Statistics show that less than 20% of candidates pass all three levels of CFA exams on the first attempt. Question banks, study materials, and getting a tutor are usually needed to guarantee a candidate great results. There are several formulas that they should memorize and understand before the exams. A CFA formula sheet is an excellent supplement to the above studying techniques. They give a general overview of CFA level 1, 2, and 3 formulas and mathematical foundations tested on each level of exams.

Below are the nine formulas you will need for your CFA exam formula sheets.

## Future Value of A Single Cash Flow

It is the amount of money invested today at a given interest rate. It is a simple formula that you can do on your financial calculator. It is also an essential building block for complex formulas used to calculate the time value of money.

$$FVN=PV(1+r)N$$

$$FV=$$ Future Value of a single sum of money

$$r=$$ Interest Rate per period

$$PV=$$ Present Value of the investment

$$N=$$ Number of periods

$$(1+r)N=$$ future value factor

## NPV and IRR

Capital budgeting uses net Present Value(NPV) and Internal Rate of Return(IRR). This is when a company determines whether a new investment will generate profits or losses for the company.

NPV is used when determining the dollar amount difference between the present amount value between discounted cash inflows and fewer outflows over a certain period.

IRR is used to estimate the profitability of potential investments using the percentage values.

Their formulas are:

$$Rt =$$ Net cash inflow-outflows during a single period, $$t$$.

$$I =$$ Discount rate or return that one can earn in an alternative investment.

$$t =$$ Number of periods.

You can also calculate NPV and IRR using a financial calculator, though knowing the formula is always good in case of complex questions.

## Sharpe Ratio

Sharpe ratio is a formula used in comparing the return of an investment with its risk. It is a straightforward calculation that can be done using the following formula:

$$\text{Sharpe ratio} = \frac{(\text{Asset Return} – \text{Risk-Free Rate})}{\text{Asset standard deviation}}$$

## Capital Asset Pricing Model(CAPM)

It describes the relationship between systematic risk and expected return for assets, especially stocks. This is done using the expected return on both the market and the risk-free asset and the asset’s sensitivity to the market(beta). It is frequently used because it is simple and allows for comparisons of investments and alternatives.

The formula for CAPM is:

$$\text{ER}_i = \text{R}_{f} + β_{i}(\text{ER}_{m} – \text{R}_{f})$$

where,

$$\text{ER}_{i} =$$ Expected Return on Investment

$$\text{R}_{f} =$$ Risk-Free Rent

$$\beta_{i}=$$ Beta of the Investment

$$(\text{ER}_{m}-\text{R}_{f}) =$$ Market Risk Premium

However, CAPM has the following limitations:

1. Unrealistic assumptions.
2. A linear interpretation of Risk vs. Return.

## DuPont Analysis of Return On Equity(ROE)

The DuPont analysis separates the ROE into the profit margin, asset turnover, and equity multiplier. DuPont analysis is used to trace a company’s financial achievement.

There are two ways in which it can be calculated: the three-step decomposition and the five-step decomposition. The formulas are:

3-step decomposition:

$$\text{DuPont Analysis} = \text{Net Profit Margin} \times \text{asset turnover} \times \text{Equity Multiplier}$$

Where,

$$\text{Net Profit Margin} = \frac{\text{Net Income}}{\text{Revenue}}$$

$$\text{Asset Turnover} = \frac{\text{Sales}}{\text{Total Average Assets}}$$

$$\text{Equity Multiplier} = \frac{\text{Average Total Assets}}{\text{Average Shareholder’s Equity}}$$

5-step decomposition:

$$\text{ROE} = \frac{EBT}{S} \times \frac{S}{A}\times \frac{A}{E} \times (1-\text{Tr})$$

Where;

EBT= Earning Before Tax

S= Sales

A = Assets

E = Equity

Tr = Tax Rate

## Dividend Discount Models

It is a quantitative method used to speculate a company’s stock price based on the assumption that its present-day price is equivalent to its future dividend payments when discounted to its present value. It is used in calculating the fair value of stock regardless of the current market conditions.

The DDM formula is:

$$\text{Value of stock} = \frac{\text{EDPS}}{(\text{CCE} – \text{DGR})}$$, where;

EDPS = Expected Dividend per share

CCE = Cost Of Capital Equity

DGR = Dividend Growth Rate

## Weighted Average Cost of Capital

WACC consists of a company’s after-tax cost of capital of every source: bonds, common stock, preferred stock, and any kind of debt. It is the average rate a company should pay to finance its assets. The formula for WACC is:

$$\text{WACC} = (\frac{E}{V}\times Re) + (\frac{D}{V}\times Rd\times (1-Tc))$$, where;

E = Market value of firm’s equity

D = Market value of firm’s debt

V = E+D

Re = Cost of equity

Rd = Cost of debt

Tc = Corporate tax rates

## Free Cash Flows

Free cash flow is the money left after a company pays off its operating and capital expenses. FCF can be calculated in the following three ways:

#### I. Using Operating Cash Flow

$$\text{FCF} = \text{Operating cash flow} – \text{Capital expenditures}$$

#### II. Using sales revenue

$$\text{FCF} = \text{Sales revenue} – (\text{operating cost}+\text{taxes}) – \text{Required investment in operating capital}$$,

Where;

Required investment capital = Year 1 total net operating capital – year two total net operating capital

Total net operating capital = Net operating capital + Net plant operating long-term assets

Net operating working capital = Operating capital assets – Operating current liabilities

Operating current assets = Cash +accounts receivables + inventory

Operating current liabilities = Account payables + accruals

#### III.Using net operating profits

$$\text{FCF} = \text{Net operating profit after taxes} – \text{Net investment operating capital}$$

Where;

$$\text{Net operating profit after taxes} = \text{Operating}\times \text{Income (1-tax rate})$$

$$\text{Operating income} = \text{Gross profits} – \text{operating expenses}$$.

Turnover ratios

It represents the percentage of the mutual fund or other portfolio holdings replaced in a particular year. It varies depending on the type of mutual fund, its investment objective, and the portfolio manager’s investing style. It is series of ratios: accounts receivable, inventory turnover, number of days receivable, number of days payable, and number of days inventory. All this calculates the net operating cycle and all individual ratios.

Formula sheets are excellent supplements to have as you prepare for CFA exams. The following formulas are the most essential as they are building blocks of other formulas used in exam calculations. Memorizing them will guarantee you a good score in your CFA exams.

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