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Exam 1 Review

1. Corporate Governance

What are the potential conflicts of interest that face a business and how do they manifest themselves in practice?

Short answer or multiple choice questions.

2. Beta Regressions

How would you use the intercept to measure stock price performance?

What does the slope of the regression measure?

What does the R squared of the regression tell you about risk?

Jensen’s Alpha

As we discussed in class, Bloomberg’s regressions require an adjustment to get to the correct Jensen’s Alpha.

Past exams may have asked for that adjustment. Your exam will not.

What is the annualized Jensen’s Alpha? Evaluate it.

What is the estimate of the beta of the company based on the regression and what is the 95% confidence interval of that estimate?

What is the annualized Jensen’s Alpha? Evaluate it.

The annualized Jensen’s alpha is (1 + (-0.01258))12 – 1 = -14.09%

The company did 14.09% worse than it ‘should have’, per year, given its riskiness and given the return on the market.

What is the estimate of the beta of the company based on the regression and what is the 95% confidence interval of that estimate?

The beta is 1.261 and the standard error of the beta is 0.298

The 95% confidence interval is +/- 2 standard deviations

1.261 +/- 2*0.298 -> 0.665 – 1.857

From betas to expected returns

Beta is a measure of the market risk in an investment.

The expected return on an equity investment, which is also the cost of equity, can be written as Cost of Equity = Risk-free Rate + Beta (Risk Premium)

We will focus on the risk-free rate and the market risk premium in this question.

Risk-free rates and Market Risk Premiums

The risk-free rate should generally be long-term, default free and currency matched.

The risk premium is often estimated from historical data. The risk premium can also be estimated from current market data, in which case it is called an implied equity risk premium.

For emerging markets, an additional country risk premium may have to be added on. The country risk premium can be estimated

Simply by added the default spread based on the country rating to the mature market risk premium

In a more sophisticated way, by estimating the relative equity market volatility and then adjusting the default spread for this relative volatility.

For investments across different countries, we can average the risk premiums in those countries (weighted by size of investment).

Rather than using the beta from the regression, you decide to compute a bottom-up beta and you estimate that it is 1.10. (This is the levered beta.) Next you collect some data to use in estimating risk-free rates and country risk premiums

You have estimated that the market risk premium for mature markets is 5.00%. Chile and Brazil have the same rating on their local currency bonds as they do on their foreign currency bonds. (Not the same rating as each other.)

Estimate the US dollar cost of equity for LATAM’s Brazilian operations.

Estimate the Chilean Peso cost of equity for LATAM’s Chilean operations.

Estimate the US dollar cost of equity for LATAM’s Brazilian operations.

US dollar cost of equity means US$ risk-free rate = 3%

Brazilian operations means Brazil’s Market Risk Premium

Mature market risk premium = 5%

Brazil’s default risk premium (on bonds) = 5% – 3% = 2%

Ratio of riskiness of Brazil’s stocks to bonds = 28/20

Brazil’s Country Risk Premium = (28/20) * 2% = 2.8%

Brazil’s Market Risk Premium = 5% + 2.8% = 7.8%.

Cost of equity = 3% + 1.1 * 7.8% = 11.58%

Estimate the Chilean Peso cost of equity for LATAM’s Chilean operations.

Peso cost of equity means Peso risk-free rate.

Chile’s default risk premium = 4% – 3% = 1%

Peso Risk-free Rate = 6.25% – 1% = 5.25%

Chilean operations means Chile’s Market Risk Premium

Mature market risk premium = 5%

Ratio of riskiness of Brazil’s stocks to bonds = 24/16

Chile’s Country Risk Premium = (24/16) * 1% = 1.5%

Chile’s Market Risk Premium = 5% + 1.5% = 6.5%.

Cost of equity = 5.25% + 1.1 * 6.5% = 12.4%

How would we find the cost of equity for the whole company?

Betas and fundamentals

The beta of a firm reflects three fundamental decisions a firm makes.

The type of business it is in, and the products and services it provides. The more discretionary these products or services, the higher the beta.

The cost structure of the business as measured by the operating leverage.

The financial leverage that the firm takes on; higher financial leverage leads to higher equity betas.

A multi-industry firm

Hercules Workout Centers is a publicly traded company that operates gyms across the United States.

The company has 50 million shares outstanding trading at $16 per share and $200 million in debt outstanding.

In addition to its operations, the company has $100 million in cash.

The marginal tax rate for all companies is 40%.

Assume that the unlevered beta for the gym business is 0.8. Estimate the levered beta for Hercules (as a company).

Estimate the levered beta for Hercules (as a company).

Step 1: Create Balance Sheet

Equity = 50M * 16 = 800 ; Debt = 200

Gym = 1,000 – 100 (Cash) = 900

Gym 900 Debt 200
Cash 100 Equity 800
1000 1000

Estimate the levered beta for Hercules (as a company).

Step 2: Compute unlevered betas of divisions

In this problem, it is given:

βGym = 0.8

βCash = 0

Estimate the levered beta for Hercules (as a company).

Step 3: Compute unlevered beta of assets

900/1000 * 0.8 + 100/1000 * 0 = 0.72

Step 4: Lever beta

0.72 * [1 + (1 – 0.4) * 200/800] = 0.828

A change …

Now suppose that Hercules plans to borrow $200 million and to use this money, plus their $100 million in cash, to buy an exercise equipment manufacturer for $300 million.

If the unlevered beta of the exercise equipment business is 1.20, estimate the levered beta of the company after this acquisition.

Estimate the levered beta of the company after this acquisition.

Step 1: Create Balance Sheet

New debt = 200 + 200 = 400

New Equipment asset = 300

New cash = 100 – 100 = 0

No change to equity.

Gym 900 Debt 400
Equipment 300 Equity 800
1200 1200

Estimate the levered beta of the company after this acquisition.

Step 2: Compute unlevered betas of divisions

In this problem, it is given:

βGym = 0.8

βEquipment = 1.2

Estimate the levered beta of the company after this acquisition.

Step 3: Compute unlevered beta of assets

900/1200 * 0.8 + 300/1200 * 1.2 = 0.9

Step 4: Lever beta

0.9 * [1 + (1 – 0.4) * 400/800] = 1.17

Another Problem

You have been asked to estimate the levered beta for GenCorp, a corporation with food and tobacco subsidiaries. The tobacco subsidiary is estimated to be worth $15 billion and the food subsidiary is estimated to have a value of $10 billion. The firm has a debt to equity ratio of 1.00. You are provided with the following information on comparable firms:

All firms are assumed to have a tax rate of 40%. The risk-free rate is 3.5% and the market risk premium is 5.5%. What is GenCorp’s cost of equity?

Unlevering betas

This is the lever beta formula in reverse:

Food = 0.92 / [1 + (1 – .4) * (.25)] = 0.8

Tobacco = 1.17 / [1 + (1 – .4) * (.5)] = 0.9

Unlevered Beta of GenCorp

Remember our financial balance sheet:

Assets Liabilities
Tobacco $15 billion Debt $12.5 billion
Food $10 billion Equity $12.5 billion
Total $25 billion Total $25 billion

The unlevered beta of GenCorp will be

15/25 (0.9) + 10/25 (0.8) = 0.86

The Beta of the whole is the weighted average of the betas of the parts.

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Levered Beta and Cost of Capital

Unlevered beta = 0.86

D = $12.5B; E = $12.5B

Tax rate = 40%

Rf=3.5%; Risk Premium = 5.5%

Levered Beta for the Firm = 0.86 (1+(1-.4)(12.5/12.5))

= 1.376

Cost of Equity = 3.5% + 1.376 (5.5%) = 11.068%

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A complication – divestiture

Suppose GenCorp sells the food division for $10B. What happens to the firm’s cost of equity?

Assets Liabilities
Tobacco $15 billion Debt $12.5 billion
Food Cash $10 billion Equity $12.5 billion
Total $25 billion Total $25 billion

The beta of cash is 0. Nothing else changes.

The unlevered beta of GenCorp will be 15/25 (0.9) + 10/25 (0) = 0.54

Levered Beta for the Firm = 0.54 (1+(1-.4)(12.5/12.5))

= 0.864

Cost of Equity = 3.5% + 0.864 (5.5%) = 8.252%

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A complication – use cash to pay debt

Suppose GenCorp uses the $10B to pay off debt. What happens to the firm’s cost of equity?

Assets Liabilities
Tobacco $15 billion Debt $2.5 billion
Cash $0 Equity $12.5 billion
Total $15 billion Total $15 billion

The unlevered beta of GenCorp will be 0.9 – no problem, but the debt/equity ratio is now 0.2 (2.5/12.5)

Levered Beta for the Firm = 0.9 (1+(1-.4)(2.5/12.5))

= 1.008

Cost of Equity = 3.5% + 1.008 (5.5%) = 9.044%

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A complication – use cash to buy back stock

Suppose GenCorp uses the $10B to buy back stock. What happens to the firm’s cost of equity?

Assets Liabilities
Tobacco $15 billion Debt $12.5 billion
Food Cash $10 billion 0 Equity $2.5 billion
Total $15 billion Total $15 billion

The unlevered beta of GenCorp will be still be 0.9, but NOW the debt/equity ratio is now 5.0 (12.5/2.5)

Levered Beta for the Firm = 0.9 (1+(1-.4)(12.5/2.5))

= 3.6

Cost of Equity = 3.5% + 3.6 (5.5%) = 23.3%

It is not enough to just say there is a divestiture. We need to know what they will do with the money in order to say what happens.

We could do any other choice the same way. (What if they pay a dividend of $2.5M and pay down debt of $7.5M?)

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What if we use the $10B to buy an internet firm (Asset Beta = 1.8)?

The unlevered beta of GenCorp is now

15/25 (0.9) + 10/25 (1.8) = 1.26

Levered Beta for the Firm = 1.26 (1+(1-.4)(12.5/12.5))

= 2.02

Cost of Equity = 3.5% + 2.02 (5.5%) = 14.61%

Assets Liabilities
Tobacco $15 billion Debt $12.5 billion
Internet $10 billion Equity $12.5 billion
Total $25 billion Total $25 billion

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What if we use the $10B and borrow another $5B to buy a $15B internet firm (Beta = 1.8)?

The unlevered beta of GenCorp is now

15/30 (0.9) + 15/30 (1.8) = 1.35

Levered Beta for the Firm = 1.35 (1+(1-.4)(17.5/12.5))

= 2.48

Cost of Equity = 3.5% + 2.48 (5.5%) = 17.14%

Assets Liabilities
Tobacco $15 billion Debt $17.5 billion
Internet $15 billion Equity $12.5 billion
Total $30 billion Total $30 billion

Always make sure that your financial balance sheet balances. No matter how complicated I make this, you can handle it.

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Test yourself…

Assets Unlevered Beta D/E ratio Levered Beta
Sell Asset Replace asset with cash Decrease No effect Decrease
Buy asset with cash on hand
Buy asset with equity issue
Buy asset with new debt
Pay dividend
Buy back stock
Retire debt

Figure out what each action will do to a financial balance sheet and to the beta. (You may not have enough information for every answer.)

Take GenCorp and do the most complicated restructuring you can think of. Find one in the WSJ and replicate it. After a couple you will see this is not rocket science

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