## The CFA's 5 Most Testable Concepts about Time Value of Money (TVM)

The Time Value of Money (TVM) reading kicks off Quantitative Methods, and is the first thing many Candidates see after Ethics (although some Candidates skip Quantitative methods and economics to start with FSA).

Whenever you do cover this material, rest assured that its placement at the beginning is not an accident. Time value of money and interest rates are crucially important to many of the financial calculations found throughout the L1 curriculum. Furthermore, even when they are not directly tested these calculations often are the last step in a different calculation question.

In the rest of this post we break down the key testable takeaways that you should expect to see show up on the CFA Level 1 Exam.

## The 5 Most Testable Concepts from TVM

### 1. The three definitions of interest rates

What is an interest rate? There are three main ways it can be interpreted. As:

- The required rate of return
- The discount rate
- As an opportunity cost

You should also be able to define what we mean by each of these.

### 2. What components go into determining the interest rate?

The interest rate consists of several different risk factors (premiums) that we add up to find the overall interest rate. We usually break these different factors into the (a) risk free rate, (b) inflation, and (c) various other premiums that can include things like illiquidity and security specific factors.

In the CFA Institute reading, the equation we are given is:

Those different risk premiums explain why the expected rate of return (you remember that's one way to interpret the interest rate right!?) varies for different asset classes. Finally, while it's only hinted at in this reading, you will eventually also need a good understanding of the difference between the nominal and real interest rates.

### 3. Compound interest rates and how they link Present Value, and Future Value

The concept of present value and future value is essential. You won't get far in the CFA curriculum (or in finance) without understanding that money today is more valuable than money in the future. Exactly how much more valuable is determined by the compound interest rate and the amount of time that passes between now and then.

The equation you'll need to memorize for the rest of your CFA exam life that models this relationship is:

If that equation isn't familiar yet go read this article

### 4. Indexing different cash flows to one point in time

Future value/present value calculations on the exam will attempt to layer in different levels of complexity into what looks like a basic calculation in order to make a given problem more difficult than a simple formulaic plug and play. The most common way they do this is by requiring you to use the * cash flow additivity principle* to index different future values to a single point in time where they can then be added together. To handle this, practice using a timeline to determine different net present values and adding them up.

This becomes especially relevant with problems addressing annuities and annuities due. Practice those types of problems repeatedly. Why? First because they'll be directly tested on the Level 1 exam. Second, because once you have the intuition of when cash flows start and can successfully solve those present value calculations you know you've mastered this reading.

### 5. Dealing with Different Frequencies of Compounding

You should be confident taking time periods and converting them to the relevant compounding periods and doing the same with given interest rates. For example, if a problem gives you the interest rate as an annual number and the time in years, but the loan whose PV you are solving for has quarterly compounding what do you do?

**You would divide r by 4 to get your quarterly interest rate (I/Y) and you would multiply the number of years by 4 to get N.**

If you can't perform that type of conversion you'll end up inputting incorrect variables into the formula or your financial calculator and miss a lot of easy points. Plus if you can do that there's also an entire set of equations dealing with different compounding frequencies you can ignore trying to memorize.

**If nothing else always remember that th****e HIGHER the interest rate or the MORE TIME we are taking into consideration the HIGHER the FV of an investment will be.**

## 6. Mastering your Financial Calculator

OK we snuck in a bonus.

This reading is the first introduction to your financial calculator. Being able to use it across functions will let you circumvent a lot of the formulaic memorization that often plagues L1 Candidates as they grapple with hundreds of different equations. At a bare minimum you should emerge from the EOC questions in this reading being able to toggle between BGN and END and navigating NPV, IRR, and uneven cash flow problems (see our post on how to do this).

This will not only up your chances of actually getting specific problems right, but will let you get to other problems more quickly (and trust us for an exam where you need to answer 1 problem every 90 seconds saving time matters a lot more than you might think).

### Recap

To summarize you need to walk away from the TVM reading knowing:

- How to interpret an interest rate
- What factors go into determining the interest rate
- How Present Value and Future Value are related
- How to bring multiple cash flows from the future back to today or vice versa
- How to deal with different compounding frequencies and manipulating the interest rate accordingly
- How to use that financial calculator you'll fail without