What is a Public Budget?

“Budgets are not the solution to a multivariate resource allocation optimization problem.  Rather at each decision point, they represent a temporary equilibrium of the views of the salient actors and salient voices at that stage of the process.”
–Professor Phil Candreva, Naval Postgraduate School


Today, the President released his budget for fiscal year 2015.  In it, NASA is “budgeted” for $17.5 billion.  Now is as good of a time as ever to talk about what a “budget” is, and what it is not.

Most of us think about budgets in terms of our household finances.  That is, we categorize our past expenses into categories, such as food, mortgage, gas for the car, whatever.  The process of building a good household budget is rooted firmly in economic decisions.  How much did I spend last year on gas for the car?  How much do I think I will drive next year?  And so on.  The purpose of a household budget is to guide our spending so that we stay within the limits we established, so that we can achieve the goals we set forth in the budget (such as save for a new car, or to go on a vacation).  Used in such a manner, a household budget is a very powerful personal finance tool.

A public budget created by the federal government is not like this.

Instead, a public budget such as NASA’s serves many purposes.  According to the Navy Budget Guidance Manual, a budget is defined as “a document that expresses in financial terms the plan for accomplishing an organization’s objectives for a specified period of time.”  Furthermore, a public budget serves as “an instrument of planning, performance measurement, decision-making, and management control, as well as a statement of priorities.”

That’s a mouthful.  What does that mean?  Basically it means that the functions of a public budget are different and more nuanced than a household budget[1].  First, a public budget serves as a contract between the legislative and executive branches of government once it is enacted.  It also serves as a contract between layers of the executive branch (for instance, between the White House and NASA). A public budget is also an expression of expectations and aspirations – you have no farther to look than the introduction to the NASA budget for fiscal year 2015 to see an example of this.

A public budget, for better or worse, also establishes a precedent that influences future decisions, because once something gets budgeted, it is extremely difficult to remove it from the budget.  A public budget is also a call to stakeholders to mobilize support for what is in the budget.  It is a reflection of choices, priorities, and relative power of the stakeholders and influencers of the budget.  Lastly, a public budget is an influencer of the economy.

Does your household budget do all that?  (Mine doesn’t.)

There is one more important difference between a household budget and a public budget.  As I mentioned earlier, a household budget is built based mostly on economic decisions.  We’d like to think that a public budget also results from a similar comprehensive, rational economic process.

But if we thought that, we’d be wrong.

Instead, because of all the functions of a public budget, the decision process is much more complicated.  Sure, there is an element of economic decisions in the process.  However, those economic decisions are often overshadowed by other concerns.  Public budgeting is primarily political.  It is a group decision-making process where members of the group represent competing and often conflicting interests.  Yet somehow, every year, we have a public budget.

So as we listen to the various opinions on the President’s budget for fiscal year 2015, I urge you to keep in mind that a “budget” is more than a “budget.”



[1] I’m indebted to lecture notes from Professor Phil Candreva.

LED Versus Incandescent Bulbs

Have you switched to LED bulbs for your indoor lighting?

I was giving this question some thought recently as I pulled out the ladder once again to change one of the indoor floods in the kitchen.  I seem to be constantly replacing these bulbs, since the center of my family’s home life revolves around the kitchen.  Those lights are among the most heavily used in the house.  The prices of LED bulbs have dropped, and the light quality from LED bulbs is quickly approaching what we are accustomed to with incandescent bulbs.  Among all the considerations that factor into the decision of incandescent versus LED bulbs, I decided to apply my MBA skills and focus on one: does it make economic sense to switch to LED bulbs?

To answer this question, let’s examine the underlying total cost for a bulb.  First, there is the “fixed cost” of buying the bulb itself.  Browsing on Amazon, I found a typical 65-watt BR30 incandescent flood that outputs 635 lumens (think of “lumens” as the brightness over an area) at a color of 2700K (this is the warm color I prefer) that costs $28.47 for a 12-pack.  That equates to about $2.37 per bulb.

Pretty cheap.

I found an equivalent LED BR30 flood that requires 10.5 watts to operate, outputs 730 lumens at a color of 2700K, for $19.98.  From a brightness and color standpoint, these are comparable bulbs.  Obviously, the LED bulb costs more to purchase, but because of the lower operating power required – 10.5 watts versus 65 watts – it is cheaper to operate than an incandescent bulb.

This is a classic tradeoff problem between the combinations of fixed and variable costs.  In the case of a bulb, the variable cost is driven by the electricity cost and the amount of power necessary to operate the bulb.  If I have the resources to invest up front in a larger fixed cost to gain a lower variable cost, I will come out ahead in the longer term.

I pay about 12 cents per kilowatt-hour for electricity.  Typical regional average costs for residential power range from about 10 cents per kilowatt-hour to 18 cents per kilowatt-hour.  Let’s suspend credulity for a moment and compare the totals costs of a “magic” incandescent bulb that never burns out versus an LED bulb.  At the lower operating cost for an LED bulb, when do I “break even” on its higher fixed cost?  Basically, we need to find the operating time required where the total cost of an incandescent bulb is the same as an LED bulb when all costs are taken into account.

At 12 cents per kilowatt-hour, the breakeven occurs at 2692 hours of operation.  Beyond 2692 hours of operation, the LED bulb is more cost effective.  Conversely, it does not make economic sense to replace working incandescent bulbs that are used so infrequently that the total operating time falls below 2692 hours.


Depending on where you live, your electricity rate may be something other than $0.12 per kilowatt-hour.  Different rates shift the breakeven point; higher rates move the breakeven point sooner, lower rates move the breakeven point later.  If your rates are a lot higher then mine, you’ll reach the breakeven point a lot sooner.


That is the short-term view.  How about the long-term view?  Doesn’t the high price of LED bulbs somehow cause the economics to work out differently?  To address this, we need to recognize that bulbs have a lifetime, and factor in bulb replacement into our analysis.

An incandescent bulb has a mean time to failure that is expressed as lifetime hours.  Let’s suspend credulity in another way.  Let’s pretend our incandescent bulb lasts until the rated lifetime exactly, then burns out and must be replaced.  The typical 65-watt BR30 incandescent floods are rated for 2,000 hours.

What about LEDs?  The equivalence to lifetime for an LED is when its brightness degrades to 70% of original, at which point the degraded LED performance becomes perceptible.  The LED BR30 floods I found are rated for 25,000 hours.  Some other LED bulbs are rated for 50,000 hours and even higher!  I’ll use 25,000 hours for the next step.

The long-term analysis shown next takes into account replacement of incandescent bulbs every 2,000 hours of operation, and replacement of LED bulbs every 25,000 hours.  When the cost to operate each bulb is taken into account, it is clear that the long-term cost of using LEDs is well below the long-term cost of using incandescent bulbs.


 The lifetime of an LED bulb would have to be much shorter – less than 4,000 hours – for the LED not to be more cost effective than incandescent bulbs.


What do I conclude from this analysis? Based on an economic viewpoint, for bulbs that see medium to high usage the LED is superior to the equivalent incandescent bulb.  I consider high usage as 6 hours per day or more, such as my kitchen and home office.  At 6 hours per day, 2,000 hours is reached in less than a year.  Medium usage is cited on bulb packages – 3 hours per day.  For 3 hours per day, 2,000 hours is reached in a little less than two years.  One to two years to reach the breakeven point sounds very reasonable.

For low-usage bulbs, it does not make sense to replace them with LEDs unless the price per bulb drops even further. Low-usage bulbs are those that might see a few minutes per day.  Assuming 10 minutes per day of usage, 2,000 hours is not reached until after 30 years have elapsed.  That is a long time to wait to get close to the breakeven point.

What’s my plan?  A few weeks ago, the 40-W incandescent bulbs in a desktop lamp located in my home office burned out.  As I mentioned earlier, lamps in the home office see a lot of operating time.  I replaced the burned-out bulbs with a pair of 7-W A19 LEDs I bought from Amazon for $14.20 each.  I purposely picked LEDs with ratings in lumens and color to mimic the incandescent bulbs they replaced, and waited to see if anyone noticed anything different.  Other than noticing the lamp was working once again, no one has said anything.

In all fairness, I have a few bulbs around the house that see very little operating time.  Bulbs in the garage and bathrooms around the house are still original and going strong after 9 years.  I see no sense in replacing them with LED equivalents while the current bulbs are still operating.  Economic reasoning says that I’ll probably never reach the breakeven point on them at the current cost of LED bulbs.

However, my next target is to slowly replace the floods in the kitchen, which get the most use of any lights at my house, with LEDs as the current bulbs burn out.  I‘ll continue by replacing other medium- to high-usage bulbs in the house as they burn out.  Low-usage bulbs I won’t touch.  Given the current brightness and color output qualities of LED bulbs, I bet no one notices the difference with the replaced bulbs – that is, except for me since I pay the electricity bill!

Do you have a Flexible Spending Account?

Perhaps you are like me, and don’t. My excuse for not having one is that my medical expenses vary from year to year, and therefore I’m reluctant to set aside dollars into an FSA, only to lose those dollars if I don’t spend them.

Is that the situation you are in as well?

While conducting research on my part of the capstone project for completing the Executive MBA program at the Naval Postgraduate School, I had an epiphany that is changing my mind about the FSA. My new insight is that the FSA problem resembles in many respects the kind of resource management decision I encountered several times in the EMBA program. The decision of how much to invest in an FSA is related to a classical problem in resource management called the newsvendor problem.

The newsvendor problem is often described as the problem one faces when given a single buying opportunity where that choice maximizes profit in the face of uncertain future demand. This is often illustrated in the classroom with the situation faced by a paperboy, who buys a block of newspapers once per day (and only once per day) at a particular cost, and sells those papers for a profit. If he runs out, he is done for day and can’t buy any more papers until the next day, thus missing out on potential profit. Leftover papers are worthless, since they are yesterday’s news. How many papers should he buy at his one buying opportunity for the day if he wants to maximize his profit?

Some may say that he ought to buy the historical average. However, this assumption was shown in a different context in the late 1800’s not to provide the optimal solution. Instead, the best solution is found through a set of reasonable assumptions that the distribution of historical demand for papers (or whatever) follows the classical bell curve shape centered around an average value with a standard deviation that describes the width of the bell curve, and also by considering the relative cost of having too many versus the lost opportunity cost of not having enough.

The optimal solution for the newsvendor problem (which you can find on the internet, such as at Wikipedia) is found through a two-step process. First, we have to weigh the cost of overage (i.e., the cost of having too many) versus the cost of underage (i.e., the cost of having too little). The balancing probability P* that maximizes profit is found via the critical ratio:

​P* = Cu / (Cu + Co)

where Cu = cost of underage and Co = cost of overage. You can see with a little algebra that the only case for when the probability is fifty percent is when the cost of overage is equal to the cost of underage. For most cases, the cost of overage is different from the cost of underage. Therefore, this tell us that to get the optimal order quantity, we need to adjust away from the average by taking into account how the two costs relate to each other. The optimal order quantity is found by the following relationship:

​O* = average + z * standard deviation

where the average and standard deviation are determined from historical demand, and z is the number of standard deviations above the mean needed to meet all of the demand P* percent of the time, which we can find in a statistics table. Given that P* is a function of the cost of overage and underage, z represents the number of standard deviations we want to adjust from the average based on their relative weights.

Here is an example. Suppose that a paperboy buys a block of papers for 55 cents each, and sells them for $1.50 each. Suppose that history says that the average daily demand is 100 papers, with a standard deviation of 30 papers. To the paperboy, the cost of overage is 55 cents per paper – this represents the cost of not selling a paper, and thus what he has to cover from his profit for each paper he bought that was not sold. The cost of underage is 95 cents per paper – this represents the lost profit of not having a paper to sell to meet the demand for the paper he could have sold. Using the equation above,

​P* = 0.95 / (0.95 + 0.55) = 0.633

Therefore, taking into consideration the cost of overage versus the cost of underage, the paperboy ought to plan on selling enough papers to meet all the demand 63.3 percent of the time. So, how many papers is that? For that, we need to look up the z-value for 0.633 in a statistics table, or use the Microsoft Excel NORMSINV function. Doing that yields z= 0.34. Therefore, the optimal number of papers he should order is:

​O* = 100 + 0.34*30 = 110.2, rounded up to 111.

Hence, the paperboy ought to buy 111 papers to maximize his profit.

The situation of the paperboy is very analogous to what we face in deciding how much to set aside in an FSA. Similar to the paperboy, we are trying to maximize “profit” – in our case, it is tax savings. In contrast to the paperboy case, we aren’t concerned about having too many or few papers; instead, we are concerned about having too much in our FSA versus too little. How do we apply the newsvendor problem to this situation?

As an example, I pulled my financial records to see how much in medical and dental “eligible expenses” I spent each year for the last few years. (Eligible expenses are items such as doctor copays, prescription drugs, etc. Each FSA plan provides a detailed list of what are eligible expenses.) My historical average per year for the last 12 years is $678, with a standard deviation of $363. The highest I spent in any one year was a little over $1,300 and the lowest was a little less than $200. I point this out because that $1,100 spread was the basis of my concern as to why I chose not to invest in an FSA. My previous simple-minded thinking was telling me that if I saved more than $200 in my FSA, I risk losing the unspent funds. However, the newsvendor problem provides a different perspective, provided we can characterize the cost of overage versus the cost of underage. I’ll derive both for an FSA using marginal analysis.

The concept behind an FSA is to set aside pre-tax dollars to spend on eligible medical and dental expenses. In my case, I’m in the 25 percent marginal tax bracket. Let O* represent the ideal number of dollars I should set aside in an FSA to maximize my tax savings. If I let D represent the total amount of eligible medical and dental expenses in a given year, I note the following:

If O* is greater than D, I didn’t spend all the FSA dollars I had set aside. This is the cost of overage case (i.e., I had too many dollars in my FSA account). What is the overage? If I would have reduced O* by one dollar, that would have been a pre-tax dollar I could have kept, which converts to 75 cents after taxes because I’m in the 25 percent tax bracket. Therefore, the cost of overage is 75 cents – I lose 75 cents for each dollar I contribute but don’t spend in my FSA. (Said another way, you don’t lose a whole dollar in your unspent FSA since they are pre-tax dollars; instead, you lose 1 minus your marginal tax bracket for each unspent dollar.)

If O* is less than D, I didn’t have enough in my FSA account and thus am paying for expenses with after tax dollars over and beyond what was covered by my FSA account. This is the cost of underage case. What is the underage? If I would have increased O* by one dollar, I would have lost 75 cents in after tax dollars because it is now in my FSA account (again because I’m in the 25 percent tax bracket), but save the one dollar of pre-tax dollars I would have had to spend otherwise. Therefore, the cost of underage is 25 cents – I lose 25 cents for each dollar I don’t contribute to the FSA that I had to cover with after tax dollars, because I’m paying for that expense with after-tax dollars instead of pre-tax dollars from my FSA.

As you can surmise from the above, if your marginal tax bracket is different from mine, your cost of overage is found by taking 1 minus your tax bracket, and your cost of underage is your tax bracket.

In my case, the probability that balances the cost of overage and cost of underage in is found by plugging each into the P* equation from earlier. In my case, it results in the following:

​P* = Cu / (Cu + Co) = 0.25 / (0.25 + 0.75) = 0.25

This means that I will have leftover dollars in my FSA account 25 percent of the time, and that I will burn through my entire FSA allotment 75 percent of the time. Algebra reveals that no matter what your tax bracket is, Cu + Co always = 1. Therefore, the probability that balances the cost of overage and cost of underage is always equal to your marginal tax bracket.

Looking up the z-value for 0.25 yields -0.674. Yes, it is a negative number. That means that I want less in my FSA account than the historical average of my eligible expenses. The amount I want is therefore

​O* = $678 + (-0.674)*$363 = $433

Again, this means my chances are 25 percent that I’ll not spend the entire $433 in my FSA account in a given year and will have leftover dollars I lose. However, 75 percent of the time, I will burn through the $433 in my FSA account. Setting aside $433 in pre-tax dollars results in a tax savings of $108 in the 25 percent marginal tax bracket.

What about that other 25 percent of the time when I don’t use all my FSA dollars? To look at this situation, I’ll do a breakeven analysis. In my case, I’ll break even between what I gain in tax savings versus what I lose in unused FSA contributions if I have at least $325 in eligible expenses ($433 – $108 = $325). In other words, this is the point at which the amount I would lose in unspent FSA dollars equals the tax savings of $108. I want to find the z value that corresponds with $325, so that I can find the probability that I’ll spend less than $325 dollars. Rearranging the O* equation, dropping the * designation and solving for z yields

​z = (O – average) / standard deviation

With my average and standard deviation,

​z = (325 – 678) / 363 = -0.97

Looking up -0.97 in a statistic table for the corresponding probability, or using the Microsoft Excel NORMSDIST function, yields 0.165. This means 16.5 percent of the time, I will spend less than $325. A 16.5 percent chance is equivalent to a one-in-six chance of occurring. (This is corroborated from my previous expenses – I spent less than $325 per year twice in the twelve years comprising my data set). I’m willing to tolerate that risk.

I’ve provided a spreadsheet that will do the calculations for you.

Therefore, given these odds and what the newsvendor problem is telling me, the tax saving is worth the trade to me. I’ll be signing up next year.



2013 in review

The WordPress.com stats helper monkeys prepared a 2013 annual report for this blog. Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 14,000 times in 2013. If it were a concert at Sydney Opera House, it would take about 5 sold-out performances for that many people to see it.

Click here to see the complete report.

China in Space

The final two paragraphs from the latest post from Paul Spudis's blog regarding speculation that the next launch by China, Chang'E 3, will deliver a rover to the moon:

In any event, what does it say about American leadership in space that so many prefer to put their heads in the sand and ignore or deny this disquieting series of developments? It does not require either imminent or distant hostilities to recognize the possible dangers of having one power dominate such a vital field of endeavor – particularly a political power with a mixed record of sympathies to the western values of democracy and economic freedom.

Going to the Moon and developing cislunar space may not seem to be very important to some – it clearly isn’t to the current leadership of NASA. Prior to October 4, 1957, orbiting a satellite around the Earth wasn’t seen as very important either.

In recent weeks my Strategy class has discussed a number of tools for evaluating and developing strategy. In the above article are hints at what the U.S. has been doing wrong with regards to strategy in space. I'll have more to say about this soon.


Has “Team Texas” Taken a Time Out?

An article in this morning's Houston Chronicle calls out the lack of leadership in Texas's Senate delegation:

Lawmakers are saying there have been too few delegation-wide get-togethers to map strategy on Texas-centric issues, too little top-down leadership by Cornyn, too few tangible payoffs from Cornyn's position as second ranking Republican in Senate leadership and too many ideological disputes over whether to seek federal largesse at all. “I'm hearing from members that they're not finding the support and coordination to address Texas issues,” says a former veteran member of the Texas congressional delegation. “There's just a feeling that Team Texas has gone by the aside and we don't have the continuity that Texas has been known for.”

Although the article does not mention NASA and space specifically, I can't help but wonder about the associated impact to space policy and implementation. It's clear that the Executive Office of the President has been focused on other policy issues for the last three-plus years, leaving it to the space-based congressional delegations such as Texas to fill the void in leadership. The most recent example of this was the bipartisan push-back on the administration's space policy a few years ago, leading to the crafting of the Space Launch System through the actions of (now retired) Senator Hutchinson (R-TX) and Senator Nelson (D-FL). With some of the recent refinements in space policy failing to gain traction (read: Asteroid Redirect or Retrieval Mission, the R depending on your choice of the day), and continuing budgetary pressures putting the squeeze on NASA's funding, one has to wonder whether the failings of the Texas delegation to effectively lead across the board will make the situation worse for human spaceflight.


On Supply Chains and Space Policy

The latest from Paul Spudis on his Lunar Resources Blog:

In brief, “to Augustine” something is to structure a report in such a way that a space goal or architecture is deemed “unaffordable.” From the outset, the resulting report must conclude that the program being evaluated is unaffordable and “sadly,” dropping it must be laid at the door of Congress for fiscal and programmatic restrictions and not by any desire on their part to kill the program.

Dr. Spudis's words hit home as I reflected on my experiences this quarter in supply chain management and government policy. I may have more to say on this in the coming weeks. For now, suffice it to say that some hard decisions will need to be made if a workable supply chain to low Earth orbit, based on a fully legitimized space policy, are to be realized.


150 Years Ago…

July 1-3 marks 150 years since the battle at Gettysburg was fought during the U.S. Civil War. A few years ago, while I was a participant in NASA's leadership development program, I was fortunate to receive a guided tour of the site with a young Captain from the Army War College. Afterwards, I wrote these words, as true today as they were then:

As I reflected on that point while actually walking the fields of Gettysburg, I wondered about that point as well as the decisions and failings of leadership that led to the ultimate of consequences those three days. My analytic thoughts turned to more emotional ones as I walked the fields in chronological order of the three days of battle. I sensed the ebb and flow of the first day as the Confederacy made contact with Buford’s cavalry on the rolling hills to the west of town, when the leadership on both sides had no real sense of the battle yet to come. I felt the split-second decisions of leadership as I stood on Little Round Top where Joshua Chamberlain gave the order to fix bayonets and charge. I wondered about the certainties and uncertainties of leadership decisions as I stood where Lew Armistead died as one of the few in Pickett’s charge to make it beyond the Union lines. I sought parallels of the consequences of the decisions of leadership at Gettysburg with the work of my organization at NASA – after all, we deal with decisions that can kill people – and felt deeply the loss of the crews of Challenger and Columbia. When the day at Gettysburg drew to a close, I found that words failed me. In some sense, they still do.

Read the rest here.


Why SLS?

From a recent post by Dr. Paul Spudis, “'Where, Why and How?' – Concerns of the House Subcommittee on Space“:

An interesting moment in the hearing came when Squyres expressed concern that even if the Space Launch System (SLS) is completed, there will be no money to operate it or provide payloads for it. I believe this concern comes from a misunderstanding of the fundamental purpose of the SLS – the launch vehicle mandated in the 2010 NASA authorization bill. I have written previously that because of the peculiar wording of that bill, there may have been an ulterior motive involved in such specificity, viz., that the SLS is Congress’ way of retaining a semblance of spaceflight capability within the agency, a national technical capability that they believed was discarded with undue haste and little serious thought. In such a scenario, the operational cost of SLS is not relevant, at least until an attainable, strategic horizon is recognized and adopted by a future administration. SLS is merely a mechanism to retain a national capability and operational spaceflight team, the hard-fought-for-and-won national treasure of space expertise which otherwise would be scattered to the winds.

This paragraph highlights for me the difficulty of decision making in the public sector.