Peeling back the cover on your CFA Level 1 books can be a shock at first. Thousands of pages and hundreds of formulas sit in front of you and can seem overwhelming.

Before you freak out, it’s not really so bad. While formulas become crucial on the CFA level 2 exam and its quantitative focus, the formulas on the first exam are much more about learning relationships and the process. Learn the ‘why’ of the formula and you’ll remember how to work it on the exam easily.

I thought I would cover some of the most important formulas in the CFA level 1 exam and how to approach the mountain of equations. Practice problems and flash cards are going to be your best friends. There’s really no substitute for working formulas over and over again for remembering them on the exam. Write out practice problems of the most difficult and most important formulas and then practice them daily until you can do them easily.

**Equation #1: Future Value of a Single Cash Flow**

The future value of cash flows is not a difficult formula and one that you’ll do on your financial calculator but it’s really a building block to a lot of the more difficult formulas for time value of money. Make sure you understand this basic formula and what the different notations mean.

FV_{N}=PV(1+r)^{N}

i.e. if your savings account earns interest at a 5% rate and you have $100 deposited, how much will it be worth in 20 years?

FV_{20}=$100(1+.05)^{20
}=$265.33

**Equation #2: NPV and IRR**

Both NPV and IRR are also found easily with the calculator but they pop up many times in conceptual questions so you really need to understand the idea behind each. Remember that a key assumption of IRR is that cash flows are reinvested at that rate, which may not be realistic. Also, if there are multiple cash outflows, there will be multiple IRRs or none at all. There may be a conflict between NPV and IRR when projects are mutually exclusive or when there are multiple cash outflows. In this case, NPV is preferred.

Using the calculator is relatively easy,

The initial project cost or investment is a negative (outflow) as CF_{0
}CO_{1 through x} are the stream of cash flows and entered as a positive (inflow)

If cash flows are an equal amount, you can enter them as F (frequency)

Press the NPV button and enter the interest rate

Down arrow

CPT NPV

For IRR, just press the IRR button and CPT

**Equation #3: Sharpe Ratio**

The Sharpe Ratio is a measure for adjusting risk across investments and measuring return on the same scale. While bonds may offer a much lower rate, are they a better or worse investment than stocks given their lower volatility? It’s a pretty easy calculation and you’ll see it come up in all three exams so make sure you can remember it quickly.

Sharpe ratio = (Asset Return – Risk Free Rate) / Asset Standard Deviation

**Equation #4: Capital Asset Pricing Model**

There are a lot of flaws in the CAPM and it’s used more in academics but it is still a very useful formula and will appear throughout the CFA exams. Beyond the formula, you should pay attention to drawbacks of using the CAPM.

R_{a} = r_{f} + B_{a} (r_{m}-r_{f})

The required return (R_{a}) is the amount of return required given a specific asset’s additional risk relative to the market and the risk free rate. You multiple an asset’s beta (B_{a}) by the difference between the expected return on the market (r_{m}) and the risk free rate (r_{f}). You then add back in the risk free rate.

The difference between the market’s expected return and the risk free rate is called the market premium, the additional return required for taking on market risk.

**Equation #5: DuPont Analysis of ROE**

DuPont analysis breaks down the return on equity (ROE) into three components, profit margin – asset turnover – equity multiplier.

ROE = (Net Income/Sales)*(Sales/Assets)*(Assets/Equity)

Which becomes (Net Income/Equity) in its simplest form.

The formula provides another layer of analysis on which to compare company profitability. It’s not enough to be able to say that one company has a high return on its shareholder equity but you need to know the source of the return.

**Equation #6: Dividend Discount Models**

The Gordon Growth Model (GGM) is arguably one of the most used formulas in the curriculum. It is a single-stage model, assuming that dividends will grow at a constant rate into perpetuity. The general formula is:

Price = Div_{0} (1+growth) / (R_{ce} – growth)

An important note is that the required return must be higher than the growth rate in dividends to use the formula. This is not usually a problem in single-stage models because the long-term growth rate will probably be fairly low. Be ready to calculate some of the data points on the exam (like finding the discount rate through CAPM or the growth rate through ROE and the payout ratio).

The GGM is not appropriate when the company is experiencing super-normal growth for a period before it slows to perpetual growth. For this scenario, you need one of the multi-stage models.

**Equation #7: Weighted Average Cost of Capital**

Understanding and calculating the WACC is another foundational concept that you will need to master. The concept is pretty intuitive, a firm’s cost of capital (spending) is a weighted average of the cost from each source (debt or equity). Debt is normally less expensive and tax shielded but can be risky at high amounts.

**WACC = E/V * R _{e} + D/V * R_{d} * (1-T_{c})**

The WACC is equal to the percentage of financing from equity (E/V) times the cost of equity (R_{e}) plus the percentage of financing from debt (R_{d}) times the cost of debt, adjusted for the tax shield.

Use the market value of debt or equity when available**. **Remember, the company’s capital structure may change over time so it is preferable to use target weights instead of current market value weights.

**Equation #8: Free Cash Flows**

FCF models acknowledge that investors have a right to all cash flows from a company and not just those paid out as dividends. Free cash flows are the cash generated from operations after that needed for continued operations is deducted.

The advantage is that FCF compared to dividend models is that FCF can be calculated regardless if the company pays a dividend. FCF models are also appropriate for investors that may be able to exercise a control premium on the company. The major disadvantage is in valuing those companies with high capital expenditures, making free cash flow negative at times.

Free cash flow is shown two different ways, Free Cash Flow to Equity and Free Cash Flow to the Firm, each appropriate to two different ownership perspectives. FCFF is the cash flow from operations after capital expenditures that is available to both levels of ownership (debt and equity). FCFE is that left over after paying debt holders, since they have a prior claim.

**Free Cash Flow to the Firm (FCFF) **is the cash flow available to all capital providers (debt and equity) and equals:

Net income + Net noncash Charges (depreciation and amortization) – Investment in working capital – Investment in Fixed capital + after tax interest expense

**Free Cash Flow to Equity (FCFE) **is the cash flow available to common shareholders and equals:

Net income + Net noncash Charges (depreciation and amortization) – Investment in working capital – Investment in Fixed +/- net borrowing

- Notice that FCFE is FCFF except without adding back interest expense and taking net borrowing into account.
- Understand how to arrive at FCFE or FCFF with CFO

- FCFF = CFO + INT (1-t) – invest fixed capital
- FCFE= CFO – invest fixed capital +/- net borrowing

**Equation #9: Turnover Ratios**

The last formula is actually a series of ratios but all relatively easy to remember. These are the turnover ratios: accounts receivable, inventory turnover, number of days receivables, number of days payable and number of days inventory. You’ll use these to calculate the net operating cycle and all individual ratios are fair game on the exam.

The most important thing here is to remember that when you are combining income statement data and balance sheet data, you need to use an average of the balance sheet data. For example, the inventory turnover ratio is the cost of goods sold (income statement) divided by the average inventory from the current and previous period balance sheet.

Most of these formulas are not difficult and are pretty intuitive if you just think through them for a moment. You’ll need that deep understanding of what is going on in the formula more than you’ll need the formula itself. Make sure you have this conceptual mastery and you’ll have no trouble on the CFA level 1 exam.

‘til next time, happy studyin’

Joseph Hogue, CFA