Week 5 Review for Midterm

2007-1-26 Corporate Finance 1

Important Information: MidtermTime: Feb. 13, 6-8p.m.

Location: Bahen Center for Information Technology, 40 St George St

Exam room: L0201: BA1180 L0601: BA1190

For those who cannot make it from 6-8pm, please give me your names and IDs so that your seats in the conflict room can be arranged.

Conflict room I: WB 116 (4-6pm) same day. Wallberg Building 184-200 College St.

Conflict room II: BH 3116, 8-10pm, same day


Important Information: Midterm

Cover: Chapters 9, 11, 13-17, 20, 21

If you have missed one midterm exam, please try not to miss this one as a make up exam will cover everything since the beginning of the year.

A one-sided 8.5*11 crib sheet and a calculator are allowed.

It is strongly recommended that you do the past exam questions to get a feeling about the level of difficulty of the midterm.


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To reach good diversification, 30-50 securities is needed in a portfolio.

As the number of securities in a portfolio increases, the total variation of the portfolio approaches the average covariance of the securities asymptotically.



The relevant risk of a security is its contribution to the risk of a well diversified portfolio.

As the number of securities increases, the marginal contribution of an asset’s variance to portfolio variance decreases, the marginal increase in the portfolio variance comes from the asset’s covariance with other assets in the portfolio.


Market Portfolio & Efficient Portfolio

Market portfolio: A market portfolio is a portfolio consisting of all securities where the proportion invested in each security corresponding to its relative market value.

If everyone holds the tangency portfolio (optimal mix of risky assets), tangency portfolio is the market portfolio,.

CML connects the (0, rf) and (σm, rm ) Efficient Portfolio: Every efficient portfolio can be constructed by holding the market portfolio and risk free asset.

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Efficient Set & Minimum Variance

Capital Market Line: For a given rf, the optimal market portfolio is M

The slope of the CML is the Sharpe ratio.

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Every efficient portfolio lies on the CML line


The Concept of CAPM

Assumptions:

No transaction costs; No taxes

Infinitely divisible assets

Perfect competition

Quadratic utility function

Unlimited short sales and borrowing and lending at the risk free rate

Homogeneous expectation

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BetaBetas are standardized around one

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β>1 E(rS)>rm the risk premium of the asset > the market risk premium Above average risk investment asset magnifies the effect of market

0<β<1 E(rS)<rm Below average risk investment

β=0 E(rS)=rf Risk-less investment

β<0 E(tS)<rf Useful as hedgeAverage beta cross all investments is 1


Portfolio Beta

Portfolio beta

(wAβA) is the proportion of the risk of the market portfolio contributed by asset A.

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The Properties of CAMP

Systematic risk is the only risk which is compensated.

The correct risk measure for a portfolio is variance, the correct risk measure for a security is its beta.

Risk premium of an asset does not depend on its own risk, rather is proportional only to its contribution to market portfolio risk.

Every efficient portfolio can be constructed by holding risk-free asset and optimal mix of risky assets (tangency portfolio, market portfolio)


Estimating BetaModel: rj-rf=αj+βj(rm-rf)+εj

where rj= returns of stock j, rm= returns of market portfolio, rf =risk free rate

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2 represents unsystematic risk, the corresponding value is given by the SS (residual)/df term in regression analysis output.

αj= abnormal return. Measures the deviation of the stock’s performance from what is predicted using the CAPM


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Alpha<0, stock is overvalued

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Risk premium = Quantity of risk*Price of risk

Measure of riskCML – σSML – β

Applicability, in CAPM world CML is applicable only to an investor’s final portfolio

Everyone holds portfolios which lie on the CML

SML is applicable to any security, asset, or portfolio

Every asset lies on the SML


Summary

Portfolio beta and weights.

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Review: EMH

The level/degree/form of efficiency in a market depends on two dimensions:

The type of information incorporated into price (which information is available?)

The speed with which new information is incorporated into price (how fast information is reflected?)

Why study EMHIf market prices reflect at a given date only information of a particular type, then one can profit by trading based on information relevant for pricing but not yet reflected in prices.


Review : EMHTo assess the level of market efficiency one often needs to know the security’s value, which requires knowing how assets are priced.

Joint test problem in empirical tests of the EMHTesting market efficiency often requires a pricing model to assess an asset’s expected return, as the question whether price reflects a given piece of information depends on the benchmark to which the actual returns are compared. It is a joint test of market efficiency and the pricing model used in a research. Therefore, research results can be biased if the model is not correctly specified or the data set used in the research is biased.


Review : EMHThe basic concept of EMH is that efficient market fully reflects available information. Whether market participants reveal certain information or not has nothing to do with whether market is efficient or not. Market cannot reflect the information that is not available.

Biased research results cannot tell if the market is efficient or not. An empirical study can be meaningful only if the study results can be replicated by many other researchers. A single outlier case cannot refute the EMH.

Public information cannot lead to abnormal profits does not mean investors cannot profit from good news. An investor bought a stock and later the firm announced a good news, the investor enjoyed an abnormal return associated with the news.


Review : EMHAt the time when he bought the stock, however, the “good news” was not public information, rather it was an event unknown to him.

Semi-strong EMH says fundamental analysis cannot do investors any good. This statement does not imply that one cannot profit from inside information, or that a group of fund managers who actually participate in management of firms which they own shares cannot generate consistent abnormal return over years.

Efficient market prices information asymmetry in a way that firms’ attempts to take advantage of information asymmetry only lead to market’s adverse reactions. Market assumes that


Review : EMH

management knows more about firm’s future prospect than investors do. Hence market tends to act adversely to seasoned equity offering. Equity offering is interpreted as a signal that the firm’s stock is overvalued. A firm cannot take advantage of its overvalued stock price through a SEO, as the problem of overvaluation is corrected at the time of the SEO announcement if market is semi-strong efficient.

EMH implies that after adjusting for risk, investments in financial securities are zero NPV projects. Investors can only expect to earn fair return on their investments after adjusting for risk. Certain mutual funds do earn higher returns than others


Review : EMHbecause the risk levels associated are higher as well. For example, growth funds have higher risk than income funds or money market funds. And on average growth funds are expected to deliver higher returns than income funds.

CAPM model deals with expected return, not a unique outcome of return. When we say the expected return is E(r), we mean that, with a large sample, the average return is approximately equal to E( r ). With a large sample, there is a distribution. It is only nature that some have returns higher than E( r) and others below E (r ). Some mutual funds do outperform others from time to time.


Review : EMH

For one fund to outperform others consistently over an extended period of time, there must be other factors at work, such as information that is not publicly available or the fund managers have superior ability to derive insightful information from public information, which most other market participants fail to accomplish. The latter case is very rare and cannot serve as an evidence that market is not efficient.


The Cost of Debt

The cost of debt is the rate at which the company borrows today

Corrected for the tax benefit it gets for interest payments rB(1-Tc)

The cost of debt is not the interest rate at which the company obtained the debt it has on its books

To estimate the cost of debt:If the firms has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no specific features) bond can be used as the interest rate.

If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the cost of debt

If the firm is not rated, and it has recently borrowed long term from a bank, use the interest rate on the borrowing or estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt

The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation.


Example 1You have found a stock which has a beta of 1.5, and an expected return of 10%. The current risk free rate is 2%. The return on market portfolio is 8%. Should you own this stock or is it better to hold the market portfolio in some combination with the risk free asset? If so, give the weights of your portfolio.

E(ri)=rf+βi (rm-rf)=0.02+1.5(0.08-0.02)=0.11 >0.10

Thus, the stock is overvalued. Now let’s construct a portfolio with the same level of beta. Notice that market beta is 1 and beta of risk free asset is 0, the following portfolio has a beta of 1.5: βP =wfβf +wmβm=(-0.5)(0)+1.5(1)=1.5

The return on the portfolio =(-0.5)(0.02)+1.5(0.08)=0.11


Example 2

You currently have 50% of your wealth in a risk-free asset and 50% in the four assets below:

Asset i

Expected return on asset i

Beta i Weight i

i=1 7.60% 0.2 10%i=2 12.40% 0.8 10%i=3 15.60% 1.2 10%i=4 18.80% 1.6 20%


Example 2(cont)

A) If you want an expected rate of return of 12%, you can obtain it by selling some of your holdings of the risk-free asset and using the proceeds to buy the equally weighted portfolio A. If this is the way you decide to revise your portfolio, what will the set of weights your revised portfolio be?

B) If you hold only the risk-free asset and the portfolio A, what set of weights would give you an expected rate of return of 12%?


Example 2(cont)

A) Liquidate x percentage of your wealth from risk free asset holding and invest it equally in the four assets

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Example 2(cont)

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B) To obtain 12% return by holding risk free asset and portfolio A.


Example 3The market data of S&P 500, an efficient portfolio E, and two technology stocks TX and TY are given below. The correlation coefficient of the return of TX and return of TY is 0.5.

Security Standard Dev. Beta Expected Return

S&P 500 15.5% 1.00 ?

TX 19.2% 1.07 12.68%

TY 36.3% 1.02 10.96%

E 17.0% ? ?

A) Calculate the market risk and the unique risk for TX and TY


Example 3(cont)

B) Is TY riskier than TX? Explain.

C) In order to reduce risk you consider a portfolio A with a weight 0.6 of TX and 0.4 of TY. Calculate the expected return, the beta, and the variance of portfolio of A.

D) Calculate the diversification effect between portfolio A and stock TX and stock TY.

E) Calculate the expected return on the efficient portfolio E.


Example 4The management of firm A is considering to start a new project. The project requires an initial investment equal to $1m. The risk of the project is identical to that of the firm’s current risky assets. The expected rate of return on the new project is 15% annually, forever. The firm’s balance sheet (market values) prior to the announcement of the investment project is as follows:

Risky Assets $5m Equity $4m

Cash $1m Debt $2m

Total $6m $6m

There are 100,000 shares outstanding. The beta of the firm’s stock is 1.35, the beta of its debt is 0.15, the risk free rate is 4% and the expected market risk premium is 7%.


Example 4 (cont)

A) Calculate (1) the beta of the firm, and (2) the beta of the firm’s risky assets

B) Calculate the NPV of the new project, Ignore tax considerations

C) Within the board of directors there is a discussion about the optimal financing choice. The CFO prefers debt since this increases the firm’s profit per share, and thus, the value of the shares. Do you agree with the CFO (ignore taxes)? Motivate your answer. Limit your answer to a maximum of 3 sentences.


Example 4 (cont)

D) The CEO also wants to finance with (risk-free) debt. However, she claims that due to a tax advantage of debt financing, using risk-free debt will reduce the firm’s weighted average cost of capital (WACC), and thus also reduce the hurdle rate for future investments. Do you agree with the CEO? Again, motivate your answer and limit your answer to three sentences.


Example 5In an IPO, “money left on the table” refers to the difference between the offering price per share and the price at which the stock trades in the secondary market shortly thereafter (usually at the close of trading on the issuance date), multiply by the number of shares sold. For example, if firm TheGlobe issued 4m shares at an offering price of $9, and the share price closed at $63.50 on the offering day, TheGlobe could be said to have left $218.0 million on the table. Both TtheGlobe and its underwriter (Bear Sterns) seem to forgo money on this, since underwriter commissions are based on a percentage of the offering price. Why would Bear Stearns not have selected a higher offering price for TheGlobe, (i.e. What pressures and tradeoff does the underwriter face in pricing an IPO?


Example 5(cont)

First, we should not assume that Bear Sterns knew that TheGlobe would rise to $63.50 per share in the first day of trading. The $63.50 figure is based on hindsight. However, Bear Sterns has an incentive err on the side of pricing too low rather than too high. An offering price that is too high results in a failed offer, something that would be very costly, reputation-wise, to both the firm and the underwriter. In addition, Bear Sterns has only a single transaction relationship with the firm, but an on-going multiple transaction relationship with the investors who will be buying the TheGlobe shares from Bear Sterns. The underwriter wants very much for its regular customers to earn a positive return on the IPO so that they will be willing to subscribe to Bear Sterns’


Example 5 (cont)

future underwritten offering. This matters much more to Bear Sterns than TheGlode, resulting in another example of the agent-principal problem.


Example 6 GBU is bidding to take over its smaller competitor, NER Electronics. GBU has 3 million shares outstanding selling at $40 per share and has no debt. NER has 2 million shares outstanding selling at $25 per share and is an all equity firm. GBU believes that it can streamline NER’s operation and bring in a perpetual EBIT of $12 million from the NER division after the acquisition. The equity beta is 1.89 for GBU and 1.60 for NER. The cost of risk free debt is 5% and market risk premium is 6%. The industrial debt to equity ratio is 1, which is considered to be optimal. After the acquisition, both firm will undergo restructuring and bring the new firm’s leverage ratio to the industrial average. If the acquisition is not successful, GBU will restructure its capital mix through an


Example 6 (cont)exchange offer. The tax rate for both firm is 40%. Assume there are no other market imperfections.

A) If NER can be acquired for $30 per share, what is the NPV of the acquisition to GBU?

B) What will GBU’s stock price be when the market learns it plans to acquire NER for $30 per share and the leverage restructuring plan? How many shares should GBU offer NER stockholders per each NER share?

C) Often in acquisition bids, target firms reject the initial bid because they believe the bidder will offer a higher price. Suppose NER rejects GBU’s bid of $30 per share, but says it will approve an offer of $35 per share. Will GBU shareholders approve of this offer? What will GBU’ share price be if the firm agrees to pay $35 per share for NER?


Example 7

A firm has 5,000,000 shares of common stock outstanding with a market price of $9.00 per share. It has 25,000 bonds outstanding, each selling for $1,100. The bonds mature in 12 years, have a coupon rate of 8.5% and pay coupons annually. The firm’s equity beta is 1.4, the risk free rate is 5%, and the market risk premium is 9%. The tax rate is 35%. Calculate the WACC

1,100=85{[1-1/(1+YTM)12]/YTM}+1,000/(1+YTM)12

YTM=7.23%

rS=0.05+1.4(0.09)=17.6%

WACC=17.6(45/72.5)+7.23(27.5/72.5)(1-0.35)=12.71%


Example 8DayTop Inns is a publicly traded company, with 10 million shares trading at $70 a share and $300 million in debt (market value) outstanding. The firm derives 60% of its value from hotels and the remaining 40% from transportation. The unlevered beta is 0.8 for firm’s in the hotel business and 1.2 for the firms in the transportation business. DayTop is rated A and can borrow money at 5%. The risk free rate is 4.5% and the market risk premium is 4%, the corporate tax rate is 40%

A) Estimate the WACC for DayTop Inns.


Example 8

B) DayTop Inns is considering acquiring SwissHotels, another hotel company (which derives 100% of its revenues from hotels) for $400 million, three quarters of the $400 is to be fund by a new debt issue (which will cause its rating to drop and its cost of debt to rise to 5.5%) and a quarter by issuing new stock. Set up the market value balance sheet for DayTop Inns before, at the time of announcement and after the announcement. Estimate the firm’s WACC after the acquisition. Assume stock price remains unchanged after the acquisition.


Example 9

A firm with $2m in assets and 50% debt in its capital structure is considering a $250,000 project. The firm’s after tax weighted average costs of capital is 10.4%, the (before tax) cost of debt is 8%, and the tax rate is 40%. If the project does not change the firm’s operating risk and is financed exclusively with new equity, what rate of return should it earn to be acceptable?


Example 9(cont)

Since the project does not change the firm’s operating risk, the project’s required rate of return on unlevered equity must be the same as the firm’s. And since the project is all equity financed, the required rate of return for accepting the project is 13.9%.

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Example 10You are asked to advice the board of directors about the discount rate to be used for evaluating new projects. The board of directors discussed this issue and made the following comments:

Director 1: The firm should not worry about setting a discount rate since majority of our projects are financed with retained earnings which do not cost us anything.

Director 2: Since the firm uses particular sources of finance such as debt, and/or equity and the costs of


Example 10 (cont)these sources vary, hence each project should be discounted at the rate related to the sources of financing.

Director 3: Each project has the risk level associated with the industrial sector where it operates. The discount rate should reflect the risk level of a particular project.

Write your report and give your recommendation. Critically evaluate the issues raised by the directors. Address the key factors that they should consider in deciding upon a discount rate for the company.


Example 10 (cont)Assume we are in a world with taxes but no other market imperfections.

There are two sources of risk: business risk and financing risk. The required rate of return on equity reflects both business and financing risk. A project is financed by retained earning means all equity financing. A project is in the form’s core business implies that the project has the same business risk as the firm’s. If the project has the same business risk and it is all equity financed then the firm’s cost of unlevered equity is the appropriate discount rate.

If a project has the same business risk but a different financing risk because it uses a debt level different from that of the firm, then the appropriate method to evaluate the project is to


Example 10 (cont)discount the cash flow from the project by the rate of return on firm’s unlevered equity, which reflects the firm’s business risk. Then add the value of tax shield generated by the debt amount used in the project, which reflects the project’s financing risk.

If a project has different business risk as well as a different financing risk, one needs to analyze the business risk of that particular industry where the project operates, and incorporate the financing risk into the discount rate.


Example 11

You are hired by EBB to estimate the firm’s equity beta. EBB is newly listed on a stock exchange and there is not enough data for a reliable estimate. You advised the firm that the equity beta can be estimated by examining the betas of other firms in the same industry. You have identified three firms:

(1). Point has a reported beta of 1.3. This firm has been listed for many years. Point has equity of $19.5m and bond of $9m.

(2). Green has a reported equity beta of 1.2. It is reported that 50% of Green’s business has an estimated beta of 1.5. The remaining activities of Green are believed to be of the same level of risk as those of EBB. Green has recently repaid in full


Example 11(cont)

its outstanding debt, and thus at this point in time Green is financed entirely by equity.

(3) Blueriver has $15m of equity and $10m of debt, and a reported beta of 1.63.

You are told the current tax rate is 20%. Assume that the debt is risk free, debt beta is zero.


Example 11 (cont)

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Example 11(cont)

Assume EBB is all equity financed then the firms’ equity beta equals 0.9708.


Example 12

In order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures to a market value basis. KJM corporation's balance sheet as of today, January 1, 2006, is as follows:

Long-term debt (bonds, at par) $10,000,000

Preferred stock 2,000,000

Common stock ($10 par) 10,000,000

Retained earnings 4,000,000

Total debt and equity $26,000,000

The bonds have a 4 percent coupon rate, payable semi-annually, and a par value of $1,000. They mature on January 1, 2016. The yield to maturity is 12 percent, so the bonds now sell below par. What is the current market value of the firm's debt?


Example 12 (cont)

Market value of the firm’s debt (bonds):

Bonds are semiannual, so we need to make adjustments before calculating the PV per bond:

M=10 years, N=20 period; Yield=12% period discount rate=12%/2=6%; per period coupon payment=$40/2 = $20

PV = 20 (1/0.06 – 1/0.06(1.06)^20) + 1000/(1.06)^20 = 229.4 + 311.8

= $541.2

The book value of the bonds: $10,000,000, each bond has a par value of $1000. This means that 10,000,000 / 1000 = 10,000 bonds outstanding.

The market value of bonds = 10,000 * 541.2 = 5,412,000 $.


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Review: Costs of Capital-WACC

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Review: CAPM– Which Beta

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Taxes withLevered

SB

S

SB

B

Taxes withoutLevered

Taxes withoutor withUnlevered

U

SL

LB

LAU

AWACC

SL

LB

LAU

S U

)1()1(

)1(


Review: Relationship Between Costs of Capital

0Tc whenrBS

Br

BS

Sr

rTcBS

TcBr

TcBS

Sr

BL

SL

L

BL

SL

L

0

0 )1(

)1(

)1(


Factors Affect Target B/S Ratio

TaxesIf corporate tax rates are higher than bondholder tax rates, there is an advantage to debt. TB < TC

Types of AssetsHigh bankruptcy cost <= Intangible assets <= R&D costs, human capital costs

Uncertainty of Operating IncomeTechnological changes; Competitions; Demands; Costs.State of economy; New regulations.

Pecking Order TheoryCash reserve => debt => equity

Static Tradeoff TheoryTarget D/E ratio in a given industry

Documents

Week 5 Review for Midterm