Today, we’ll look at a few of the basics in reading 39 which cover present value models for valuation.

There are three basic models given: dividend discount, free cash flow, and residual income.

Besides being able to plug data and calculate valuation, you are expected to understand the differences between the models and decide which model to use given different scenarios.

As with many of the formulas in the CFA curriculum, you should start with the concept behind the calculation and understand what it means.

This will help you get the conceptual points on the exams, which I would say are easily more than half of total points, and will help you memorize the formula.

Valuation revolves around estimating future cash flows from an investment and the rate of return that investors expect.

With these two points, as well as a time component, you can know how much the investment is worth in today’s dollars.

Of course the problem with equities is that you do not know this information with certainty. The models are an attempt at measuring the most accurate and important components of cash flow and assigning a discount rate.

## Dividend Discount Models

Dividends are used as a proxy for cash flows because they are less volatile than earnings and average investors do not have control over the timing or receipt of cash flows.

The disadvantages with dividend models is that not all companies pay dividends and that the models are highly sensitive to input estimation.

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.

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.

The H-model looks intimidating at first but is actually fairly easy. It is just the GGM (with the long-term growth rate) plus another GGM equation using half the difference between short-term and long-term growth.

It is an attempt to estimate a linearly declining growth rate across the two periods.

## Free Cash Flow Models

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 is the cash generated from operations after that needed for continued operations is deducted.

If this cash stream were taken from the company (and paid to investors or debt holders) it would not affect the company as a going concern.

The advantage 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.

For brevity, I will defer the calculations to a prior post which showed how to arrive at FCFE from FCFF, FCFF from CFO and from EBITDA.

Once again, the ultimate importance is not so much being able to mindlessly plug numbers into the equations but to understand what these formulas mean.

Being able to derive different components by changing around the equations is something you must be able to do (i.e. estimate P/E from the different valuation models).

## Residual Income Models

Residual income is the net income left after discounting for a minimum required return for equity.

Its advantage is that it can be used when a company does not pay dividends and when free cash flow is negative.

The main disadvantage is the adjustments needed to the income statement. We know that management has an incentive to manipulate earnings (net income), so the adjustments can be fairly complicated.

The basic formula for residual income is net income minus beginning book value times required return on equity.

RI = NI – r_{ce }BV

The curriculum does not go over the adjustment process here in valuation but is applicable to the material in Financial Reporting & Analysis.

On the exam, you may be asked to do some fairly basic adjustments (maybe normalizing EPS) but will probably not have to do major adjustments.

The calculations for the formulas in equity valuation are fairly simple once you understand the concepts, so we haven’t spent much time looking at the formulas themselves.

The study guide and summary sheets do a better job of breaking the formulas down than I could anyway.

Understand and be able to calculate each one, including arriving at the discount rate through CAPM and Bond-yield plus methods.

Flash cards lend themselves well to learning the separate formulas. Write out a word problem (not just a list of numerical data) on one side and then the solution (with calculations on the other.

Some cards, like the single-stage DDM, you will probably get pretty quickly and be able to pass over after a couple of reviews.

Other cards, like the H-Model, will take longer. Do not neglect the more detailed and difficult formulas! Spend a little extra time and get this stuff down because you still might see it at the Level III exam as well.

‘til next time, happy studyin’

Joseph Hogue, CFA