Corporate Finance Quiz: Cost Of Equity

20 questions · exam conditions

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Cost Of EquityQuestion 1 of 20

Two companies in the same industry have identical systematic risk profiles, but Company X trades at a significant liquidity discount compared to Company Y. When estimating the cost of equity using CAPM for both companies, which statement is most accurate?

Company X should have a higher beta coefficient to reflect its liquidity risk premium

CAPM will underestimate Company X's true cost of equity relative to Company Y's cost of equity

The risk-free rate component should be adjusted upward for Company X to account for liquidity

Both companies will have identical CAPM-derived costs of equity since they have identical systematic risk

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Corporate Finance Quiz

Corporate Finance Quiz: Cost Of Equity

Practice Cost Of Equity in Corporate Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Cost Of Equity, giving you a quick way to practice the rules, question types, and explanations that matter most for Corporate Finance.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Company X should have a higher beta coefficient to reflect its liquidity risk premium
CAPM will underestimate Company X's true cost of equity relative to Company Y's cost of equity (correct answer)
The risk-free rate component should be adjusted upward for Company X to account for liquidity
Both companies will have identical CAPM-derived costs of equity since they have identical systematic risk

Explanation: CAPM only captures systematic (market) risk through beta and does not account for liquidity risk, which is largely unsystematic. Since Company X trades at a liquidity discount, investors require additional compensation beyond what CAPM predicts, making CAPM's estimate too low for Company X. Choice A is wrong because beta measures systematic risk correlation, not liquidity. Choice C incorrectly suggests adjusting the risk-free rate rather than recognizing CAPM's limitation. Choice D ignores that CAPM doesn't capture all relevant risk factors.

Question 2

An analyst expects heightened inflation and increased investor risk aversion over the next several years. Assuming the CAPM holds, what is the most likely combined effect of these two factors on the Security Market Line (SML) and the cost of equity for an average-risk stock ( $\beta = 1$ )?

The SML will shift up and become steeper; the cost of equity will increase. (correct answer)
The SML will shift up but become flatter; the cost of equity could increase or decrease.
The SML will shift down and become steeper; the cost of equity will decrease.
The SML will shift up, but its slope will not change; the cost of equity will increase.

Explanation: The Security Market Line (SML) is a graphical representation of the CAPM:

R_e = R_f + \beta(R_m - R_f)

Effect of heightened inflation: Higher expected inflation will lead to a higher nominal risk-free rate ( $R_f$ ). This increases the y-intercept of the SML, causing the entire line to shift upward in a parallel fashion.
Effect of increased risk aversion: Increased investor risk aversion means that investors will demand a higher premium for taking on risk. This causes the market risk premium ( $R_m - R_f$ ) to increase. The market risk premium is the slope of the SML. Therefore, an increase in the MRP makes the SML steeper.

Combined Effect: The SML's intercept shifts up, AND its slope becomes steeper. For any stock with a positive beta, both effects will increase the required rate of return. For an average-risk stock (

\beta = 1

), the cost of equity is the expected return on the market (

R_m = R_f + MRP

). Since both

R_f

and the MRP are increasing, the cost of equity must increase.

Question 3

A firm is restructuring its operations. It plans to divest a high-beta division ( $\beta = 1.8$ ) and acquire a firm in a stable, low-beta industry ( $\beta = 0.7$ ). Both the divested division and the acquired firm represent 20% of the firm's total value. The firm's pre-restructuring beta was 1.2. What is the most likely immediate impact of this restructuring on the firm's cost of equity, assuming all else remains constant?

It will increase because the acquisition adds new, unfamiliar operations.
It will decrease because the firm's overall systematic risk is reduced. (correct answer)
It will remain the same because the market risk premium has not changed.
It will remain the same because the weights of the divested and acquired units are equal.

Explanation: The firm's equity beta is a weighted average of the betas of its individual divisions. By selling a high-beta division and replacing it with a low-beta one of the same size, the company is lowering its overall systematic risk. The new beta will be a weighted average of the old portfolio and the change. The original beta was 1.2. The remaining 80% of the firm has a beta that can be inferred:

1.2 = 0.80 \times \beta_{rem} + 0.20 \times 1.8 \implies 1.2 = 0.8\beta_{rem} + 0.36 \implies 0.84 = 0.8\beta_{rem} \implies \beta_{rem} = 1.05

. The new firm beta will be:

\beta_{new} = 0.80 \times 1.05 + 0.20 \times 0.7 = 0.84 + 0.14 = 0.98

. Since the new beta (0.98) is lower than the old beta (1.2), the firm's cost of equity will decrease according to the CAPM formula

R_e = R_f + \beta(R_m - R_f)

. Distractor A confuses total risk/operational risk with systematic risk (beta). Distractors C and D provide incorrect reasoning for why the cost of equity would remain unchanged.

Question 4

The market's consensus cost of equity for a stock is 11.0%. The stock currently trades for $40 per share and is expected to pay a dividend of $1.80 next year. An analyst uses the CAPM with a risk-free rate of 3.0% and a market risk premium of 6.0% to value the stock. What must the analyst's estimate of the stock's beta be for their CAPM-derived cost of equity to be consistent with the implied growth rate from the dividend model?

1.08
1.25
1.33 (correct answer)
1.83

Explanation: This question requires recognizing that for the valuation to be consistent, the cost of equity from CAPM must equal the cost of equity implied by the market price and dividend expectations. This requires solving for beta from CAPM, using the market's consensus cost of equity.

The problem states the market's consensus cost of equity is 11.0%. This is the $R_e$ we should use.
The information about the stock price and dividend is provided to potentially confuse the test-taker into using the dividend growth model first. While one could calculate an implied growth rate ( $g = R_e - D_1/P_0 = 11\% - 1.80/40 = 11\% - 4.5\% = 6.5\%$ ), this is not needed to find the beta.
Use the CAPM formula and solve for $\beta$ $β$ .
- $R_e = R_f + \beta(MRP)$
- $11.0\% = 3.0\% + \beta(6.0\%)$
- $11.0\% - 3.0\% = \beta(6.0\%)$
- $8.0\% = \beta(6.0\%)$
- $\beta = \frac{8.0\%}{6.0\%} = 1.333... \approx 1.33$

Distractor B (1.25) is derived by using the dividend yield as the risk premium:

\beta = (11.0\%-3.0\%)/(1.80/40) = 8.0/4.5

- this is not right. Let's make a better one. Distractor A (1.08) might come from

(11.0-4.5)/6.0 = 1.08

. This is a plausible error where the dividend yield is subtracted from the cost of equity first. Distractor D (1.83) comes from

11.0/6.0

, ignoring the risk-free rate.

Question 5

An analyst is valuing a growth-oriented technology firm whose cash flows are expected to extend for several decades. The analyst has access to the following current U.S. Treasury yields:

3-Month T-Bill: 5.1%
2-Year T-Note: 4.5%
10-Year T-Bond: 4.2%
30-Year T-Bond: 4.4%

Which of these yields is the most theoretically sound choice for the risk-free rate in a CAPM valuation of this firm?

5.1%, because it is the most frequently used rate in practice and has the lowest interest rate risk.
4.5%, because it represents an average of short-term and long-term expectations.
4.2%, because it is a common benchmark, and the yield curve is currently inverted.
4.4%, because its duration most closely matches the long-term nature of the firm's cash flows. (correct answer)

Explanation: The principle of duration matching suggests that the risk-free asset used in valuation should have a duration similar to the duration of the cash flows being valued. For a firm whose value is derived from cash flows extending for many decades, the 30-year Treasury bond is the most appropriate proxy for the risk-free rate. While shorter-term rates are sometimes used in practice for convenience, the long-term bond yield is the most theoretically consistent choice. The fact that the yield curve is inverted (short-term rates are higher than long-term rates) is an observation about the current market but does not change the theoretical principle of matching durations.

Question 6

An analyst evaluates a stock with a beta of 1.3. The risk-free rate is 2.5% and the expected market return is 9.5%. The analyst independently forecasts that the stock will have a return of 12.0% over the next year. Based on the Security Market Line (SML), the stock is most likely:

underpriced, because its expected return is above its required return. (correct answer)
overpriced, because its expected return is below its required return.
fairly priced, because its expected return is positive.
overpriced, because its beta is greater than 1.0.

Explanation: This question requires comparing the stock's required return (from CAPM/SML) with its expected return (from the analyst's forecast).

Calculate the required return using CAPM: The required return is the return predicted by the SML.
- Market risk premium (MRP) = $R_m - R_f = 9.5\% - 2.5\% = 7.0\%$ .
- Required Return ( $R_e$ ) = $R_f + \beta(MRP) = 2.5\% + 1.3 \times 7.0\% = 2.5\% + 9.1\% = 11.6\%$ .
Compare expected return to required return:
- Analyst's expected return = 12.0%.
- CAPM required return = 11.6%.

Since the expected return (12.0%) is greater than the required return (11.6%), the stock is expected to deliver a return higher than what is needed to compensate for its systematic risk. This means the stock is currently underpriced. A rational investor would buy the stock, which would drive its price up and its expected future return down until it equals the required return of 11.6%.

Question 7

An analyst uses CAPM to determine that a company's required rate of return on equity is 13.0%. The company's stock currently trades for $75.00 per share, and it is expected to pay a dividend of $3.00 per share next year. If the analyst believes the stock is fairly priced, what is the long-term dividend growth rate implied by this information?

4.0%
8.7%
9.0% (correct answer)
17.0%

Explanation: If a stock is fairly priced, its required rate of return (from CAPM) should equal its expected rate of return (from the Dividend Growth Model). This question requires using this equivalence to solve for the implied growth rate (g).

Set up the Dividend Growth Model (DGM) formula for the cost of equity:
- $R_e = \frac{D_1}{P_0} + g$
Rearrange the formula to solve for g:
- $g = R_e - \frac{D_1}{P_0}$
Substitute the given values:
- $R_e = 13.0\%$ (from CAPM analysis)
- (D_1 = $3.00)
- (P_0 = $75.00)
Calculate the dividend yield and then g:
- Dividend Yield = (\frac{ $3.00}{$ 75.00} = 0.04) or 4.0%.
- $g = 13.0\% - 4.0\% = 9.0\%$

Distractor A (4.0%) is only the dividend yield component, not the growth rate. Distractor D (17.0%) incorrectly adds the dividend yield to the required return instead of subtracting it (

13\% + 4\% = 17\%

Question 8

A biotechnology firm announces that its revolutionary new drug unexpectedly failed its final clinical trial. The news is a complete surprise to the market and is specific to this one firm; the broader market remains stable. How does this firm-specific negative event, in and of itself, immediately affect the firm's equity beta?

Beta increases significantly because the firm's total risk has increased.
Beta decreases significantly as investors flee the now-riskier stock.
Beta becomes negative because the stock's price moved opposite to the stable market.
Beta is fundamentally unchanged because it measures systematic risk, not firm-specific risk. (correct answer)

Explanation: When you encounter questions about how firm-specific events affect beta, remember that beta specifically measures systematic risk—the portion of a stock's volatility that correlates with overall market movements. It doesn't capture total risk. Beta is calculated as:

\beta = \frac{\text{Covariance(Stock, Market)}}{\text{Variance(Market)}}

. A single firm-specific event, no matter how dramatic, doesn't immediately change this fundamental relationship between the stock and market movements. The clinical trial failure affects only this biotechnology firm and doesn't alter how the stock typically moves relative to broader market fluctuations. Choice A incorrectly conflates total risk with systematic risk. While the firm's total risk has indeed increased due to the negative news, beta measures only the systematic component—the part that moves with the market. Choice B makes a similar error, assuming that increased perceived risk automatically changes beta. The mechanism of investors fleeing doesn't alter the stock's correlation with market movements. Choice C reflects a common misconception that a single price movement opposite to the market creates negative beta. Negative beta requires a consistent pattern of moving opposite to the market, not just one instance. The correct answer is D because beta measures systematic risk, which represents how a security moves relative to the overall market. Firm-specific events, by definition, don't change this market relationship. Study tip: Remember that beta captures systematic risk only. When you see questions about company-specific news or idiosyncratic events, think "unsystematic risk"—these don't immediately affect beta calculations.

Question 9

A financial analyst calculates a company's cost of equity using two methods. The CAPM yields an estimate of 10.5%. The Dividend Discount Model (DDM) yields an estimate of 12.0%. The analyst has high confidence in the DDM inputs (current price, dividend, and growth forecast) but believes the company's historical beta may be a poor predictor of its future beta. Which of the following is the most reasonable conclusion?

The market is pricing higher risk than the historical beta suggests. (correct answer)
The CAMP estimate should be used as it is theoretically superior.
The stock is undervalued since DDM exceeds the required return.
The estimates should be averaged to get 11.25% cost of equity.

Explanation: The DDM-implied cost of equity (12.0%) reflects the return that current market participants are demanding, given the stock price and expected dividends. The CAPM cost of equity (10.5%) is a model-based estimate using historical beta. When the DDM-implied return exceeds the CAPM-calculated return, it suggests the market is discounting future cash flows at a higher rate than the CAPM predicts. Given concerns about historical beta's predictive power, the most plausible explanation is that the company's true systematic risk is higher than historical beta indicates, and the market price reflects this higher risk through the 12.0% required return.

Question 10

Company A and Company B operate in the exact same line of business and are identical in terms of size, operations, and business risk. Company A is financed entirely with equity. Company B has a debt-to-equity ratio of 1.0 and a tax rate of 30%. Which of the following statements about their respective equity betas ( $\beta_A$ and $\beta_B$ ) is most accurate?

Their equity betas will be identical because their business risk is identical.
$\beta_A$ will be higher than $\beta_B$ because all-equity firms have more volatile earnings per share.
$\beta_B$ will be higher than $\beta_A$ because Company B's equity holders bear additional financial risk. (correct answer)
The relationship cannot be determined without knowing the risk-free rate and market risk premium.

Explanation: Equity beta (levered beta,

\beta_L

) reflects both business risk (asset beta,

\beta_U

) and financial risk from leverage. Since both companies have identical business risk, their asset betas are the same. Company A is all-equity, so its equity beta is equal to its asset beta (

\beta_A = \beta_U

). Company B uses debt, so its equity beta is levered up from the asset beta:

\beta_B = \beta_U [1 + (1-t)(D/E)]

. Since

D/E > 0

and

t < 1

, the term in the brackets will be greater than 1. Therefore,

\beta_B

will be higher than

\beta_U

, and thus higher than

\beta_A

. This is because the debt amplifies the systematic risk borne by Company B's equity investors.

Question 11

A company's stock is currently trading at $60 per share. The company just paid its annual dividend of $2.40 ( $D_0$ ). Due to a major lawsuit settlement, the company's stock price drops to $50 overnight. Analysts believe the settlement will not affect the company's long-term ability to increase dividends, and they maintain their forecast for the long-term dividend growth rate. According to the constant-growth dividend model, what is the immediate effect of the price drop on the company's implied cost of equity?

It decreases, because the lower stock price signals lower risk.
It remains unchanged, because the dividend and growth rate are unaffected.
The effect cannot be determined without knowing the dividend growth rate.
It increases, because investors now require a higher return for the same expected cash flows. (correct answer)

Explanation: When analyzing changes in stock price using the constant-growth dividend model, you need to understand what drives the cost of equity. The model states:

P_0 = \frac{D_1}{r - g}

, where

P_0

is current price,

D_1

is next year's dividend,

r

is the cost of equity, and

g

is the growth rate. Since the lawsuit doesn't affect the company's dividend-paying ability or growth prospects, both

D_1

and

g

remain constant. However, the stock price dropped from $60 to $50. When you rearrange the formula to solve for the cost of equity: $

r = \frac{D_1}{P_0} + g

. With a lower

P_0

and unchanged

D_1

and

, the cost of equity

r$ must increase. This makes economic sense: investors are getting the same expected future cash flows (dividends) but paying a lower price today, which mechanically increases their required return. Let's examine why the other answers fail. Choice A incorrectly assumes lower stock prices always signal lower risk – but here, the price drop reflects a one-time settlement, not reduced business risk. Choice B misses that even when dividends and growth rates stay constant, the relationship between price and cost of equity still holds. Choice C suggests we need the growth rate to determine the effect, but the directional impact is clear regardless of the specific growth rate value. Remember this key principle: in dividend discount models, when expected cash flows remain unchanged but current price falls, the implied required return always increases. This inverse relationship between price and required return is fundamental to all valuation models.

Question 12

A company currently has an equity beta of 1.4 and a debt-to-equity ratio of 0.25. The company plans to undergo a leveraged recapitalization that will change its D/E ratio to 0.75. Assuming a tax rate of 20%, what will be the company's new equity beta after the recapitalization?

1.17
1.40
1.87 (correct answer)
2.24

Explanation: This is a three-step problem: 1) unlever the current beta to find the asset beta, 2) re-lever the asset beta using the new capital structure, 3) the result is the new equity beta.

Unlever the current equity beta ( $\beta_L$ ) to find the asset beta ( $\beta_U$ ):
- Current $\beta_L = 1.4$ , current D/E = 0.25, tax rate $t = 0.20$ .
- $\beta_U = \frac{\beta_L}{1 + (1-t)(D/E)} = \frac{1.4}{1 + (1-0.20)(0.25)} = \frac{1.4}{1 + (0.8)(0.25)} = \frac{1.4}{1 + 0.2} = \frac{1.4}{1.2} \approx 1.1667$
Re-lever the asset beta using the new target D/E ratio:
- New D/E = 0.75, $\beta_U = 1.1667$ , tax rate $t = 0.20$ .
- New $\beta_L = \beta_U [1 + (1-t)(D/E_{new})] = 1.1667 [1 + (1-0.20)(0.75)] = 1.1667 [1 + (0.8)(0.75)] = 1.1667 [1 + 0.6] = 1.1667 \times 1.6 \approx 1.8667$

Rounding to two decimal places gives 1.87. Distractor A (1.17) is the unlevered (asset) beta, an incomplete calculation. Distractor B (1.40) is the old beta, incorrectly assuming the recapitalization has no effect. Distractor D (2.24) might result from ignoring taxes in both steps:

\beta_U = 1.4/1.25 = 1.12

; New

\beta_L = 1.12 * 1.75 = 1.96

. Still not 2.24. This distractor may reflect a more complex calculation error.

Question 13

A large, stable food-processing company (equity $\beta = 0.8$ ) is evaluating a high-risk investment in a new biotech venture. The average equity beta for firms in the biotech industry is 1.7. The company plans to fund the venture using its existing capital structure. When calculating the net present value (NPV) of the biotech venture, which rate is most appropriate to use as the cost of equity?

A rate based on the company's beta of 0.8, as this reflects the cost to its current investors.
A rate based on the biotech industry's average beta of 1.7, adjusted for the company's leverage. (correct answer)
A rate based on the simple average of the company's beta and the industry's beta, (0.8 + 1.7)/2 = 1.25.
The company's weighted average cost of capital (WACC), since the project is funded by the company.

Explanation: The discount rate used to evaluate a project must reflect the systematic risk of that specific project, not the average risk of the parent company. Since the biotech venture has a very different risk profile from the core food-processing business, using the company's overall cost of equity (based on

\beta=0.8

) would be incorrect and would likely lead to overvaluing the risky project. The most appropriate approach is to use the beta of comparable firms in the project's industry (biotech,

\beta=1.7

) as a starting point. This industry beta should then be unlevered and re-levered to reflect the parent company's financing policy for the project, resulting in a project-specific cost of equity.

Question 14

An investment banker is tasked with estimating the cost of equity for a private, family-owned construction company. The company has a target debt-to-equity ratio of 0.5. Since the company's stock is not traded, a direct beta calculation is impossible. What is the most appropriate procedure for the banker to follow?

Use the dividend growth model, as CAPM is not applicable to private firms.
Assume a beta of 1.0, as the company's specific risk cannot be measured relative to the market.
Find public construction firms, unlever their average beta, and re-lever it using the private firm's target D/E ratio. (correct answer)
Regress the private company's annual accounting earnings against the market index's annual returns to estimate an 'accounting beta'.

Explanation: This describes the standard 'pure-play' method for estimating the cost of equity for private companies or specific projects. The steps are: 1) Identify a set of publicly traded companies that are comparable in business risk. 2) Estimate the equity beta for each comparable company. 3) Unlever each comparable's equity beta to remove the effect of its specific capital structure, yielding an asset beta. 4) Average the asset betas to get an estimate of the industry's business risk. 5) Re-lever this average asset beta using the private company's target capital structure (D/E = 0.5) to arrive at an appropriate equity beta for the private firm. This method properly isolates the relevant business risk and applies the financial risk specific to the company being valued.

Question 15

A company's cost of equity is estimated to be 11.5%. The current risk-free rate is 3.5% and the expected market risk premium is 6.0%. The company is planning a major debt issuance that will increase its debt-to-equity ratio. Assuming the debt issuance does not affect the firm's asset beta, what was the company's equity beta before the financing change?

0.77
1.25
1.33 (correct answer)
2.50

Explanation: This question requires rearranging the CAPM formula to solve for beta (

\beta

). The information about the upcoming debt issuance is extraneous information designed to distract the candidate; the question asks for the beta before the change. The CAPM formula is:

R_e = R_f + \beta(R_m - R_f)

Identify the given values:
- Cost of equity ( $R_e$ ): 11.5%
- Risk-free rate ( $R_f$ ): 3.5%
- Market risk premium ( $R_m - R_f$ ): 6.0%
Rearrange the formula to solve for $\beta$ :
- $R_e - R_f = \beta(R_m - R_f)$
- $\beta = \frac{R_e - R_f}{R_m - R_f}$
Substitute the given values:
- $\beta = \frac{11.5\% - 3.5\%}{6.0\%} = \frac{8.0\%}{6.0\%} = 1.333... \approx 1.33$

Distractor B is calculated by incorrectly dividing the cost of equity minus the risk-free rate by the market return (not given) assuming a market return of 11.5%-3.5% = 8.0%. Distractor A is calculated as

\frac{R_m-R_f}{R_e-R_f} = \frac{6.0}{8.0} = 0.75

. Distractor D is calculated as

\frac{R_e}{R_m-R_f} = \frac{11.5}{6.0}

with an arithmetic mistake. It tests whether the student can correctly identify and isolate the relevant information.

Question 16

A company's stock has a beta of 1.25, and the risk-free rate is 3.5%. Market analysts estimate that the equity risk premium will decrease from 8% to 6% over the next year due to improved economic conditions. If the company maintains its current level of systematic risk, what will be the change in its cost of equity?

The cost of equity will decrease by 2.5 percentage points (correct answer)
The cost of equity will decrease by 2.0 percentage points
The cost of equity will decrease by 1.5 percentage points
The cost of equity will increase by 0.5 percentage points

Explanation: Using CAPM: Cost of equity = Risk-free rate + Beta × Market risk premium. Initial cost of equity = 3.5% + 1.25 × 8% = 13.5%. New cost of equity = 3.5% + 1.25 × 6% = 11.0%. The change is 11.0% - 13.5% = -2.5 percentage points (decrease). Choice B incorrectly uses the raw change in risk premium (2%). Choice C uses beta of 1.0 instead of 1.25. Choice D incorrectly adds rather than multiplies the beta adjustment.

Question 17

A company's dividend growth model suggests a cost of equity of 12%, while CAPM indicates 10.5%. The stock's beta is 1.3, calculated over 5 years of monthly data with an R-squared of 0.35. Given this information, which statement best explains the divergence and appropriate analyst response?

The low R-squared suggests beta is unreliable; the dividend growth model estimate should be given more weight in the final assessment
The dividend growth model likely overestimates cost of equity due to temporary growth expectations; CAPM should be preferred
The CAPM estimate should be adjusted upward to reflect the additional unsystematic risk indicated by the low R-squared (correct answer)
Both estimates should be averaged since they represent different but valid approaches to measuring required returns

Explanation: When you encounter cost of equity calculations that yield different results, focus on the quality and reliability of the underlying data rather than simply choosing one method over another. The key insight here lies in the R-squared of 0.35, which indicates that only 35% of the stock's price movements are explained by market movements. This low R-squared signals high unsystematic (company-specific) risk that isn't captured in the standard CAPM formula. Since CAPM assumes investors are compensated only for systematic risk, it underestimates the required return when significant unsystematic risk exists that cannot be diversified away. The CAPM estimate of 10.5% should therefore be adjusted upward to reflect this additional risk premium, making answer C correct. The adjustment accounts for the uncertainty and company-specific factors that make this stock riskier than CAPM alone suggests. Answer A incorrectly assumes the dividend growth model is automatically more reliable—but we have no information about the quality of growth assumptions used. Answer B makes an unfounded assumption about temporary growth expectations without supporting evidence. Answer D oversimplifies by averaging two estimates that measure different risk components, which doesn't address the fundamental issue of uncompensated risk. Study tip: When you see low R-squared values in beta calculations (typically below 0.4), this is a red flag that CAPM alone may underestimate required returns. Look for adjustments that account for the additional unsystematic risk, especially in corporate finance problems involving cost of capital estimation.

Question 18

A financial analyst observes that a company's stock price has been highly volatile, leading to a calculated beta of 2.1 over the past two years. However, the company recently underwent a major restructuring that significantly reduced its business risk. When estimating the forward-looking cost of equity, which approach would be most appropriate?

Use the historical beta of 2.1 since it reflects actual market relationships over a meaningful time period
Adjust the beta toward 1.0 using statistical techniques while incorporating industry comparables for the new business model
Calculate a new beta using only post-restructuring data, even if the time period is very short
Use an unlevered beta approach by examining comparable companies in the same restructured business segments (correct answer)

Explanation: After major restructuring, historical beta may not reflect future risk characteristics. The best approach is to find comparable companies operating in the same business segments as the restructured company, calculate their unlevered betas, and re-lever for the subject company's capital structure. Choice A ignores the structural change. Choice B (beta adjustment toward 1.0) is a mechanical approach that doesn't account for the specific business change. Choice C would use insufficient data and high estimation error.

Question 19

An emerging market company's stock has a local beta of 1.2 against its domestic market index. The local risk-free rate is 8%, and the domestic market risk premium is 12%. However, international investors also face currency risk and country risk. If the currency risk premium is 2% and country risk premium is 4%, what should be the cost of equity for international investors using an adjusted CAPM approach?

The cost of equity should be 22.4% reflecting only local CAMP without additional risk premiums
The cost of equity should be 25.6% using beta adjustment for additional risk factors
The cost of equity should be 24.4% since currency risk is already captured in the local beta
The cost of equity should be 28.4% incorporating all risk premiums additively with local CAPM (correct answer)

Explanation: Local CAPM cost of equity = 8% + 1.2 × 12% = 22.4%. For international investors, additional risk premiums are added to account for currency and country risks not captured in the local market model: 22.4% + 2% (currency risk) + 4% (country risk) = 28.4%. Choice A ignores additional risks faced by international investors. Choice B incorrectly applies beta to the additional risk premiums rather than adding them directly. Choice C incorrectly assumes currency risk is captured in the domestic beta calculation.

Question 20

A leveraged company is considering a major acquisition that would double its size but maintain the same debt-to-equity ratio. The company's current equity beta is 1.6, and the acquisition target operates in the same industry with an equity beta of 1.2. If both companies have similar capital structures, what will be the approximate post-acquisition equity beta?

The post-acquisition beta will be approximately 1.6, dominated by the acquirer's higher systematic risk
The post-acquisition beta will be approximately 1.4, representing the weighted average of the two equity betas (correct answer)
The post-acquisition beta will be approximately 1.3, weighted by relative equity values in the combined entity
The post-acquisition beta cannot be estimated without knowing the specific debt levels of both companies

Explanation: When analyzing the beta of a combined entity after acquisition, you need to understand that equity beta measures systematic risk and should reflect the weighted characteristics of the merged companies. Since the acquisition doubles the acquirer's size while maintaining the same debt-to-equity ratio, and both companies operate in the same industry with similar capital structures, the post-acquisition equity beta becomes a straightforward weighted average. The acquiring company (beta = 1.6) represents 50% of the combined entity, while the target (beta = 1.2) represents the other 50%. Therefore:

\text{Combined Beta} = 0.5(1.6) + 0.5(1.2) = 1.4

Option A incorrectly assumes the acquirer's beta dominates simply because it has higher systematic risk. Beta weighting depends on relative size, not risk levels. Option C suggests weighting by "relative equity values" as if this differs from company size, but since both have similar capital structures and the problem states one doubles the other's size, this creates unnecessary confusion and arrives at an incorrect 1.3 figure. Option D incorrectly claims you need specific debt levels, but since both companies maintain similar capital structures and the same debt-to-equity ratio post-acquisition, the equity betas can be directly weighted. The correct answer is B because portfolio betas are weighted averages of component betas, weighted by relative size. Study tip: For acquisition beta calculations, remember that when companies have similar capital structures, simply weight the equity betas by relative company size. Don't overcomplicate with unnecessary adjustments unless capital structures significantly differ.