Lesson 1

How Not to Get Outwitted
in Your CFA Exam: Question Analysis

Have you ever analyzed an exam-type question word by word?

Try and you’ll be surprised how much it can help you.

I’ve spent some time back in April to go through thousands of CFA exam-type questions (hideous hours...) to be able to tell you what kind of information such questions contain and what it means for you in the context of your upcoming December exam.

Because the whole concept of *question analysis* may be new to you, in this first lesson I’d like to explain what it’s all about using an example.

Below, you’ll find a question on WACC (exam format applied). It uses some techniques that can outsmart you even if you’re confident of your skills. Your goal is not to get caught in the traps and solve the question correctly!

Here you go:

Healthy Brain, Inc. operates in Healthcare Information and Technology industry which is characterized by low total debt to assets ratios. Health Brain’s D/E ratio is equal to 25%. The cost of equity for the company and the after-tax cost of debt amount to 12% and 8.5%, respectively. Assuming that the tax rate is equal to 15%, the WACC for Health Brain, Inc. is closest to:
a. 10.81%
b. 11.13%
c. 11.30%

This seemingly simple question contains 4 traps.

However, before we discuss them and name the techniques applied to outwit you, let’s take a look at the WACC formula first:

\(WACC=w_{d}\times R_{d}\times (1-t)+w_{e}\times R_{e}\)

• \(WACC\) - weighted average cost of capital
• \(w_{d}\) - the weight of debt
• \(R_{d}\) - the before-tax marginal cost of debt
• \(t\) - the company's marginal tax rate
• \(w_{e}\) - the weight of equity
• \(R_{e}\) - the marginal cost of equity

OR:

\(WACC=w_{d}\times R_{d}\times (1-t)+w_{p}\times R_{p}+w_{e}\times R_{e}\)

• \(WACC\) - weighted average cost of capital
• \(w_{d}\) - the weight of debt
• \(R_{d}\) - the before-tax marginal cost of debt
• \(t\) - the company's marginal tax rate
• \(w_{p}\) - the weight of preferred stock
• \(R_{p}\) - the marginal cost of preferred stock
• \(w_{e}\) - the weight of common stock
• \(R_{e}\) - the marginal cost of equity

There are 2 forms of the WACC formula. If you are a level 1 candidate, the second one – with preferred and common stock – must look familiar. At the level 2 exam, you’ll be using the first formula more often. In essence, the 2 forms mean the same.

The idea behind the WACC formula is simple: the cost of capital for the company is equal to the weighted average of costs from different sources. Every company has different sources of capital used to finance its operations. These sources of capital include common stock, debt or preferred stock and each of these sources has a different cost. The company can also use different sources of capital in different proportions. Therefore, if an analyst wants to compute the average cost of total capital – he or she uses the weighted average, where the sum of weights equals 100%. Additionally, if you take a look at the WACC formula, you’ll see that the cost of debt is multiplied by 1 less tax rate. This is because of the tax shield (interest on debt decreases the earnings before tax and, as a consequence, it lowers the tax that the company needs to pay). This \(R_{d}\times(1-t)\) is called an after-tax cost of debt, in contrast to Rd which is called a before-tax cost of debt.

OK, now the traps.

Healthy Brain, Inc. operates in Healthcare Information and Technology industry which is characterized by low total debt to assets ratios. Health Brain’s D/E ratio is equal to 25%. The cost of equity for the company and the after-tax cost of debt amount to 12% and 8.5%, respectively. Assuming that the tax rate is equal to 15%, the WACC for Health Brain, Inc. is closest to:
a. 10.81%
b. 11.13%
c. 11.30%

Here is how you should understand our WACC question:

A company with the D/E ratio of 25% (which gives us weight of debt equal to 20% [\(w_{d}=20\%\)]) is characterized by cost of equity=12% [\(R_{e}=12\%\)] and after-tax cost of debt=8.5% [\(R_{d}\times(1-t)=8.5\%\)]. WACC??

And here are the traps you can fall into if you fail to understand it that way (or miss the right things):

1st trap: We start from the very beginning. Look at the first sentence of our example. There’s no numerical data that you’d need to solve the question. The sentence is there for 2 reasons. First of all, it gives you some context, which is in line with the CFA Institute’s approach to make the examples more real. Secondly, it may misdirect you owing to the low total debt to assets ratios part, which brings us to trap no. 2.

Applied Technique: noise (no meaningful info)

2nd trap: You are given the company’s D/E ratio (25%), which is a proportion of debt to equity. However, to compute the WACC you need to know the value of debt to total assets (D/A) and the value of equity to total assets (E/A). So, you have to transform this D/E ratio into the D/A [=D/(D+E)] ratio. But the first sentence of the question says about low total debt to assets ratios for the industry. Lose your focus for a sec and you may wrongly assume that this D/E is actually D/A and use the D/E value for your computations (25% instead of 20%).

Applied Technique: misleading data

3rd trap: Those of you who like to skim for data to do “easy” questions quickly and fail to pay enough attention to detail (NOTE: analysts should pay attention to detail!) are vulnerable to this third trap. One word: “after-tax” in front of “cost of debt” changes everything. Miss it and you’re in for big trouble. See trap no. 4 to understand why.

Applied Technique: one word changes everything

4th trap: Now look at the last sentence. You are asked to compute the WACC knowing that the tax rate amounts to 15%. But you don’t need this tax rate because we have the after-tax cost of debt given. Also, pay attention to wording: “Assuming that the tax rate amounts to...” – it makes an impression that this tax rate is important, though in fact it’s not.

Applied Technique: irrelevant data

Applied Technique: tricky wording

As you can see the analysis of the question helped us avoid mistakes.

We escaped the traps set up to trick us. We stayed careful about the 2 important aspects of WACC, namely the weights of capital sources and the cost of debt, which led us to correct solution:

\(WACC=w_{d}\times r_{d}\times (1-t)+w_{e}\times r_{e}\)

\(WACC=20\%\times8.5\%+80\%\times12\%\)

\(WACC=11.3\%\)

The correct answer is C.

Had we fallen into the 1st trap and supposed it must be the total debt to assets ratio given in the second sentence, we would confuse D/A with D/E and walk straight into the 2nd trap. This means we would get the weights of capital sources wrong (\(w_{d}=25\%\) & \(w_{e}=75\%\) instead of \(w_{d}=20\%\) & \(w_{e}=80\%\)).

WRONG!!! >> \(WACC=25\%\times8.5\%+75\%\times12\%\)

The same goes for the cost of debt to calculate which – you need to know the tax rate. The tax rate is stated but the point is you don’t need it because you have \(R_{d}\times(1-t)=8.5\%\), i.e. after-tax cost of debt, already given. If you get caught either in the 3rd or 4th trap, you’ll end up multiplying the 8.5% after-tax cost of debt by (1-t) and choosing the wrong answer.

WRONG!!! >> \(WACC=25\%\times8.5\%\times(1-15\%)+75\%\times12\%\)

Lesson 1: Key Takeaways

Various techniques are employed in CFA exam questions to test your knowledge as thoroughly as possible. In this lesson, we named 5:
1. noise (no meaningful info)
2. misleading data
3. one word changes everything
4. irrelevant data
5. tricky wording

You can learn how to efficiently recognize those techniques thanks to regular question analysis.

While doing practice exam-type questions, always pay attention to how they are formed and what they exactly say. This way you’ll prepare yourself to spot potential traps and tricks also in your CFA exam.

Wrapping Up

Don’t get me wrong. It’s not like every question in your exam is full of traps. There will be questions that will be pretty straightforward. However, as an analyst-to-be, you definitely need the ability to tell relevant and irrelevant data apart and be able to decide which info you can build on and which is superfluous.

The next lesson is a continuation of today’s lesson because it talks about how CFA Institute designs answers. Hope it helps!

P.S. I’m very interested in your feedback. Share it with me by clicking the chat icon on the right side of your screen.

P.P.S.
How to calculate the weight of debt, i.e. D/[D+E], the quickest way if you have D/E given?

If D/E is 25% (which is 25/100), you can assume that D=25 and E=100. Then, the weight of debt is:
25/[100+25]=20%. And the weight of equity is the rest, i.e. 80%.