CFA® Level I Quantitative Methods

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It is essential to grasp the time value of money and probability concepts within the quantitative section to pass the CFA exam. Time value of money (TVM) is a foundational principle in the quantitative part of the CFA exam that cascades into many other areas of the curriculum, such as equity investments, fixed income valuation, and corporate finance. At a high level, TVM involves relating different amounts of money over time after accounting for some return rate. If you invest $100 today into a bank account that pays 5% effective annual interest, you will have $105 in a year. The 5% rate of return, and the duration of one year, are the factors that bridge the present value of $100 to the future value of $105. 

Of course, actual exam questions are more complex and may involve discounting or compounding a series of cash flows over many periods. Such questions may ask you to determine present value, future value, the discount rate, or the size of the intermittent cash flows. For example, the timeline diagram below illustrates how depositing €100,000 annually for five years into a bank account that earns 5% annual interest will result in €552,263 at the end of Year 5. As a CFA candidate, it is crucial to understand the mechanics first. However, once you do, most of the questions will be easily solved with a financial calculator. The two approved calculators are the TI BAII plus and the HP12c.

Once you have grasped the time value of money concepts in the quant section, you will apply these principles to capital budgeting in the corporate finance section. Capital budgeting involves analyzing forecasted cash flows to select the high-stake project(s) that maximizes company wealth. Questions may include using discounted cash flow analysis to calculate and compare net present values (NPV) and internal rate of return (IRR) across many projects. NPV is the current value of a project’s forecasted cash inflows and outflows discounted at the weighted average cost of capital (WACC). IRR is the discount rate that results in an NPV of zero. It is theoretically the annual rate of return investors will earn from financing a project. Generally, it is beneficial for firms to select projects with high NPV and IRR. When the two metrics conflict, firms should abide by the NPV.

Similarly, TVM can be used to value financial securities such as stocks or bonds. The framework is the same with differences in the type of cash flow and the discount rate. It is common for stocks to discount equity-free cash flow (FCFE) at the cost of equity. Equity free cash flow is the firm’s cash after accounting for working capital investments, capital expenditures, and change to net debt. It is common for bonds to discount coupon payments at the yield to maturity (i.e., market discount rate). Investors can use such discounted cash flow analysis to assess whether to buy a security based on whether its intrinsic value is less to the market price. Now that we have covered TVM concepts at a high level let’s shift gears to probability concepts.

Probability concepts center around probability distributions and lay the foundation for almost all sections of Quantitative Methods. From a forecasting perspective, probability distributions can estimate an asset’s expected return range based on historical patterns, utilizing averages and standard deviations. This allows investors to predict an expected range of future returns with a certain level of confidence. Furthermore, probability concepts can be used to assess the expected value of an asset-based on the conditional events that occur before it. For example, option pricing models are used to calculate the expected value of options conditioned on the underlying stock price relative to the strike price.

From a research angle, probability concepts are beneficial for sampling or hypothesis testing. Both scenarios may arise when it is too costly or time-consuming to test all the underlying population members. For example, a production manager may want to verify whether the product’s actual defect rate is at or beneath some acceptable threshold. If there are millions of units, then it may be difficult and expensive to determine the exact defect percentage so that the manager might apply sampling and hypothesis testing to a smaller subset, calculate the sample’s defect rate and assess whether it is indicative of the population based on the mean rate and standard deviation.

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