Book 4: Equity

Question 1

What are some different definitions of value?

Answer 1

Intrinsic value: valuation with complete understanding of characteristics of asset or issuing firm. Most relevant metric.

IV = actual mispricing + valuation error

IV_analyst - price = (IV_actual - price) + (IV_analyst - IV_actual)

Liquidation value: estimate of what assets would be worth if sold separately, net of company’s liabilities. (versus going concern value, which assumes going concern).

Fair market value: price at which willing, informed and able seller would trade asset to willing, informed and able buyer. Market price should reflect fair market value over time.

Investment value: value of a stock to a specific buyer, taking into account his synergies and expectations.

Question 2

What’s the difference between an absolute valuation and relative valuation model?

Answer 2

Absolute: estimates asset’s intrinsic value, without regard to value of other firms. Eg FCF approach, dividend discount model, residual income approach, asset-based models (sum of market value of assets).

Relative: determine value of asset in relation to other assets. Eg comparing multiples (P/E).
- pairs trading: 2 similar stocks, buy undervalued one and short overvalued one.

Question 3

What is sum-of-parts valuation?

Answer 3

Adding up individual parts of firm to determine value of whole. aka breakup value or private market value.

Conglomerate discount: investors apply markdown to value of company operating in multiple unrelated industries, compared to one with a single industry focus. This market value under-represents sum-of-parts value. Due to:

• Internal capital inefficiency
• Endogenous (internal) factors
• Research measurement errors

Question 4

What is the holding period return (HPR)?

Answer 4

HPR is the increase in price of an asset + any CF received, divided by initial price of the asset.

HPR = (P1 - P0 + CF1) / P0

HPR = [(P1 + CF1) / P0] - 1

HPR = CF1 / P0 + [(P1 - P0) / P0]

HPR = dividend yield + price appreciation return (aka capital gains yield)

If CF is received before end of period, then CF1 should be cash received plus any interest on reinvestment of the CF.

HPR = (end of period value / beginning of period value) - 1

HPR = (Price at end of period + Dividend over period / Price at beginning of period) - 1

Expected alpha = Expected return - required return

Realised alpha = Actual HPR - Contemporaneous required return

Question 5

What is price convergence to intrinsic value?

Answer 5

If expected return != required return, there can be a “return from convergence of price to intrinsic value”.

expected return = required return + [(V0 - P0) / P0]

V0 = intrinsic value

Question 6

What is equity risk premium (ERP) and how is it used to get required RoR?

Answer 6

ERP is the return in excess of the RFR that investors require.

Equity risk premium = require return on equity index - RFR

Required RoR = RFR + Beta*equity risk premium

Beta provides adjustment for systematic risk inherent in stock. If systematic risk is > than market, then B > 1.

Required RoR = RFR + equity risk premium + other risk premia/discounts

Question 7

What are historical vs. forward-looking estimates of the equity risk premium?

Answer 7

Historical: Consist of difference b/w historical mean return for a broad-based equity index and a RFR over a time period. Objective and simple. However, assumes mean and variance of returns are constant over time, which is not always realistic. Historical estimates can also be upward bias due to survivorship bias (only firms that have survived are included in sample). Also take care whether determining with geometric mean or arithmetic mean. Geometric mean increasingly preferred for historical estimates. And if yield curve slopes upward, whether using LT or ST bonds to estimate RFR. LT generally preferred.

Forward-looking (ex ante): Use current info an expectations concerning economic and financial variables. Does not rely on assumption of stationary and is less subject to problems like survivorship bias. Includes Gordon growth model, supply-side models, and estimates from surveys (use consensus of opinions from survey of experts).

Question 8

What is the Gordon growth model (aka constant growth model)?

Answer 8

Forward-looking estimate of ERP.

GGM ERP = expected dividend yield + expected LT growth rate - current LT govt bond yield.

GGM ERP = (1-year forecasted dividend yield on market index) + (consensus LT earnings growth rate) - (LT govt bond yield)

GGM ERP = (D1 / P) + g - rLTg0

Weakness: assumes stable dividend and growth rate. If growth rate is too variable could use:

equity index price = PV of projected CFs during rapid growth stage + …transitional growth stage + …mature growth stage

Also can be used to determine stock price:

P0 = D1 / (ke - g)

ke = RoR on equity (not the expected return for market, don’t be fooled, solve it by CAPM)

g = dividend growth

Question 9

What are supply-side (macroeconomic) models (ie Ibbotson-Chen) for estimating ERP?

Answer 9

Forward-looking estimate of ERP based on relationships b/w macroeconomic and financial variables. Uses proven models and current info. Weakness: estimates only appropriate for developed countries where equity represents large share of economy.

ERP = {[(1 + i) * (1 + rEg) * (1 + PEg) - 1] + Y} - RFR

i = expected inflation (eg difference in YTM of 20 year T-bond vs 20 -year TIPS)

rEg = expected real growth in real earnings per share (eg expected growth in corporate earnings, estimated as GDP growth, or labor productivity growth rate + labor supply growth rate, or)

PEg = expected changes in P/E ratio (depends whether analyst thinks market is overvalued (P/E ratios would tend to decrease))

Y = expected (dividend) yield on the index

RFR = expected (LT) RFR

Question 10

Estimating required return via CAPM?

Answer 10

Required RoR on stock j = RFR + Bj*(ERP)

E(Ra) = Rf + Ba[E(Rmkt) - Rf]

The relationship between beta and expected return. In equilibrium, the expected return on risky asset E(Ra) is the RFR (Rf) plus a beta-adjusted market risk premium, Ba[E(Rmkt) - Rf].

Strength is it’s simple and uses only one factor. Weakness is choosing appropriate factor and low explanatory power in some cases.

Question 11

Estimating required return via multifactor model?

Answer 11

CAPM is a single factor model.

required return = RFR + (risk premium_1) + risk premium_2) + …

risk premium_i = factor sensitivity_i * factor risk premium_i

Factor sensitivity: factor beta; asset’s sensitivity to a particular factor

Factor risk premium: expected return above RFR from a unit sensitivity to the factor and zero sensitivity to all other factors.

Strength: high explanatory power. Weakness: more complex and expensive.

Question 12

Estimating required return via the Fama-French model?

Answer 12

Fama-French is a multifactor model that attempts to account for higher returns associated with small-cap stocks. Incorporates market, size, and value risk (eg financial distress) factors.

Required return of j = RFR + Bmkt,j * (Rmkt - RFR) + Bsmb,j * (Rsmall - Rbig) + Bhml,j * (Rhbm - Rlbm)

(Rmkt - RFR): return on value-weighted market index less 1-month T-bill RFR

(Rsmall - Rbig): small-cap return on premium, equal to avg return on 3 small-cap portfolio less avg return on 3 large-cap portfolio

(Rhbm - Rlbm): value return on premium, equal to avg return on 2 high book-to-market portfolios less avg return on 2 low book-to-market portfolios

Baseline value for Bmkt,j is 1, baseline value for Bsmb,j and Bhml,j is 0. We expect a positive size beta if entity’s market cap is small.

Question 13

Estimating required return via the Pastor-Stambaugh model?

Answer 13

Adds a liquidity factor to the Fama-French model. Baseline for liquidity factor is zero. Less liquid assets should have positive beta, while more liquid assets should have negative beta.

Required return of j = RFR + Bmkt,j * (Rmkt - RFR) + Bsmb,j * (Rsmall - Rbig) + Bhml,j * (Rhbm - Rlbm) + [Bliquidity,j * liquidity premium]

(Rmkt - RFR): return on value-weighted market index less RFR

(Rsmall - Rbig): small-cap return on premium, equal to avg return on small-cap portfolio less avg return on large-cap portfolios

(Rhbm - Rlbm): value return on premium, equal to avg return on high book-to-market portfolios less avg return on low book-to-market portfolios

Question 14

Estimating required return via macroeconomic multifactor models?

Answer 14

Burmeister, Roll and Ross model incorporates 5 factors:
- Confidence risk: unexpected change in difference b/w return of risky corporate bonds and govt bonds

• Time horizon risk: unexpected change in difference b/w return of LT govt bonds and treasury bills
• Inflation risk: unexpected changes due to inflation
• Business cycle risk: unexpected change in level of real business activity
• Market timing risk: equity market return not explained by other four factors

In a problem:

required return = RFR + (different risks * their respective sensitivity facotrs)

Question 15

Estimating required return via build-up method?

Answer 15

Similar to risk premium approach. Usually applied to closely held companies where betas are not readily obtainable.

Required return = RFR + ERP + size premium + specific-company premium

Size premium depends on size of company, larger premium for smaller companies.

Strength: simple and can apply to closely held companies. Weakness: use historical values as estimates that may or may not be relevant to current market conditions.

Question 16

Estimating required return via bond-yield plus risk premium method?

Answer 16

A build-up method that is appropriate if company has publicly traded debt.

Adds a risk premium to the YTM of company’s LT debt.

BYPRP cost of equity = YTM on company’s LT debt + ERP

YTM of bonds includes effects of inflation, leverage and sensitivity to business cycle. Because these are taken into account already, can simply add premium for added risk arising from equity.

Question 17

Explain beta estimation for public companies?

Answer 17

Can compute beta for public company by regressing returns of company’s stock on returns of overall market.

When forecasting ERP, may adjust beta for beta drift (tendency of an estimated beta to revert to a value of 1 over time).

adjusted beta = (2/3 * regression beta) + (1/3 * 1)

Question 18

Explain beta estimation for thinly traded stocks and nonpublic companies?

Answer 18

1) Identify benchmark company that is publicly traded and similar to yours
2) Estimate beta of that benchmark company via regression analysis
3) Unlever beta estimate for benchmark company with:

Unlevered beta = Beta * {1 / [1 + (debt / equity)]}

4) Lever up the unlevered beta using the debt and equity of your company:

estimate of your beta = Unlevered beta * [1 + (your debt / your equity)]

Question 19

What international considerations in required return estimation?

Answer 19

Should compute required return in home currency then adjust it using forcasts for changes in relevant exchange rate.

Country spread model: use a corresponding developed market as a benchmark and add a premium for the emerging market.

Country risk rating model: estimate a regression equation using ERP for developed countries as dependent variable and risk ratings for those countries as independent variable.

Question 20

Calculate the WACC?

Answer 20

WACC can be measured as:

WACC = [(market value of debt / market value of debt and equity) * rd * (1 - tax rate)] + [(market value of equity / market value of debt and equity) * re]

rd = required return on debt
re = required return on equity

WACC = (Wd)(Kd(1 - tax rate)) + (Wps)(Kps) + (Wce)(Kce)

The weighted cost of debt (after tax, using interest rate on new debt) + weighted cost of preferred stock + weighted cost of common stock (equity).

Question 21

What are the 5 forces?

Answer 21

Attractiveness (LT profitability) is determined by 5 competitive forces:

1) Threat of new entrants into industry
2) Threat of substitutes

3) Bargaining power of buyers
4) Bargaining power of suppliers

5) Rivalry among existing competitors

Question 22

How does [1) Threat of new entrants into industry] drive profitability?

Answer 22

Higher barriers to entry = weaker threat of competition and greater pricing power of existing participants.

EG:

• economics of scale
• product differences and brand identity
• switching costs
• capital requirements
• access to distribution channels
• govt policy
• cost/quality advantages enjoyed by incumbents

Question 23

How does [2) Threat of substitutes] drive profitability?

Answer 23

Existing and future potential substitutes.

EG:

• relative price performance of substitutes (can the possible subs really do the job current products fill?)
• buyer propensity to substitute
• switching costs

Question 24

How does [3) Bargaining power of buyers] drive profitability?

Answer 24

How strong negotiating power of buyers is = affects price can sell product.

Bargaining leverage: low switching costs and readily available substitutes give buyers leverage and help strengthen this force for buyers.

Price sensitivity: buyer’s price sensitivity depends on qualitative factors (brand identity, product differences, quality, performance) and quantitative (relative price).

Question 25

How does [4) Bargaining power of suppliers] drive profitability?

Answer 25

Affects price of inputs.

EG:

• amount of different inputs acceptable to industry
• presence of substitute inputs
• supplier concentration
• importance of volume to supplier (higher volume desire lowers supplier’s bargaining power)
• threat of forward integration (supplier may want to enter industry)
• switching costs (higher costs mean more supplier power)

Question 26

How does [5) Rivalry among existing competitors] drive profitability?

Answer 26

Follow sensible pricing policies or engage in price competition? Engage in non-price competition that increases costs?

EG:

• number of competitors (more = harder)
• industry growth = strong demand and less need to compete
• high operating/financial leverage = more likely to have price competition to protect market share and cover fixed costs
• greater participant’s commitment to business = greater likelihood of competitive behaviour
• product differences = more difficult to compete directly on price
• product shelf life = shorter life = greater price competition at end of life
• exit barriers = costly to leave industry = increased competition
• informational complexity = difficult for competitors to communicate discretely = reduced damaging competition

Question 27

What factors affect an industry on a temporary basis but don’t determine profitability and structure in the LT?

Answer 27

Industry growth rate: high growth reduces competition but does not ensure profitability

Innovation and technology: improved tech does not improve profits if it attracts competitors

Govt policies: prone to change

Complementary products: products used in conjunction with firm’s products. Some complements can create or increase barriers to entry and reduce competition, while others can increase competition.

Question 28

What are four types of strategy?

Answer 28

Classical (predictible and unchangeable environments): setgoal, target, and try to build that position through orderly, successive rounds of planning, using quantitative forward-looking methods.

Visionary strategy (predictable and changeable environments): know the future and can predict the path to realising it (eg UPS preparing for e-commerce)

Adaptive (unpredictable and unchangeable environments): strategy is tightly linked with operations, planning cycles are short, and plans are rough based on best available data.

Shaping (unpredictable and changable environments): short planning cycles, flexibility, but unlike “adaptives” focus beyond boundaries of own company and define new markets, standards and practices (eg internet companies).

Question 29

What are three predominant definitions of future CFs in valuation models?

Answer 29

Dividends:

• Advantage: theoretically justified. less volatile than other measures
• Disadvantages: difficult to implement for firms that don’t currently pay dividends. can’t control dividends if own minority stake.

-Best used when: history of dividends related to earnings of firm, from perspective of minority shareholder.

Free CF to firm (FCFF): CF generated by operations in excess of capital investment to sustain operations. FCFE is the above plus expenses to finance debt.

• Advantage: can apply to many firms, regardless of dividend policies or structure. More pertinent to controlling holder who can influence.
• Disadvantage: may be difficult; firms with significant capital requirements may have negative FCF.

-Best used when: no or unclear dividend history; FCF that corresponds with profitability; from perspective of controlling shareholder.

Residual income: amount of earnings that exceeds investors’ required return.

• Advantage: can be applied to negative CF and non-dividend firms.
• Disadvantage: require accounting analysis of accruals.

-Best used when: no dividend history; negative FCF; transparent financial reporting

Question 30

What is the one-period DDM?

Answer 30

V0 = (D1 + P1) / (1 + r)

V0 = fundamental value
D1 = dividends expected to be received end of Year 1
P1 = price expected at end of year 1
r = required return on equity

vs. two-period:
V0 = [D1 / (1 + r)^1] + [(D2 + P2) / (1 + r)^2]

or multi-period:
V0 = [D1 / (1 + r)^1] + [(D2 + P2) / (1 + r)^2] + … + [(Dn + Pn) / (1 + r)^n]

Question 31

What is the two-period DDM?

Answer 31

V0 = [D1 / (1 + r)^1] + [(D2 + P2) / (1 + r)^2]

V0 = fundamental value
D1/2 = dividends expected to be received end of Year 1/2
P2 = price expected at end of year 2
r = required return on equity

vs. one-period:
V0 = (D1 + P1) / (1 + r)

or multi-period:
V0 = [D1 / (1 + r)^1] + [(D2 + P2) / (1 + r)^2] + … + [(Dn + Pn) / (1 + r)^n]

Question 32

What is the multi-period DDM?

Answer 32

V0 = [D1 / (1 + r)^1] + [(D2 + P2) / (1 + r)^2] + … + [(Dn + Pn) / (1 + r)^n]

V0 = fundamental value
D1/2 = dividends expected to be received end of Year 1/2
Pn = price expected at end of year n
r = required return on equity
n = length of holding period

vs. one-period:
V0 = (D1 + P1) / (1 + r)

or two-period:
V0 = [D1 / (1 + r)^1] + [(D2 + P2) / (1 + r)^2]

Question 33

What is the Gordon growth model?

Answer 33

DDM model assuming that dividends increase at a constant rate indefinitely.

V0 = (D0 * (1 + g)) / (r - g) = D1 / (r - g)

V0 = fundamental value
D0 = dividend just paid
D1 = dividend expected at end of Year 1
r = required return on equity
g = dividend growth rate

Warning: may be required to use the above equation to solve for g.

Question 34

Calculate the PV of growth opportunities and use to compute leading P/E ratio?

Answer 34

V0 = (E / r) + PVGO

V0 = fuindamental value
E = no-growth earnings level (expected EPS in problem)
r = required return on equity

After solving for PVGO, use the PVGO as the EPS to compute the P/E ratio. Then, say:

P/E firm = 60CU / 5CU = 12x

P/E PVGO = 10CU / 5CU = 2x

then 2/12 or 16.7% of leading P/E ratio is attributable to PVGO.

Question 35

Calculate justified P/Es?

Answer 35

Justified P/E: uses ‘fundamental’ data (ie P0 = price derived from Gordon growth model).

Leading P/E: for the next period.

P/E = P0 / E1 = (D1 / E1) / (r - g) = (1 - b) / (r - g)

Trailing P/E: for the previous period.

P/E = P0 / E0 = [D0 * (1 + g)] / (r - g) = [(1 - b) * (1 + g)] / (r - g)

P0 = fundamental value
D0 = dividends just paid
D1 = dividends expected in one year
E0 = current earnings
E1 = earnings expected in one year
b = retention ratio = dividend per share / EPS
(1 - b) = dividend payout ratio
g = dividend growth rate

Question 36

Calculate justified leading P/E?

Answer 36

Leading P/E: for the next period.

P/E = P0 / E1 = (D1 / E1) / (r - g) = (1 - b) / (r - g)

P0 = fundamental value
D1 = dividends expected in one year
D1 = earnings expected in one year
b = retention ratio = dividend per share / EPS
(1 - b) = dividend payout ratio
g = dividend growth rate

Question 37

Calculate justified training P/E?

Answer 37

Trailing P/E: for the previous period.

P/E = P0 / E0 = [D0 * (1 + g)] / (r - g) = [(1 - b) * (1 + g)] / (r - g)

P0 = fundamental value
D0 = dividends just paid
E0 = current earnings
b = retention ratio = dividend per share / EPS
(1 - b) = dividend payout ratio
g = dividend growth rate

Question 38

Retention ratio?

Answer 38

b = retention ratio = dividend per share / EPS

Question 39

Calculate value of noncallable fixed-rate perpetual preferred stock?

Answer 39

value of perpetual preferred shares = Dp / rp

Dp = preferred dividend (assumed not to grow)
rp = cost of preferred equity

Question 40

What are the (dis)advantages of the Gordon growth model?

Answer 40

Advantages:

• Applicable to stable, mature dividend-paying firms
• Appropriate for valuing market indices
• Easily communicated and explained
• Can determine price-implied growth rates, required RoR, and value of growth opportunities
• Can be used to supplement other, more complex valuations

Disadvantages:

• Sensitive to estimates of growth rates and required RoRs
• Cannot easily apply to non-dividend stocks
• Unpredictable growth patterns of some firms

Question 41

Multi-stage DDMs?

Answer 41

Gordon growth model is unrealistic because it assumed constant dividend growth.

Most growth rates tend to revert to a long-run rate approx. equal to LT growth rate in real GDP + the LT inflation rate.

Two-stage DDM: Assume grow at high-rate then revert to long-run

H-Model: same as two-stage, but that growth rate declines linearly over time to long-run, rather than reverting suddenly

Three-stage DDM: three distinct stages of earnings growth

Question 42

Explain the growth, transitional and maturity phase of a business?

Answer 42

Initial: rapidly increasing earnings, little or no dividends, and heavy reinvestment

Transition: earnings/dividends increasing but at slower pace

Mature: earnings grow stable but slower rate, payout ratios stabalize

Question 43

Estimate terminal value for a DDM model?

Answer 43

DDM model needs a terminal value, can use Gordon growth model or market multiple approach.

GGM:

V0 = (D0 * (1 + g)) / (r - g) = D1 / (r - g)

V0 = fundamental value
D0 = dividend just paid
D1 = dividend expected at end of Year 1
r = required return on equity
g = dividend growth rate

Market multiple:

Simply P/E * earnings estimate.