides determined to be justified using these rules)

  1. Was the deceased provably (video, non-police witnesses) attacking officers or a victim with a firearm? If so, set to 100% justified
  2. Did the deceased kill anyone else prior to or during police intervention?
    If so, set to 100% to justified
  3. Was the deceased armed with a firearm or knife? If so, add 25% to the probability. (Cars, tools, and other implements are not counted here)
  4. According to the police, was the deceased threatening the police or a victim with a weapon? Is so, add 25% to the probability.
  5. According to non-police witnesses or footage, was the deceased threatening the police or a victim with a weapon? If so, add 25% to the probability
  6. Was the deceased shot in the back, while running away, or while driving away? If so, set the probability to 0%. (Shooting at drivers in cars has been proven to be extremely dangerous to the public and to officers, and is outlawed in many countries)

For the automated data analysis, I used only data available within the Mapping Police Violence spreadsheet.

Rules Used in Automated Scoring: (54% of police homicides determined to be justified using these rules, with all data per police reports)

  1. Was the deceased armed in any fashion? If so, add 25% to the probability.
  2. Was the alleged weapon a firearm? If so, add 25% to the probability.
  3. Was the deceased attacking the police or others at the moment they used lethal force? If so, add 25% to the probability.
  4. Was the deceased holding their ground and not fleeing? If so, add 25% to the probability.
  5. Was the deceased fleeing at the moment the police used lethal force, whether by car, foot, or other means? If so, subtract 25% from the probability.
  6. Did the deceased exhibit symptoms of mental illness? If so, subtract 25% from the probability.

Both analyses show that roughly half of all police homicides were found to be justified. When reading through and scoring individual homicides, I noted a wide range of cases ranging from truly heroic action to absurd and ridiculous [3]:

  • Heroic: Killing active assailants engaged in firing on officers or the public
  • Dubious: Shooting suspects in the back or in a car while they were trying to run away or drive away, even when they posed no threat
  • Absurd: A mentally ill person called 911 too many times, resulting in 911 dispatching officers to arrest him for excess calling, leading to his death unarmed and in his own home, after struggling with police

If half of all police homicides are not justified, then police are responsible for over 500 preventable deaths per year. This result cries out for change, even before potential racial inequities are studied! For those who think the police deserve the benefit of the doubt – the numbers indicate that the problem is real, and needs real attention. For those who think the police are always wrong – there are hundreds of instances in 2019 where the police rightly used lethal force. As usual in America these days, the solution is not binary – we need to acknowledge this and take reform seriously, but not to absurdity.

[1] Through August 24th 2020, policed had killed 751 people, according to Mapping Police Violence – that’s through the first 237 days of the year. Multiplying by 365 / 237 to normalize for a full year yields a rate of 1157 homicides per year for 2020 thus far.

[3] It’s important to note that the vast majority of the data for this analysis comes directly from the police. By 2019 anti-police violence protests movements had already gained traction across much of the country, leading police departments to proactively provide evidence when shootings are justified. When a police department refuses to comment or provide evidence on a shooting, the innocent-until-proven-guilty standard should be applied, meaning that the justification percentage is 0% in the absence of evidence.

Could The Fed replace QE with a Basic Income?

Should the Federal Reserve provide liquidity via bank deposits for all Americans instead QE?

The purpose of quantitative easing is to lower interest rates, inject liquidity into the economy, and prevent the collapse of financial markets. It’s the ultimate top down approach to the problem – funnel money into too-big-to-fail financial institutions, and hope that this settles the market’s nerves and trickles down into the real economy.

In a sense, quantitative easing is the ultimate form of trickle down economics – inject money into the wealthiest parts of the  economy to keep them wealthy during a downturn, and hope that this trickles down to Main Street.

During the 2020 COVID19 pandemic the Fed has taken a broader view of its powers than ever before, instituting over a dozen new programs in record time. The Federal Reserve balance sheet hit $7 trillion in 2020, far exceeding total Fed intervention in the financial crisis, and unleashed at unprecedented speed. This has stabilized the stock market, with essentially zero downside for the year after a sharp tumble and equally sharp recovery from February to April. The Fed made this recovery possible by pledging to buy unlimited quantities of securities, and for the first time stepped into multiple new roles, buying individual bonds, buying ETFs, creating a Main Street lending program, and more.

All of this begs the question – why not dispense with all the hijinks and provide liquidity directly to the people, where it’s much more likely to be utilized within the real economy? Various proposals like Andrew Yang’s freedom dividend and others peg the cost of providing $1000/month to American adults at around $2T per year. If the Fed were to engage in such a program, how might it work, and what are the potential benefits and risks?

Potential Structure of a Federal Reserve-Funded Basic Income:

  • The Fed would offer funding for deposits at 0% interest to the banks.
  • Any bank that deposited these funds in equal amounts in every individual account at the bank would receive a 10bp servicing fee for providing this service. The bank would also not be required to repay these funds to the Federal Reserve.
  • The total amount offered to a bank would be dependent on the number of individual customers served by the bank.
  • Safeguards would have to be established to ensure that individuals with accounts at multiple banks only received funds once.

Potential Benefits of the Program

  • Given that individuals have a much higher marginal propensity to consume than banks or corporations, these funds would get spent, thus powering the real economy and GDP growth
  • Banks would be empowered to lend against the deposits on their balance sheet – this is the opposite of what’s happening with reserves that banks have parked at the Fed earning interest
  • The Federal Reserve would still have QE and control of the yield curve in its toolbox, but could use these tools much less, which would result in more normal interest rates across the yield curve.

Potential Risks and Downsides

  • Inflation is the principle risk of such a program – give the people money, and inflation will run wild – right? A basic income of about $500/month would cost $1T per year – this is the same rate of money supply expansion since 2008. The Fed could also use higher interest rates to keep overall money supply growth in check.
  • The Federal Reserve could simply swap this form of money supply expansion for its current use of QE. But individuals might expect this to be a stable, recurring payment – would this rob the Fed of flexibility?

Now that the Federal Reserve has opened Pandora’s box with numerous programs not codified within its charter, it’s time to reexamine a fundamental premise – are these the best ways to inject liquidity into banks? Or should the Fed put the reserves in checking deposits at banks? This serves a dual purpose of both capitalizing the bank and the public at the same time, and with a direct and dramatic impact on the economy. It may sound like heresy, but the ZIRP alternative was not exactly showing great economic growth prospects even prior to the pandemic.

The US is the world leader in innovation – can the Fed break out of the box and consider a program to help all Americans?

List of Warmest Years on Record Globally

9 of the top 10 hottest years globally have occurred over the past decade, when measured using three different global temperature data sets. The top 20 warmest years have all occurred during the last 24 years.

How do the record high temperatures over the spring and summer in the US compare on a global basis? While numerous articles on global temperature trends exist [1], I decided to go to the primary temperature data sources to find out. Below I have created a list of the 20 warmest years on record globally, using three data sets: NASA GISS, the UK Meteorogical Office, and NOAA / UAH [2]. While the three data sets vary in length from 40 to 150 years, the 20 warmest years turn out to have all occurred in the last 24, making it possible to construct an average temperature for the hottest 20 years.

Rank Year Global Avg Temp (F) [3]
1 2010 58.28
2 1998 58.22
3 2005 58.15
4 2007 58.06
5 2002 58.05
6 2009 58.04
7 2003 58.03
8 2006 58.02
9 2011 57.98
10 2004 57.90
11 2001 57.89
12 2008 57.75
13 1995 57.70
14 1997 57.68
15 1999 57.65
16 1990 57.64
17 1991 57.64
18 2000 57.64
19 1988 57.59
20 1987 57.54

Since this is a divisive topic prone to political obfuscation, it’s worth noting that both the NASA Goddard Institute and the UK Meteorological Office officially support the theory of anthropogenic global-warming, while the research scientist responsible for the University of Alabama-Huntsville data set does not support this theory.

[1] This has been a popular topic: Economist, Live Science, ArsTechnica, Science Daily, and Wikipedia

[2] Here are the original data sets:

GISS Data: http://data.giss.nasa.gov/gistemp/tabledata_v3/GLB.Ts.txt and www.movingandstoragesite.com moving and storage

NOAA/UAH: http://vortex.nsstc.uah.edu/data/msu/t2lt/resume builder online/uahncdc.lt

Hadley Meteorological Centre UK: http://www.metoffice.gov.uk/hadobs/hadcrut4/data/download.html#regional_series

[3] The data in this blog post was constructed by averaging data from the three underlying data series. The NASA GISS estimate of global mean baseline temperature of 14 degrees Celsius was used to adjust the temperature deltas provided by the original data series in order to show global mean temperature in Fahrenheit terms here.

Here is my excel spreadsheet with data and calculations.

How High Would Soccer Scores Be With No Goalies?

I’m an American, and while following the World Cup has been interesting, I will admit freely that I mentally tinker with the game as I watch it, since it is so different from most American sports. The big three American sports (football, baseball, and basketball) have higher scoring and are chock-full of statistical record keeping, so that fans can assess their teams’ progress even when scores are low. While I am learning to appreciate the explosive joy that a goal can bring in a game with so few of them, I thought it worthwhile to ask a question: how many goals would be scored in World Cup-level soccer if there were no goalies at all?

According to FIFA, 2.2 goals have been scored per match thus far in the World Cup, though 1-0 has been the most common outcome thus far. While teams have combined for almost 28 shots per match thus far, they have managed only 10.2 shots on target per match thus far. By definition, total goals in a match would thus rise to at least 10 if matches were played without goalies.

But if there were no goalies, game play would be altered in a number of ways. Teams would be more likely to shoot, raising scoring further. Defenders would spend more time in the box as “armless goalies”, so that not all shots-on-target were converted. Even without goalies, the percentage of shots-on-target might not rise dramatically, since the presence of defensive players alters many shots. As an upper bound, assume that total shots per match doubled to around 56, with 35% of shots-on-target (same as today). This yields roughly 20 goals per match, with scores of the 12-8 or 11-9 variety quite normal.

While scores like 12-8 and 14-6 sound astronomically high to the die-hard soccer fan, these are still less than one-fourth of basketball scoring, similar to high scoring baseball games, and about double football scoring. With rules change governing the offside rule or otherwise floated as a way to increase scoring, it’s interesting to note that even a radical proposal would not turn soccer into basketball. It’s difficult to score in soccer, even if there are no goalies!

The True Cost of Gun Ownership

The gun industry generates a total economic loss of $15B per year in the United States.

Guns are a part of American culture, and guns are also a part of the economy in the US. While not a large industry, the small arms and hunting industries contribute roughly $29B annually to the US economy [1]. While many industries have externalities (think pollution), the gun industry’s externalities are particularly damaging: 31,000 deaths and 70,000 injuries per year [2].  From an economic standpoint, the cost-benefit of US gun ownership and the gun industry can be measured by weighing the economic benefit of the gun industry against the economic loss caused by premature deaths and injuries.

What is the annual economic loss associated with 31,000 deaths and 70,000 injuries? By looking at loss of income alone, each gun death can be valued at roughly $1.4M, or $43 Billion in total lost income [3]. A 1994 study published in JAMA concluded that medical costs from gun injuries cost another $2.3B, or $4B today including inflation [4]. The total economic costs of $47 Billion per year from gun industry externalities thus greatly exceed the economic benefit of the industry!

Perhaps this is not surprising. Guns were invented as military weapons, and while hunting and recreation are part of today’s industry, guns’ primary use remains human combat. In the 20th century, the arms industry split into two industries: a hugely profitable defense industry which sells only to the government, and a tiny small arms industry accessible to ordinary American citizens. Despite causing a $15B loss every year to the American economy, the American small arms industry exists because it is protected from its liabilities by the Second Amendment and its political allies.

Can this situation can be improved? The gun industry has thus far successfully resisted efforts at further regulation, and the NRA and other organizations have created a potent political alliance to prevent a change in the status quo. Eventually, an industry with huge negative externalities has to improve its behavior as attitudes shift, or public sentiment and politicians will force the issue (the oil and tobacco industries come to mind). The gun industry would do well to cooperate with reasonable regulations that decrease its negative side effects, or it risks harsher regulations down the road.

[1] The gun industry’s estimated total value in 1999 was $24B, or $29B today when adjusted for inflation.

[2] According to the CDC, there were roughly 31,000 deaths involving firearms (including homicides, suicides, and accidents), and  70,000 non-fatal injuries related to guns annually.

[3] Gun death rates peek in the 18-24 age range, and fall sharply after 30, according to the CDC (select Age under Output Group). Assume that the average person killed by a gun loses 35 years of productive life (from 35-70) . 35 years * US per capita income of roughly $40,000 equals $1.4 Million per person. No NPV adjustment is needed, because gun deaths are cumulative over time – last year’s gun deaths contribute to this year’s losses as well.

[4] This study concludes that the medical costs associated with firearms injuries were roughly $2.3B per year in 1994. Assuming a health care rate of inflation of 4% over the last 15 years (lower than the real rate!), this $2.3B equals $4B in 2009 dollars.

US Defense Spending Is Out Of Control

In the federal budget, there are three untouchable categories of spending: Medicare, Social Security, and Defense. Which of these expenditures has grown fastest over the past decade? While the media is constantly pointing to runaway healthcare spending, defense spending has grown at 10% per year in the past decade, faster than any part of the budget. The Korean and Vietnam Wars were fought on 2/3 the current defense budget, and those were much larger conflicts than Iraq and Afghanistan! In his proposed budget, President Obama has indicated that he will attempt to make defense spending more efficient. Nonetheless, the budget shows defense spending rising from $600 Billion this year to nearly $700 Billion by 2019.

US defense spending during the Cold War (1946-1991) averaged $400 Billion per year in 2008 dollars, including both the Korean and Vietnam wars. By comparison, the 2008 defense budget including the Iraq War and troop surge was $676 Billion. It’s absurd enough that we defeated the Soviets with a much smaller military budget, but proposed budgets increase spending further, when the winding down of the Iraq war should enable a $100 Billion dollar decrease.

Winslow Wheeler at the Center for Defense Information notes that the military budget has doubled while the quantity of weaponry and quality of military readiness has actually declined. Department of Defense accounting is so poor (perhaps intentionally?) that the DoD has no idea how much money is really spent on its weapons programs. Rather than increasing the defense budget, President Obama should consider freezing it at the 2007 level for the balance of his presidency. This would eliminate almost $1 trillion in deficit spending, and would finally force the DoD to focus on accountability and efficiency. A $600 Billion defense budget is still triple that of our potential adversaries’ defense budgets combined, and would ensure our safety while forcing fiscal discipline on an untamed federal department.


[1] $258 Billion in 1998, $676 Billion in 2008 = 10% growth per year. Health care spending and social security also rise rapidly over the same period, but neither grew at this rate. See the following links for data:

http://www.defenselink.mil/comptroller/afr/fy2008/Fiscal_Year_2008_Department_of_Defense_Agency_Wide_Financial_Statements_and_Notes.pdf – Figure 1-5 and 1-6 show actual expenditures for 2008

Click to access tables.pdf

Click to access budget.pdf

[2] $676 Billion in 2008 vs. $400 Billion per year in 2008 dollars during the Cold War including Vietnam and Korea


How Big is the Mortgage Problem?

How big is the bad or “toxic” mortgage and loan problem in the US? Nouriel Roubini says the total losses on US mortgages and loans will be 3.6 Trillion, while the IMF has a lower estimate at 2.2 Trillion. Is there an easy way to gauge the size of this problem and check the veracity of these estimates?

Total US mortgage debt outstanding, including residential, commercial, and farm properties, stood at $14.7 Trillion dollars in December 2008. Of this, $4.9 Trillion in residential mortgage debt is guaranteed by the federal government through Fannie Mae, Freddie Mac, and Ginnie Mae, and does not expose holders of this debt to any risk of loss.

During the depths of the Great Depression, roughly half of all mortgages on homes in major cities were in default. Interestingly, home prices only fell by 20% during the same period, so that even during the Depression, banks could expect to eventually recover 80% of the value of their defaulted loans – and this is assuming 100% financing!

Housing prices are falling more sharply in the current downturn, with Economy.com predicting a peak-to-trough decline of 36%. Mortgage default rates so far have been much lower than the Great Depression, and total defaults across all mortgages are unlikely to exceed 20% during this recession. Assuming a hefty 20% default rate, and an extraordinary 50% drop in home values, banks would still lose only 10% of total loan principal. This would amount to a worst-case $1 Trillion loss in US mortgage lending. According the Federal Reserve, consumer and commercial loans together total another $4 Trillion in principal outstanding. If these loans default at a high rate of 25%, another $1 Trillion in losses would be incurred, for a total of $2 Trillion in US loan losses.

These simple calculations take into account the extraordinary default rates and real estate price drops occurring today, and yet the $2 Trillion in projected losses and is far lower than some economists’ estimates. Perhaps the problem is more tractable than suggested; while $2T is a large sum, it’s much more manageable than the $3-4T predicted by pessimists!

US Debt to exceed GDP by 2015

Here’s a more recent post – the US Debt is now likely to exceed GDP by 2010, next year!

The United States federal debt stands at 10.7 trillion today, or 75% of US GDP. The CBO projects that the US debt will reach 14.6 trillion by 2015, without accounting for the effects of the stimulus package and ongoing bank rescues. These efforts could easily add 1-2 trillion to the total debt, sending the debt over 16 trillion by 2015.

GDP growth may be negative for 2009, and will probably average 2% through 2015 according to CBO projections. Real GDP at the end of 2008 was 14.2 trillion, and is project to rise to 15.8 trillion by 2015, less than the federal debt at that time! Rising inflation may prevent this from happening, but will bring its own set of problems.

Where does a debt load of 100% of GDP put the United States relative to other nations? That would put the US among the top 10 most indebted nations in the world, with peers like Zimbabwe and Italy.

Source Links:

Current US GDP at Bureau of Economic Analysis

US Total Debt at treasurydirect.gov

CBO Budget and Deficit Projections – Click Budget Projections. This xls also includes economic growth estimates.

CIA World Factbook Ranking of Nations by Public Debt

Career Rankings by ROI and salary

A college education has many rewards, but it is primarily an investment, and its return can be calculated by measuring the increase in salary that it brings. While college has many intangible benefits that are difficult to measure, the NPV and IRR of future income can be used to measure its rate of return. Unfortunately, very few comparisons have been done to rank career paths on these metrics.

In the table below, I build on my previous research by ranking 22 different career paths by return on investment. The careers are ranked by Net Present Value and rate of return (methodology explained at bottom). The career rankings take into account numerous factors for each career, including the length and expense of education, salary potential, and unemployment risk.

Career ROI Rankings:

Career Average Salary NPV After-tax earnings (lifetime) Rate of Return
1. Law $124,230 $186,200 $4,709,000 15%
Attorneys rank high on the list since their education is complete just three years after college, and they can step right into six-figure salaries.
2. Chemical, Petroleum, Nuclear Engineering $85,000 $174,100 $3,271,000 19.3%
Petroleum and Chemical engineers step into starting salaries over 60k, leading to a high return on a 4-year education.
3. Pharmacy $98,960 $173,305 $3,833,000 16.5%
Pharmacists typically must complete a six year program before starting work, but high demand for pharmacists enables them to move directly into $90k per year positions upon graduation.
4. Computer Science $83,160 $170,000 $3,335,000 19%
Computer science grads start work immediately after college with salaries above 50k, giving them a fast payback on their investment, but lifetime earnings potential is lower than in some professional fields.
5. Medicine – Specialist $190,000 $148,000 $5,994,000 12.75%
Doctors have always enjoyed good incomes, but their educational investment is so high that it reduces their educational ROI more than is commonly realized.
6. Accounting $69,500 $144,900 $3,038,000 17.9%
Accountants can start work right after college, and their pay increases considerably once they’ve completed their CPA certification.
7. Stockbroker $90,470 $125,600 $3,194,000 16%
Stockbrokers start with a low salary, but can build up to a comfortable 90k with time and effort.
8. Civil / Mechanical Engineering $75,200 $112,000 $2,860,000 16.0%
Civil and Mechanical engineers tend to lag engineers in other fields in terms of income and career ROI.
9. Medicine – Primary Care $161,500 $108,900 $5,246,000 12.2%
Primary Care doctors have an educational investment almost as high as medical specialists, but do not receive commensurate salaries.
10. Physical Scientist (Astronomy, Physics, Chemistry, etc) $78,100 $108,600 $3,177,000 14.7%
Physical scientists have to complete eight years of education before moving into a full time research or academic position.
11. Airline Pilot $148,410 $106,241 $3,279,000 13.75%
Airline pilots must work for years at low paying regional air or charter jobs before making it to a major carrier, but the final payoff is a relatively high salary and reasonable working hours.
12. Nursing (RN) $62,480 $106,170 $2,598,000 16.75%
Nurses can finish training in as little as three years, and earn relatively good salaries right from the start, with job prospects virtually anywhere in the country.
13. Police Officer $50,000 $78,000 $1,748,000 9.6%
Police Officers are well compensated relative to the length of their education, but take risks not associated with most other careers.
14. Biological / Life Scientist $69,175 $71,720 $2,812,000 13.3%
Biological scientists earn lower salaries than their colleagues in physical sciences, but have to undergo the same amount of training.
15. Financial Analyst $81,700 $54,000 $3,042,000 12.20%
While completing an MBA can nearly double a financial analyst’s salary, the high tuition and lost earnings diminish the rate of return.
16. Insurance Underwriter/Appraiser $57,795 $54,000 $2,342,000 13.20%
Insurance underwriters and appraisers enjoy a relatively steady income after college.
17. Architecture $73,650 $50,000 $2,710,000 12.2%
Architects have decent salaries in the long run, but they must first complete a five year Bachelor’s program, and then spend several years as interns before becoming full-fledged architects.
18. Human Resources Specialist $56,740 $25,000 $2,164,000 11.50%
HR Specialists start working quickly, but their salaries don’t rise as significantly as in other careers.
19. Graphic Design $45,340 $18,220 $1,994,000 11.2%
Graphic Designers can start work right after finishing college, but competition for positions is high, keeping salaries down.
20. Psychologists $70,000 $11,000 $2,373,000 10.5%
Psychologists’ long training period and low salary compared to MDs decreases returns significantly.
21. Teaching (K-12) $52,450 -$6,630 $1,930,000 9.6%
Teachers are not particularly well compensated in the US, and since their starting salaries are particularly low, the NPV of an investment in a teaching career is actually negative.
22. English (PhD) $60,000 -$15,250 $2,165,000 9.25%
At the bottom of the rankings are Humanities majors. If an English or Humanities PhD candidate tells you that they didn’t go into it for the money, they’re not lying: this career path has a negative return on investment in income terms.

Annotated spreadsheet with all calculations: HTML | XLS with formulas

Definition of Terms:

NPV: This is the Net Present Value of the student’s investment in education, based on a 10% discount rate. 10% is a common rate of return expected for long-term investments, and it helps provides a fair benchmark of the value of each career path.

IRR: This is the Internal Rate of Return of the educational investment. IRR tends to favor shorter time horizons, so shorter educational paths like engineering are rewarded when measured via IRR.

Lifetime Earnings: This is a simple sum of the lifetime after-tax earnings of each career path from age 18 through age 65.


All salary data was taken from the BLS May 2007 Occupation Employment and Wages Estimates. The BLS data measures only base salaries, and does not include bonuses, profit-sharing, or other similar forms of compensation in its estimates. College was assumed to cost $20,000 per year (this sounds low, but is an average for public and private colleges, after all scholarships, grants, and student work are taken into account). Professional school costs, and graduate and resident stipend data were sourced variously, and are noted in the spreadsheet. Inflation at 2% and progressive taxation are also accounted for in the calculations.

The rate of return for each field was calculated by determining the IRR for each field, taking into account the cost of college and measuring total after-tax gains from age 22 to age 65. The NPV of each career path was also calculated with a discount rate of 10%. Finally, lifetime after-tax earnings were calculated as a simple sum to provide another measure of earnings potential.