Calculation Formulas

As I start to freak out a little about this exam and feel that the universe of formulas we are given is just too overwhelming, I thought it would be useful to differentiate between the formulas we are expected to explain/understand versus the formulas we are expected to use to make calculations (which is another way of saying I am procrastination in a way that makes me feel like I am actually doing something).

Below are all the LOS's for CFA Level 1 which refer to computation, estimation, or calculation:

Reading 5: The Time Value of Money
c. calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding;
d. solve time value of money problems when compounding periods are other than annual;
e. calculate and interpret the future value (FV) and present value (PV) of a single
sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows;
f. draw a time line and solve time value of money applications (for example, mortgages and savings for college tuition or retirement).

Reading 6: Discounted Cash Flow Applications
a. calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment, contrast the NPV rule to the IRR rule, and identify problems associated with the IRR rule;
b. define, calculate, and interpret a holding period return (total return);
c. calculate, interpret, and distinguish between the money-weighted and timeweighted rates of return of a portfolio and appraise the performance of portfolios based on these measures;
d. calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill;
e. convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.

Reading 7: Statistical Concepts and Market Returns
c. calculate and interpret relative frequencies and cumulative relative frequencies, given a frequency distribution;
e. define, calculate, and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean (including a portfolio return viewed as a weighted mean), geometric mean, harmonic mean, median, and mode;
f. describe, calculate, and interpret quartiles, quintiles, deciles, and percentiles;
g. define, calculate, and interpret 1) a range and a mean absolute deviation and
2) the variance and standard deviation of a population and of a sample;
h. calculate and interpret the proportion of observations falling within a specified number of standard deviations of the mean using Chebyshev’s inequality;
i. define, calculate, and interpret the coefficient of variation and the Sharpe ratio;

Reading 8: Probability Concepts
k. calculate and interpret covariance and correlation;
l. calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio;
m. calculate and interpret covariance given a joint probability function;
n. calculate and interpret an updated probability using Bayes’ formula;
o. identify the most appropriate method to solve a particular counting problem and solve counting problems using the factorial, combination, and permutation notations.

Reading 9: Common Probability Distributions
d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;
f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions;
h. describe the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform probability distribution;
j. determine the probability that a normally distributed random variable lies inside a given confidence interval;
k. define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution;
l. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion;
n. distinguish between discretely and continuously compounded rates of return and calculate and interpret a continuously compounded rate of return, given a specific holding period return;

Reading 10: Sampling and Estimation
e. calculate and interpret the standard error of the sample mean;
h. explain the construction of confidence intervals;
i. describe the properties of Student’s t-distribution and calculate and interpret its degrees of freedom;
j. calculate and interpret a confidence interval for a population mean, given a normal distribution with 1) a known population variance, 2) an unknown population variance, or 3) an unknown variance and a large sample size;

Reading 13: Elasticity
a. calculate and interpret the elasticities of demand (price elasticity, cross elasticity, and income elasticity) and the elasticity of supply and discuss the factors that influence each measure;
b. calculate elasticities on a straight-line demand curve, differentiate among elastic, inelastic, and unit elastic demand, and describe the relation between price elasticity of demand and total revenue.

Reading 16: Organizing Production
f. calculate and interpret the four-firm concentration ratio and the Herfindahl-Hirschman Index and discuss the limitations of concentration measures;

Reading 22: Monitoring Jobs and the Price Level
d. explain and calculate the consumer price index (CPI) and the inflation rate, describe the relation between the CPI and the inflation rate, and explain the main sources of CPI bias.

Reading 34: Understanding the Cash Flow Statement
h. explain and calculate free cash flow to the firm, free cash flow to equity, and other cash flow ratios.

Reading 35: Financial Analysis Techniques
d. calculate, classify, and interpret activity, liquidity, solvency, profitability, and valuation ratios;
g. calculate and interpret the ratios used in equity analysis, credit analysis, and segment analysis;

Reading 36: Inventories
c. compute ending inventory balances and cost of goods sold using the FIFO, weighted average cost, and LIFO methods to account for product inventory and explain the relationship among and the usefulness of inventory and cost of goods sold data provided by the FIFO, weighted average cost, and LIFO methods when prices are 1) stable, 2) decreasing, or 3) increasing;
f. compute and describe the effects of the choice of inventory method on profitability, liquidity, activity, and solvency ratios;
g. calculate adjustments to reported financial statements related to inventory assumptions to aid in comparing and evaluating companies;

Reading 37: Long-Lived Assets
b. compute and describe the effects of capitalizing versus expensing on net income, shareholders’ equity, cash flow from operations, and financial ratios, including the effect on the interest coverage ratio of capitalizing interest costs;
e. discuss the use of fixed asset disclosures to compare companies’ average age of depreciable assets and calculate, using such disclosures, the average age and average depreciable life of fixed assets;
j. calculate and describe both the initial and long-lived effects of asset revaluations on financial ratios.

Reading 38: Income Taxes
d. calculate income tax expense, income taxes payable, deferred tax assets, and deferred tax liabilities, and calculate and interpret the adjustment to the financial statements related to a change in the income tax rate;

Reading 39: Long-Term Liabilities and Leases
a. compute the effects of debt issuance and amortization of bond discounts and premiums on financial statements and ratios;

Reading 44: Capital Budgeting
d. calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, and profitability index (PI);

Reading 45: Cost of Capital
a. calculate and interpret the weighted average cost of capital (WACC) of a company;
f. calculate and interpret the cost of fixed rate debt capital using the yield-to-maturity approach and the debt-rating approach;
g. calculate and interpret the cost of noncallable, nonconvertible preferred stock;
h. calculate and interpret the cost of equity capital using the capital asset pricing model approach, the dividend discount model approach, and the bond-yield-plus risk-premium approach;
i. calculate and interpret the beta and cost of capital for a project;

Reading 46: Working Capital Management
e. compute and interpret comparable yields on various securities, compare portfolio returns against a standard benchmark, and evaluate a company’s short-term investment policy guidelines;

Reading 50: An Introduction to Portfolio Management
c. compute and interpret the expected return, variance, and standard deviation for an individual investment and the expected return and standard deviation for a portfolio;
d. compute and interpret the covariance of rates of return and show how it is related to the correlation coefficient;

Reading 51: An Introduction to Asset Pricing Models
e. calculate, using the SML, the expected return on a security and evaluate whether the security is overvalued, undervalued, or properly valued.

Reading 56: An Introduction to Security Valuation
c. calculate and interpret the value of both a preferred stock and a common stock using the dividend discount model (DDM);
f. estimate the dividend growth rate, given the components of the required rate of return incorporating the earnings retention rate and current stock price;

Reading 58: Company Analysis and Stock Valuation
b. describe and estimate the expected earnings per share (EPS) and earnings multiplier for a company and use the multiple to make an investment decision regarding the company.

Reading 59: Introduction to Price Multiples
b. calculate and interpret price-toearnings ratio (P/E), price-to-book value (P/BV), price-to-sales ratio (P/S), and price-to-cash flow (P/CF).

Reading 61: Risks Associated with Investing in Bonds
f. compute and interpret the duration and dollar duration of a bond;

Reading 63: Understanding Yield Spreads
e. compute, compare, and contrast the various yield spread measures;
i. compute the after-tax yield of a taxable security and the tax-equivalent yield of a tax-exempt security;

Reading 64: Introduction to the Valuation of Debt Securities
c. compute the value of a bond and the change in value that is attributable to a change in the discount rate;
d. explain how the price of a bond changes as the bond approaches its maturity date and compute the change in value that is attributable to the passage of time;
e. compute the value of a zero-coupon bond;

Reading 65: Yield Measures, Spot Rates, and Forward Rates
b. compute and interpret the traditional yield measures for fixed-rate bonds and explain their limitations and assumptions;
c. explain the importance of reinvestment income in generating the yield computed at the time of purchase, calculate the amount of income required to generate that yield, and discuss the factors that affect reinvestment risk;
d. compute and interpret the bond equivalent yield of an annual-pay bond and the annual-pay yield of a semiannual-pay bond;
e. describe the methodology for computing the theoretical Treasury spot rate curve and compute the value of a bond using spot rates;
h. explain a forward rate and compute spot rates from forward rates, forward rates from spot rates, and the value of a bond using forward rates.

Reading 66: Introduction to the Measurement of Interest Rate Risk
d. compute and interpret the effective duration of a bond, given information about how the bond’s price will increase and decrease for given changes in interest rates, and compute the approximate percentage price change for a bond, given the bond’s effective duration and a specified change in yield;
f. compute the duration of a portfolio, given the duration of the bonds comprising the portfolio, and explain the limitations of portfolio duration;
g. describe the convexity measure of a bond and estimate a bond’s percentage price change, given the bond’s duration and convexity and a specified change in interest rates;
i. compute the price value of a basis point (PVBP), and explain its relationship to duration.

Reading 68: Forward Markets and Contracts
g. calculate and interpret the payoff of an FRA, and explain each of the component terms;

Reading 69: Futures Markets and Contracts
d. describe price limits and the process of marking to market and compute and interpret the margin balance, given the previous day’s balance and the change in the futures price;

Reading 70: Option Markets and Contracts
f. compute and interpret option payoffs, and explain how interest rate option payoffs differ from the payoffs of other types of options;
h. determine the minimum and maximum values of European options and American options;
i. calculate and interpret the lowest prices of European and American calls and puts based on the rules for minimum values and lower bounds;

Reading 71: Swap Markets and Contracts
b. define, calculate, and interpret the payment of currency swaps, plain vanilla interest rate swaps, and equity swaps.

Reading 72: Risk Management Applications of Option Strategies
a. determine the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph of the strategies of buying and selling calls and puts, and indicate the market outlook of investors using these strategies;
b. determine the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph of a covered call strategy and a protective put strategy, and explain the risk management application of each strategy.

Reading 73: Alternative Investments
f. calculate the net operating income (NOI) from a real estate investment, the value of a property using the sales comparison and income approaches, and the aftertax cash flows, net present value, and yield of a real estate investment;
h. calculate the net present value (NPV) of a venture capital project, given the project’s possible payoff and conditional failure probabilities;