How to Set Up Calculations

A couple of weeks ago I wrote a post on how to solve quantitative questions. It has come to my attention that most people seem to be strong with steps 1, 3, and 4 of that process but struggle with planning out their approach. Specifically, people seem to struggle with figuring out what you’re actually supposed to calculate.

What Are You Supposed to Calculate?

For most quantitative questions, you are directly told to calculate something such as profits, revenues, costs, margin, etc. In that case, it’s pretty easy to figure out what you need to calculate because you’re directly told.

However, there are some cases where you are just given a bunch of information and you need to figure out what to calculate. In cases like that, I would suggest you do three things:

1. Figure out what your objective is with this calculation.

2. List what information you know.

3. Figure out how you can combine your givens in a logical statement (an equation) to achieve your objective. The goal is to write out an equation only in terms of what you’re given.

Example

The example we’re going to use is the Testing Equipment case, which is case # 2 in the Exotic Cases Casebook.

Basically, in the testing equipment case you’re asked to figure out if there’s a market for a new testing method called the laser test (note that there is already an existing testing method called the water test).

You’re given the following information:

Testing Equipment

So let’s do this together:

1. Objective – We’re trying to figure out if this product is economical from the customer’s perspective. Basically, we need to figure out how much the laser test costs compared to the water test.

You probably noticed that the laser test equipment (CapEx) is much more expensive but the scan rate is also much higher, meaning that the laser test can do many more scans over its lifetime.

So, if we are going to compare the water test and the laser test, it seems to compare apples to apples we need to compare the Cost per Scanned Unit of each type of test.

2. Information we know – See the table above.

3. How can we combine our givens to achieve the objective – To calculate the Cost / Scanned Item we know that we have to divide the total cost of each over its life time by the number of scanned items.

Calculating Total Cost and # of Scanned Items

From the above table there seem to be 3 sources of costs:

1. Setting up the machine before each run.

2. Operating the machine as it runs.

3. Buying the machine (CapEx)

If that is the case, then the total costs are equal to the sum of the above 3.

Total Cost = Total Cost of Setup + Total Cost of Operations + CapEx (1)

Now, let’s break down each of these cost sources into given quantities. Again, the key is to figure out how to write out each of these quantities in terms of what you know.

Total Cost of Setup = # of units over lifetime * setup time / unit * labor cost (2)

Total Cost of Operations = # of units over lifetime * average scan time / unit * labor cost (3)

We have the labor cost but we don’t know the # of units over lifetime or the scan time / unit.

So what’s the  # of units over lifetime? If you think about it, we know the machine’s lifetime. To figure out how many units it can scan in that lifetime we need to divide the lifetime by the time to scan a unit.

The time to scan a unit is the size of the unit divided by the scan rate (it has to be, check the units)

# of units over lifetime = Lifetime / (Scan Time / Unit) (4)

Scan Time / Unit = Size of the Unit / Scan Rate (5)

So, the # of units over lifetime = Lifetime * Scan Rate / Unit Size (put the second equation into the first) (6)

Now we’re ready to solve the question! (we know this because we have a series of equations that are solved in terms of a bunch of things we know)

Calculations

Now you just go ahead and calculate things starting from equation (6) and work your ways backwards for both the water and laser test. I suggest you do it yourself, but here is the answer from the casebook:

Testing Equipment Solution

Conclusion

To figure out what you need to calculate:

1. Figure out what your objective is with this calculation.

2. List what information you know.

3. Figure out how you can combine your givens in a logical statement (an equation) to achieve your objective. The goal is to write out an equation only in terms of what you’re given.

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