The road to wisdom? Well, it's plain and simple to express. Err and err and err again, but less and less and less.
Figure 1: Accounting Must Be Accurate to Run the Business Properly (Photo: www.business.rutgers.edu).
It has been reported that 90% of spreadsheets have serious errors (source). These errors occasionally are large enough that they have international implications (e.g. London Whale). In my small part of the world, one small company I worked at had an error in a cost estimation spreadsheet that cost it hundreds of thousands of dollars on one contract. This error caused that company great hardship.
My son is an accountant who provides taxation and accounting online services to individuals and firms. He recently told me about a spreadsheet that had no documentation as to how it was supposed to work, but it clearly was not working properly. I realized how important the knowledge of accounting practices could be for accountants or CPA businesses who are looking to buy accounting firm at a wholesome level as it would help their business focus on minute details such as these. Coming back to the point, some of the results which the spreadsheet generated made no sense and the problems could be seen using dimensional analysis. In fact, he compared his spreadsheet debugging with the stoichiometry he learned when he was in chemistry class. He was correct – dimensional analysis and stoichiometry are closely related.
I use Excel spreadsheets for much of my financial work and, like all software, it is very difficult to ensure that the results produced by spreadsheets are correct. Many businesses use dedicated software like lease accounting software to deal with this aspect of their finances in order to improve their workflow and other monetary expenses in regards to their venture. The importance of such an application or even something as integrated as a Top staff expense management software is not something that can be undermined. These applications prove beneficial to the business owners, but I, as an individual, work at it differently. My standard approach is to first perform a dimensional analysis of the spreadsheet formulas to ensure unit consistency. My son also used dimensional analysis to immediately expose a couple of problems with this spreadsheet.
The spreadsheet calculates (among other things), the year-over-year electrical cost changes (called variances) due to different factors. Figure 2 shows my simplified version – the variances should all be in $s. The parameters involved are:
NThisYear is the number of tons produced this year
NLastYear is the number of tons produced last year
ELastYear is the number of megawatts consumed last year
EThisYear is the number of megawatts consumed this year
CThisYear is the total electrical expense this year
CLastYear is the total electrical expense last year
ΔVolume is the cost variance attributable to changes in production volume
ΔEfficiency is the cost variance attributable to changes in electrical efficiency
Figure 2: Dimensional Analysis Reveals a Spreadsheet Error.
The fix was simple and is shown in Figure 3. It turns out that the error was in the same fraction for both variances. The spreadsheet author had flipped the numerator and denominator of the megawatts per ton term.
Figure 3: Quick Fix for the Formulas.
This was the first time my son had used dimensional analysis for an accounting problem and it made quick work of the issue.
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Start where you are. Use what you have. Do what you can.
Figure 1: Nice Demo of the Pythagorean Theorem.
You might be amazed the amount of math anxiety I deal with at work. Non-engineering folks often stop by my cube for help – I always try to help because I remember how I felt when I was in school and did not understand any math.
Usually, the math question comes in phrased as an issue with an Excel spreadsheet, which people seem more willing to ask questions about than a simple algebra problem. Make no mistake about it – the Excel questions are almost all really algebra questions. For example, I was recently asked how to create an Excel spreadsheet to compute the gross value of check given that the tax rate and net value are known. This really is an algebra problem, but it was phrased as a spreadsheet issue.
A simple geometry question walked into my cube this morning. I saw real fear on this person's face – he needed to use the Pythagorean theorem to determine some dimensions. He was very upset. You could see that he must have been traumatized by the Pythagorean theorem at some time in the past. I have dealt with this sort of trauma in my own family.
The employee wanted to know why the Pythagorean theorem worked and to apply it. My approach was to walk through a classic demonstration that I had seen on Stack Exchange, which I show in Figure 2. The employee seemed to appreciate this demonstration.
Figure 2: Classic Proof of the Pythagorean Theorem.
I then worked through some examples of how to apply the theorem and he went away smiling.
After all these years, I still do not understand what it is about math that creates such tremendous fear in people.
When you’re young, you look at television and think, there’s a conspiracy. The networks have conspired to dumb us down. But when you get a little older, you realize that’s not true. The networks are in business to give people exactly what they want. That’s a far more depressing thought.
Figure 1: British Soldiers Blinded By Chemical Weapons During WW1.
I sat down tonight and watched the History Channel, which was showing a documentary called "WW1: The First Modern War". This is an excellent multi-part series, with tonight's topic being called "Clouds of Death" and it was about the first use of chemical agents as weapons.
The show reminded me of a man I met when I was a boy (early 1970s) and I worked in a nursing home as a night janitor. At the home, we had many WW1 veterans. I will never forget one WW1 veteran who had been permanently disabled during a chemical attack. I do not know what gas he was exposed to (he mentioned chlorine gas, mustard gas, and phosgene), but I do know he had a bad case of emphysema that made his life miserable.
I learned about this gentleman's history after we had a chemical poisoning incident at the nursing home. The incident involved a nurse who mixed cleaning chemicals together, which I would argue NEVER should be done. The nurse had decided that a shower needed to be cleaned really well and it seemed like a good idea to mix chlorine bleach and an ammonia-based cleaner. Unfortunately, this mixture created a gas that sickened the nurse. The chemical reaction is rather complex, so I will refer to Ann Marie Helmenstine's excellent discussion of the topic. Some folks have inadvertently hurt themselves by mixing bleach with toilet bowl cleaner, which can generate chlorine gas (reference). Chlorine gas is also generated when mixing vinegar and bleach, another common source of cleaning agony. For the details on the chemistry behind these safety hazards, see another of Ann Marie's posts.
The nurse recovered, but it was a talk of the nursing home for days. Occasionally, you will read an article about someone dying because of their mixing of cleaning chemicals, but this is rare.
Sorry for the length of time involved in the domain transfer. I THINK everything is back. I will not go into all the gory details, but every post needed some work (latex did not transfer cleanly). This post is being sent to test out email notifications. Hopefully, this is the last function that I need to get working.
mathscinotes
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You can get help from teachers, but you are going to have to learn a lot by yourself, sitting alone in a room.
Figure 1: Common Drawer Pull.
I finished building a cabinet a couple of months ago just as the extreme cold arrived, which made my garage shop uninhabitable.. The ten-day forecast is now showing rising temperatures, so I am starting to think about my next cabinet construction effort.
One task I never like doing is putting on the drawer pulls (e.g. Figure 1). I always worry that I could be making a simple arithmetic measurement error that will result in a ruined drawer − yes, I have made this kind of error . While reading Fine Woodworking magazine (membership required), I just saw a simple layout method that I think is simple enough that I won't need to be quite so worried going forward. Woodworkers often prefer to use geometric constructions rather than measurements and arithmetic because it is too easy to make errors. For example, my most common measurement error occurs when I "burn an inch" − which means measuring from the 1 inch mark instead of from the less precisely defined end − and then I forget to subtract an inch from my measurement.
Figure 2 is a sketch I made of how the layout is drawn. You draw four lines whose endpoints are marked using the gray-shaded drawer pull locations. The intersections of the lines mark the points where I will mount the drawer pull.
Figure 2: Drawer Pull Layout Construction.
While this method is focused on a single, centered drawer pull, I am starting to think about generalizations for other pull configurations. As I come up with them, I will record them here.
If you want to be happy, think of something to be grateful about.
I had a deja vu moment this week. Yahoo had an article on how a large amount of manganese nodules have been found on the Atlantic Ocean's seafloor (Figure 1). Back in the 1970s, I remember reading about Howard Hughes building the Glomar Explorer to mine manganese nodules from the bottom of the ocean. It turned out this story was a CIA cover story for Project Azorian, but that is another tale.
Figure 1: Manganese Nodules on the Atlantic's Seafloor.
While these nodules exist in all the world's oceans, the bulk have been found in the Pacific Ocean.
Figure 2 gives you an idea of the size of these nodules.
Figure 2: Nodule Cross-Section.
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I hope that after I die, people will say of me: "That guy sure owed me a lot of money."
Introduction
Figure 1: Percentages of People with No Retirement Savings By Age Group (Data from Federal Reserve).
I have had a number of posts recently on saving for retirement. These posts ALWAYS follow discussions I have had with my family on the importance of starting to invest early – both for retirement and general financial health. I do not want my family members to get to retirement without an investment portfolio (Figure 1), a situation that I have seen and is not pretty.
Yesterday, my wife was told at an investment seminar that we should have 11 times our annual income in retirement savings. I know. I was surprised by this too. That figure is crazy if you come to think about it. Unless you have made the decision to check out 1822 direkt im Test to see how this route can help to improve your financial situation in time for your glorious retirement years, it is going to be very hard for you to achieve otherwise. Although, come to think of it, 11 times our annual income is a crazy figure to wrap my head around.
In fact, the same day, I saw an article on the Fidelity web site that recommended 8 times our annual income in retirement savings. As for me, I routinely tell my sons that they will need at least 20 times their annual incomes. Each of these rules is correct in the proper circumstances.
There is no mystery here – as I always say, the answer to all life's interesting questions is "It depends ...".
Background
Objective
I will demonstrate how to derive these retirement multiples for yourself using some basic financial mathematics. This knowledge will allow you to change the assumptions as you require for your situation and you can make your own retirement multiple rule of thumb.
Analysis Caveats
My focus here will be on 401K retirement plans because I want to make sure that my sons take advantage of their employers matching plans. Since 401K plans use deferred income, this income is subject to taxes. My analysis assumes that your retirement tax rate is the same as your working tax rate. That may or may not be true.
For example, many retirees have paid off their home mortgage and do not have mortgage deductions anymore. They may have other deductibles, however, such as how many British Seniors have a payment for life insurance to consider to name but one example. Still, keeping your personal situation in mind is important for such calculations.
I do not model the effect of inflation once you have retired. We now see people retired for twenty to thirty years and inflation will have an impact.
Young people need to decide if they think Social Security will be there for them. I sometimes wonder if it will be there for me. My sons should plan as if it will not be there. It is also important for them to think about how their health coverage will change as they get older, they will need to factor that into their monthly cost of paying for medical care so they are prepared for any additional expenses.
Definitions
There are some terms that will be important in the analysis to follow.
Retirement Multiple (Symbol: M)
The amount of retirement savings needed at the time of your retirement is expressed as a multiple of your working income at the time you retire. So if you make $100K annually at the time you retire and you have saved $800K, your retirement multiple is 8.
Replacement Income Percentage (Symbol: KR)
The percentage of your working income that you will require during retirement. For the discussion here, I will assume that you need 85% of your working income while in retirement. I base this number on my assumption that at the time your retire you will be putting 15% of your working income into retirement investments and these investments will cease when you retire.
Number of Annual Payments (Symbol: N)
The number of investment payments made per year. I will assume one payment month or 12 per year.
Number of Years in Retirement (Symbol: Y)
For this calculation, I will assume my pension investment must provide a fixed income for 25 years, say from age 67 to age 92 − no one lives forever.
Annual Rate of Return (Symbol: RA)
This is the rate of return I expect on my retirement investments annually. For my analysis here, I will assume RA =6.0%, which is a commonly used value.
Rate of Return Per Payment (Symbol: R)
This is the rate of return per payment period, which is given by the formula .
Inflation Factor (Symbol: KI)
This represents the loss of purchasing power per dollar from the time of retirement planning to retirement. I will assume that you will plan your retirement at age 30 and retire at age 67 − the case for one of my sons. I will also assume that you will average 2.3% annual inflation over your work life. Some RM values assume inflation while others do not.
Non-Investment Income Percentage (Symbol: NI)
Many retirees will have Social Security income or pensions. This income will reduce the amount of money you need to get from your investments. Note that Social Security payments are adjusted for inflation and pension payments are usually not. Some RM values assume non-investment income and others do not.
Analysis
I will be using Mathcad's Present Value (PV) function for the following work, however, Excel has the same function and you can easily perform the following analysis using Excel's PV and goal seek functions.
Formula Derivation
Figure 2 shows how to derive the key relationship for determining your retirement multiple, which really is just the standard present value formula for an annuity due. The formula I will be using is highlighted in yellow.
Figure 2: Derivation of Retirement Planning Formula.
Derive 8x Rule
We can compute RM = ~8 by assuming a nominal non-investment income (NI=25%) and no inflation (KI=1). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~8.
Figure 3: Calculation of 8x Retirement Multiple.
An M=8 is appropriate for people near retirement who expect Social Security and pensions. Since these folks are near retirement, inflation will not have time to significantly impact your planning.
Since few people receive more than $2K per month in Social Security, this calculation means that your retirement income is capped around $96K per year, which is a lot for a retiree.
Derive 11x Rule
We can compute RM = 11 by ignoring non-investment income (NI=0) and inflation (KI=1). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~11.
Figure 4: Calculation of 11x Retirement Multiple.
M=11 is appropriate for people who are near retirement and do not want to count on any Social Security income. It is a conservative approach to retirement planning, but can be justified.
Derive 20x Rule
We can compute RM = 20 by assuming a nominal non-investment income (NI=25%) and inflation (). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~20.
Figure 5: Calculation of the 20x Retirement Multiple.
M=20 is appropriate for young people that will be investing for many years and will experience significant inflation. This number also assumes Social Security will be there for them, which may not be the case.
Conclusion
This quick post summarizes discussions that I had with my wife and sons on retirement planning. I hope it prods some of you into looking at your retirement plans.
Posted inFinancial|Comments Off on Retirement Savings Rules of Thumb
"Life is like a snowball and all you need is some wet snow and a really long hill."
Figure 1: Ronald Read (left), Superinvestor.
Because I am an annoying father who wants to encourage his sons to invest, one of the things I like to collect on this blog are stories of successful, long-term, investors. I loved this story about a janitor, Ronald Read (Figure 1), who recently died at 92 and left an estate worth nearly $8 million dollars. This goes to show how great investing can be if done correctly. It doesn't have to be a lot, as little bits here and there can make a magnitude of difference. I know someone once who decided to look into finding the best helium miner 2021 to mine helium with and never did he expect to make as much money as he did in passive income. But it happened. This built over time, of course, and he was able to use this money to help create a financially stable future for himself, and it's all because he decided to make an investment. So many people want to get into the investment way of life but do not know where to start. They could start off by consulting a financial advisor, who might be more fit to navigate through the confusion that surrounds the multitude of ways money can be invested. And there are SO MANY options. We now have digital currencies that people are hot on investing and trading in, so as long as the right questions are being asked such as "which trading platform is best for me?", "can you buy crypto on commsec?", "am I able to invest in multiple areas?", then people can start making that money. What if I told you that people can also invest in casino sites? Yes, you read that correctly. Cryptocurrency has now made its way to online casinos, thanks to technological advancements. Indeed, DeFi tokens such as Crypto Snack are available for gambling enthusiasts who can invest in crypto, and play using them. This could be a fun and modern way to invest in digital currency.
However, he earned his fortune the old-fashioned way through conservative investing practices and living a frugal life. As far as his portfolio went, Newsmax reported that
Read's investments included shares of AT&T, Bank of America, CVS, Deere, General Electric and General Motors. "He only invested in what he knew and what paid dividends. That was important to him," his lawyer, Laurie Rowell, told CNBC.
Through regular contributions over a long time, he used the power of compound interest to amass an amazing amount of money. His investment approach epitomized the "snowball" approach that Warren Buffet advocates (see quote that leads this post). To illustrate that even small amounts of money regularly invested over a long-period of time can add up, Newsmax and CNBC both stated that
For example, to reach Read's $8 million fortune, Hogan [a financial analyst] calculated that investors would have to invest about $300 a month at an 8 percent interest rate over 65 years.
I illustrate this compound interest calculation below using Mathcad's Future Value (FV) function – Excel has a similar FV function.
Figure 2: Future Value Calculation.
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"When a revolutionary succeeds, he should be given five years then shot, or otherwise removed."
Introduction
Figure 1: Typical Bathroom Ventilation Scenario.
I was so happy with my previous fan installation that I am considering replacing some old fans with new, higher throughput, and quieter fans. The installations will be similar to that shown in Figure 1.
I have been using a nomograph (Figure 2) for my home HVAC calculations (example). I have decided that I am now living in the 21st century and I should figure out the formula that this graph represents. In this post, I will generate part of this nomograph to verify that I have put together the correct formula.
Background
Figure 2 shows the nomograph that I want to calculate for myself using the Darcy-Weisbach formula.
Figure 2: Air Flow Versus Static Pressure Drop.
The chart makes certain assumptions.
100 foot duct length
Fixed temperature, altitude, and humidity values that are unstated
No duct roughness factor stated
I will make some reasonable guesses and compute my version of the nomograph.
Analysis
I wanted a formula that would allow me to change the temperature, humidity, and air density. Figure 1 shows my calculation setup and how I determined the Reynolds number of the air. The model in Figure 1 for air density and specific humidity is rough. I show an alternative form in Appendix A that appears to be a bit more accurate. It does not make a huge difference in my final result.
Figure 3: Calculation Setup and Reynolds Number Determination.
Now that I have the Reynolds number, I can compute the Darcy friction factor and define my Darcy-Weisbach formula (Figure 4).
Figure 4: Creation of Functions for Graphing.
Now that I have my flow volume and velocity formulas defined, I can plot them (Figure 6) in the same manner as Figure 2. I did not plot every case shown in Figure 2 because it would take too long. However, I am quite confident that I have a formula that is close to the same one that was used to compute the graph in Figure 2.
Figure 6: Generate My Version of Figure 2.
Conclusion
I now have a formula that I can use in place of the graph shown in Figure 2. This will be more convenient for me in the analysis work that I have coming up.
Appendix A: Alternative Approach for Computing the Density and Specific Humidity of Moist Air
I worked the moist air density and specific humidity problems a couple of ways and this is one alternative (Figure 7) that I investigated. They do not give exactly the same answers, but the results are similar.
Figure 7: Alternative Approach for Computing Density and Specific Humidity of Moist Air.
"I've missed more than 9000 shots in my career. I've lost almost 300 games. 26 times, I've been trusted to take the game winning shot and missed. I've failed over and over and over again in my life. And that is why I succeed."
I saw an interesting article on Yahoo Autos about 9 car models in which zero drivers died during the time period from 2009 to 2012. I thought this was interesting information – it sure stimulated some discussion in my family. We had to buy a new car recently because our old one just got too expensive to keep repairing. We got a Toyota which are known to be safe cars but we would have preferred to see this table before we bought a new one! But still, we're confident in the new car and are in the middle of looking into car insurance and Toyota Tacoma car covers so there's no going back now! We will certainly look for articles like this in the future when we buy a new one. I show the car models in the table below.
Vehicle
Deaths per million registered vehicle years
Multi-vehicle crashes
Single-vehicle
Rollovers
Audi A4 4WD
0
0
0
0
Honda Odyssey
0
0
0
0
Kia Sorento 2WD
0
0
0
0
Lexus RX 350 4WD
0
0
0
0
Mercedes-Benz GL-Class 4WD
0
0
0
0
Subaru Legacy 4WD
0
0
0
0
Toyota Highlander hybrid 4WD
0
0
0
0
Toyota Sequoia 4WD
0
0
0
0
Volvo XC90 4WD
0
0
0
0
Posted inHealth|Comments Off on Cars With Zero Driver Deaths from 2009 to 2012
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). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~20.
