Running the Numbers

Not long ago, I was thinking of buying a new car for myself as an MBA present. I’m not anymore. Our financial advisor pointed out that any gift that comes with 60 payments isn’t much of a gift at all…and fixing the horn on my Jetta costs a lot less than a down payment.

But when I start to get interested in buying something, I get obsessed, and I knew that I’d get it out of my system if I just started to do some actual research. So in the process of looking at Consumer Reports Online, making spreadsheets, contacting dealers for quotes–and insisting that I’d give a local Toyota dealership a 5.79% gross margin on a new Highlander over my dead body–I was constantly reminded of probably the most fundamental lesson of business, and life: intuition is inherently faulty. You have to run the numbers.

That phrase smacks of Consulto-speak, so let me clarify: running the numbers is something you do when you’re making a financial decision to see if it actually makes sense or not. You take your assumptions about a decision, put them on paper, tie some numbers to those assumptions, and see what comes out. It’s a way of challenging what you believe to be true. In your head, you might think that it makes sense to buy that new car, or rent out your old condo rather than sell it, or order pizza for a party rather than make your own at home. But until you’ve considered the cost and the benefit in real terms, you’re just making a guess.

A word about assumptions: these aren’t the “makes an ass out of you and me” kind of assumptions. Think of “assumption” as another word for “variable.” For example, if I’m going to cook dinner, my list of assumptions is going to include “I have access to a stove” and “I have the ingredients I need on-hand.” That allows me to arrive at a conclusion: if I have access to a stove and I have the ingredients I need, dinner should take about 30 minutes. Later, I can play around with those variables to come up with alternative outcomes–if I don’t have the ingredients, then dinner is going to take longer. The idea is, consider all the things that could be variable in your situation, give them starting values, and then change them to see what might happen. Some things might not have as much of an impact as you think…maybe I don’t have a stove, but I have a microwave oven instead.

If you ever did a science fair project, you’ve done just this kind of experiment. But don’t worry. I didn’t like science fairs either, and I’m not going to make you go buy any poster board, test tubes or fruit flies. Just grab your copy of Excel, OpenOffice, Numbers, or any spreadsheet program you like, and follow along.

Hourly Rates

First real-world example: as a consultant, I recently had an opportunity to speak with a client about the number of hours they wanted me to work, and my hourly rate. I knew that I wanted to make as much money as possible, and I knew that I had plenty of availability to commit to more hours. So I put together a really quick and dirty spreadsheet:

In this case, my assumptions are that I will be able to work 15 hours a week at a rate of $35 per hour, giving me a weekly income of $525. That’s my baseline: it’s a place I can start from, so I can see what sort of impact adjusting the variables might have.

Next, I considered that I would try to increase my hourly rate. I figured that $40 was reasonable, so I added this line:

Great! If I could convince the client to give me an extra $5 an hour, that would translate into another $75 per week in revenue! Easier said than done…but I was getting carried away. What if I could do an extra $10 an hour? What impact would that have?

Excellent! Another $75 in my pocket! Plus, I’d have the bragging rights associated with that higher rate. Who doesn’t want to increase their hourly wage?

But then I started to consider what would happen if the client couldn’t afford to increase my rate. I knew that they were interested in having me do more work for them, and I certainly had the hours to bill. Suppose I did, oh, an extra 5 hours a week at my usual rate? I figured it probably wouldn’t be as impressive as getting my rate higher, but my goal was to make more money, however I could. So I added another line:

Wait. What?

Could my math be wrong?

I double-checked my simple little spreadsheet, looking for any errors, but everything added up. It didn’t make sense, intuitively. I should be trying to maximize my income by charging a higher rate, not by working more hours!

But it wasn’t so. I was better off just working a meager 5 more hours per week than trying to get my rate up by $10.
I ran the numbers one last time, just to see what rate I’d have to charge to make that $700 a week:

$46.67. Over an $11 hourly increase. There was no way the client would agree. And they didn’t. But when I asked them if I could do a few more hours of work, they were overjoyed. So was I.

There are a few other important assumptions that aren’t in this spreadsheet: the most important is that I didn’t expect to be able to find another client to buy those hours for a higher rate. And, of course, there was the assumption that I should try to increase my hourly rate above all else. That’s why you run the numbers: to prove or disprove these bad kinds of assumptions.

“But Mark,” you say. “I’m just not a math guy, Excel gives me hives, and I’m not a consultant.” Well, I’m not a math guy either, and putting together spreadsheets didn’t come naturally to me. Furthermore, you don’t need a business to benefit…just a desire to understand where your money is really going when you make a purchase.

Saving Green by Going Green?

Here’s another example: if I’m going to buy a new car, should I buy a hybrid?

The conventional wisdom says “Yes, buy a hybrid, you pollution-spewing urbanite.” But I wasn’t sure if it made sense from an economic perspective; would the fuel efficiency pay for itself?

This one is more complicated, and it took me some puzzling before I arrived at this spreadsheet:

First, I’ll estimate that a non-hybrid SUV might get 20 MPG, average (you could make this fancier by doing a weighted average based on your city vs. highway driving, but as I’ll mention in a bit, the idea behind this is usually to just keep it simple and avoid confusing yourself). Let’s say that gas is $3 a gallon. Divide Price per Gallon by MPG and you’ll get a gas cost of 15 cents a mile.

Now, assume that we drive an average 12K miles per year. Multiply 15 cents a mile times 12K miles, and you’re going to spend $1800 on gas each year.

Now, let’s take a hybrid SUV with a fuel efficiency around 24 MPG. Wow! You can save $300 a year with that added efficiency! Not too shabby, huh?

Not so fast. That hybrid engine adds some cost to the vehicle…in the case of this hypothetical SUV, about $7000 extra. But, we’re going to plan to keep this car for awhile. So our second spreadsheet looks like this:

Oops. Looks like the total lifetime savings of running a hybrid is $2400 over a regular SUV, which means that we should expect to pay no more than a $2400 premium to get a hybrid. But, the hybrid in our example costs $7K more.

Looks like that extra 4 MPG just isn’t worth the cost.

There are plenty of ways we can rework this example…by planning to drive the vehicle longer, for example, or estimating higher fuel costs in the future. If we drive the car for 10 years, it makes sense to pay as much as $3000 extra for an extra 4 MPG. If gas goes up to $5 a gallon, owning a hybrid for 8 years can save $4000. If you want to be more accurate, go ahead and add in a weighted average of the cost of gas over the lifetime of the vehicle. Excel (or any spreadsheet) is a wonderland for coming up with these sorts of estimates.

But to get back to our original example, we would need to get a startling 39 MPG to make that $7K premium worthwhile within 8 years. Not exactly the environmental answer, but as the authors of Freakonomics put it, “People respond to incentives.” Either a decrease in the cost of hybrid technology or an increase in the cost of fuel will almost certainly drive adoption rates.

Add it Up

So just like that, we’ve challenged the idea that getting a higher hourly rate is always the best idea, and that driving a hybrid is always a smart choice. Isn’t it interesting what you can learn when you stop being scared of numbers? Remember: the numbers work for you!

I can’t emphasize enough the “quick and dirty” aspect of this kind of analysis. In many cases, people will call this kind of analysis a “back of the envelope” estimate, meaning that, at most, you’re jotting the numbers down on some scrap paper, and, at least, you’re doing the math in your head. I recommend using a spreadsheet for two reasons: one, if you’re math-phobic like me, it’s a handy tool for getting everything added up. Two, it’s a lot easier to come back to at a later date when you might consider some additional assumptions that you want to throw into your model.

The next time you come up with an assumption that “just makes sense,” I encourage you to put your own intuition to the test: put it in a spreadsheet and run the numbers!