1308 Advanced Coporate Finance Wk8

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    Lecture Notes - Week 8

    Reading Material:BMA Chapter 9

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !"#

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    Valuation Under Risk (all equity firms)

    One of the more fruitful applications of CAPM (and other risk-return models) is valuation (capital budgeting and firmvaluation)

    Whenever a firm (or individual) evaluates an investmentopportunity, there is a need to discount future cash flows. As

    these cash flows are generally risky, the choice of discount rateis not a trivial matter

    In general, the risk return trade-off for financial investmentsdeveloped above (e.g. CAPM) also applies to investments inreal projects

    IMORTANT: The correct discount rate reflects the risk of theproject/firm that is to be acquired, NOT the risk of acquiringfirm

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !"%

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    Valuation Under Risk (all equity firms)

    Suppose firm A wants to acquire project B. If B is a firmwhich was previously traded in the stock market, then thecorrect discount rate is the required return on equity of firm B(UNLESS the acquisition by firm A will change the risk offirm Bs assets)

    Hence, we can look at firm Bs stock returns over the last 5years and estimate its Beta. The CAPM will then give us thediscount rate

    Often, it will be a good idea to look also at some other firms inthe same industry as firm B and use the average beta of severalfirms. While this means using the beta of firms which are slightlydifferent from firm B, it will make estimation much moreaccurate (i.e. the beta estimate of just firm B might be subject tosever estimation error)

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !"&

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    Valuation Under Risk (all equity firms)

    Suppose firm A wants to acquire project B. If B is a firmwhich was not previously publicly traded (or firm B is really

    just a project that we would like to invest in, or the acquisition

    by firm A changes the nature of firm Bs business and hence its

    risk)

    Then we will have to find a publicly traded firm which doesexactly the same thing as firm B (under As management),

    estimate its Beta, and use the CAPM to estimate the discount

    rate to use.

    Again, in general we will estimate the beta of several firmswhich do the same thing as B, in order to lower estimation

    error.

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !"'

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    Example

    Suppose A wants to acquire firm B. Firm B has had the following cash flows this past yearSales: $10M, Costs: $5M, Depreciation: $1M, Tax: 40%

    Sales and Costs are expected to grow at the rate of inflation (4%)

    Depreciation of existing machinery will decline by 3% each year

    If acquired by firm A, sales will grow by an additional 3% p.a.

    (costs will remain a constant proportion of sales in real terms)

    If M denotes the market portfolio, then we also have the

    following information from the securities markets:

    !A=30% !B=40% !M=20% E[rM]-rf=6%"AB=-0.3 "AM=-0.7 "BM=0.8 rf=6%

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !()

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    There are two ways of solving this

    1) We could project the firms net cash flows (Revenue minuscosts plus depreciation tax shields) into the infinite future andthen discount them

    2) Given that the different cash flows grow at different ratesmaybe its easier to calculate their present values separately

    We will do 2)After Tax Operating profits (revenues minus costs) are a growingperpetuity with growth rate 7% (inflation plus acquisition

    synergies), with the first cash flow equal to $3.21

    Depreciation tax shields are a declining perpetuity with growth

    rate -3% and first cash flow equal to $388K

    What is the correct discount rate?

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !(!

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    Example

    The beta of firm B is given by

    Hence, the discount rate is 0.06 + 1.6 x 0.06=15.6%

    Thus the value of firm B to firm A is given by

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !(*

    !B =

    Cov(rM, rB)

    Var(rM)

    =

    "BM

    #B#

    M

    #M

    2 =

    0.8!0.4!0.2

    (0.2)2

    =1.6

    V =$3.21M

    0.156!0.07+

    $388K

    0.156+0.03= $39.412M

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    Another thing that matters:

    the capital structure (i.e. debt)Debt matters for two reasons:1) Interest payments on debt are tax deductible. Since we only

    care about after tax cash flows, the cost of debt (the required

    return on debt) is best written as rDx (1-tc) where tc is thecorporate tax rate

    2) Debt is less risky than equity, because debt holders get paidfirst. Thus, the cost of debt capital is lower than equity

    capital. Furthermore, leverage (debt) makes returns on equitymore volatile (risky). Hence leverage will also affect the

    required return on equity.

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !(+

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    Valuation under Risk (firms with debt)

    IMPORTANT: The correct discount rate reflects the risk and capitalstructure of the project/firm that is to be acquired, NOT the risk of theacquiring firm

    If we know a firms capital structure, its required return on debt and itsrequired return on equity, then we can determine its WACC

    If the investment under consideration looks just like the rest of the firm(e.g. expansion of capacity), then the WACC of the existing firm is thecorrect discount rate to use.

    If the investment is different from the existing firm, then we need tocompute the WACC appropriate for the project under consideration(possibly firm comparable firms data)!

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !("

    WACC=D

    D+ErD(1! t)+

    E

    D+ErE

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    Where do we get the information we

    need to estimate the WACC?

    Capital Structure:market values if available, book value of debt

    generally OK

    Cost of Debt:debt ratings if available, debt beta less good

    Cost of Equity:CAPM, estimated from comparable firms

    Taxes:marginal tax rate if known

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !((

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    So what is remaining?

    The problem is that we only observe the equity beta of leveredfirms

    1) If a firm changes its leverage, its beta will change. Thatmeans that we cannot use the (unadjusted) past beta if thefuture calls for a different capital structure. In fact, if theamount of debt used to finance a project is different from thatof the overall firm, then the (unadjusted) beta of the overallfirm cannot be used.

    2) If we want to use the average beta of several firms in anindustry, we cannot simply use the beta estimated from theirstock prices, because this beta will be distorted by all sorts of

    different capital structures. Only the asset risk of all thecompanies is comparable (i.e. the risk that remains when allthe capital structure effects are stripped away)

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !(#

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    The strategy (I - RETURNS)

    1) Estimate the equity beta from equity prices. See whatequity return this implies. This is distorted by leverage.2) Strip the equity return of its leverage effect (un-lever)3) The un-levered return (which only depends on the riskiness of

    the assets) can be compared across firms i.e. it can be

    averaged4) Use the forward looking capital structure of the project/firm

    under consideration, and the un-levered return from above, tocome up with the (re-levered) required return on equity

    5) The re-levered required return of equity, as well as theforward looking capital structure and the expected requiredreturn of debt (from the expected debt rating) can be used tocompute the WACC

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !(%

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    The strategy (I - RETURNS)

    UNLEVERING

    RELEVERING

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !(&

    rU =

    D(1! t)

    D(1! t)+ErD+

    E

    D(1! t)+ErE

    rE = r

    U+

    D(1! t)

    E[r

    U! r

    D]

    If you are interested in derivation of this formula contact me byemail.

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    The strategy (II - BETAS):

    1) Estimate the equity beta from equity prices. This isdistorted by leverage.2) Strip the equity beta of its leverage effect (un-lever)3) The un-levered beta (which only depends on the riskiness of

    the assets) can be compared across firms i.e. it can be

    averaged4) Use the forward looking capital structure of the project/firm

    under consideration, and the un-levered beta from above, tocome up with the (re-levered) beta of equity. See what equityreturn this implies

    5) The re-levered required return of equity, as well as theforward looking capital structure and the expected requiredreturn of debt (from the expected debt rating) can be used tocompute the WACC

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !('

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    The strategy (II - BETAS):

    Remember, that since CAPM is a linear relationship betweenreturns and betas, we can equivalently write UNLEVERING and

    RELEVERING Equations in terms of Betas:

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#)

    !U =D(1! t)

    D(1! t)+E!D +

    E

    D(1! t)+E!E

    !E = r

    U

    +

    D(1! t)

    E [!U!

    !D ]

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    The strategy (II - BETAS):

    Often Debt Beta is taken as Zero i.e. it is assumed it has0 correlation with the Equity Market (is it correct?) and then

    formulae simplify to:

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#!

    !U =E

    D(1! t)+E!E

    !E = !

    U+

    D(1! t)

    E!U = !

    U

    E+ D(1! t)

    E= !

    U

    EV! Dt

    E

    Where EVis Enterprise Value

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    Use of WACC

    The easy case: if the firm is traded, and had the same capitalstructure in the past as it will have in the future, and there is little

    worry about estimation risk

    1) Estimate the equity beta2) Estimate the forward looking cost of debt (probably from the

    debt rating, or from very recently issued debt)

    3) Plug the into the WACC formula, using the target capitalstructure and the forward looking marginal tax rate

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#*

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    Use of WACC

    The more difficult case:if our own firms past risk or capitalstructure is not applicable for the valuation at hand (or you want

    to look at more than one firm to avoid estimation error), we will

    have to look at comparable companies

    1) Find a few companies with the same beta risk (i.e. in thesame line of business) as the project/acquisition under

    consideration.

    2) Measure these comparables rE, rD, t, and D/E3) Use these data to compute a WACC

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#+

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    Use of WACC IMPORTANT!

    If you used comparable firms, then there is a wrong ways to proceed and aright way

    The wrong way: average all rDs and rEs of comparable firms to get anaverage rEand rD. Then use your own firms D/E ratio to compute theWACC.

    Why it is wrong? What can reasonably be assumed constant amongcomparable firms is the operational risk. However, rEand rDwill differdepending on the firms leverage ratios (i.e. their financial risk).

    The right way un-levers comparable firms returns to get at a return thatonly depends on their assets, and then re-levers them at our target capitalstructure to reflect financial risk

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#"

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    Once we have computed the un-levered cost of capital rU, we canaverage it among all comparable firms

    The normal average is preferred if you think that any one firmprovides as much information about the beta risk as any other

    The weighted average is preferred if you think that the datafrom the larger (or otherwise weighted) firms contains moreinformation (e.g. it is more accurately measured)

    Once we have the average rUin an industry we need to then

    establish the new cost of debt and the new level of leverage ofour particular case

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#(

    rU =

    D(1! t)

    D(1! t)+ErD+

    E

    D(1! t)+ErE

    Use of WACC

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    The new cost of debt comes from (i) an estimate, (ii) a guess as towhat the firms credit rating will be, or (iii) the old cost od debt.

    Which is most appropriate depends on the situation and the firm

    The new cost of equity is determined as follows:

    Now that we have the new cost of equity and debt, we cancompute the WACC from

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !##

    rE = r

    U+

    D(1!t)

    E[r

    U! r

    D]

    WACC=D

    D+ErD(1! t)+

    E

    D+ ErE

    Use of WACC

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    You target a debt-to-equity ratio of 20%. The tax rate is 40%.Other firms in the industry are firms A & B. rf is 7%, (rm-rf)=5%

    Firm A: D/E=60%, rD=10%, #E=1.6 => rE=7%+1.6x5%=15%

    Firm B: D/E=100%, rD=12%, #E=2 => rE=7%+2x5%=17%

    Firm A: rU=0.265x10%+0.735x15%=13.675%Firm B: rU=0.375x12%+0.625x17%=15.125%

    (we average Firm A and Firm B rUs and get rU=14.4%

    Assume that your rD(with a 20% leverage) is 8%. Then you get

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#%

    Example

    rE = rU+D(1

    ! t)

    E[rU! rD ]=14.4%+20%"0.6" (14.4%!8%)=15.2%

    WACC=16.7%"8%" (1! 40%)+83.3%"15.2% =13.5%

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    1) rE: use the CAPM2) rD: from the actual price of debt of the company, or the credit rating

    (if loan interest rate)

    3) t: marginal corporate tax rate4) E: market value of equity (market capitalisation divided by number

    of shares issued)

    5) D: market value of debt: two alternatives: a) Book value, if thevalue was recorded when (i) interest rates were similar to today,

    and (ii) the firms credit rating was similar. Otherwise, b) we take

    rDand apply it to the remaining debt payments

    if D is a loan from the bank, then remaining principal amount

    Example: 9% coupon, Maturity 10 years, $100 face value, rD=7%

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#&

    WACC ingredients some comments:

    D =$9M

    7%(1!

    1

    (1+ 7%)10)+

    $100M

    (1+ 7%)10 = $114.05M

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    One of the more tricky issue is to estimate the cost of debt of anon-rated firm (or the cost of debt under some hypothetical

    target capital structure)

    In order to estimate the cost of debt under this scenario is to

    become ratings agency

    It is often not too difficult to estimate the credit rating that a

    particular firm would achieve under a particular debt scenario

    (actually, that is what banks do when estimating the interest rate

    on loan for corporates)

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !#'

    The Cost of Debt

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    Advanced Corporate Finance, Vasil Revishvili, [email protected] !%)

    Some numbers that ratings agencies look at

    Median Ratios (Actual Numbers)

    Firm Under Consideration

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    Once you have identified your likely creditrating, estimating the cost of debt is easy

    You can look up the current spread above

    the risk free rate for each ratings category

    Add this to the current risk-free rate andthis is your estimated cost of debt (mostly

    done over long rate)

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !%!

    The Cost of Debt

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    Use the CAPM to get rE=rf+ #Ex (rm-rf)

    Practical issues:

    For rfuse the maturity matched generally long dated government yield minus liquidity premium, for #Euse adjusted

    estimate, for (rm-rf) use market risk premium of the market which

    represents investment opportunities for the investors. Do

    everything in one currency

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !%*

    The Cost of Equity

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    If firms have not only debt and equity, but also other securities,then we can generalise the WACC formula

    This is the example when other source is Preferred Stock (PS).

    The cost of PS might be estimated as the required yield on the

    preferred securities

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !%+

    Other Sources of Finance?

    WACC=D

    D+E+PSrD(1! t)+

    E

    D+E+PSrE+

    PS

    D+E+PSrPS

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    If firms have multiple business lines, then their overall cost ofcapital is determined by weighted average risk of the divisions

    Ideal Measure for Value is the market value of assets (i.e. presentvalues of cash flows)

    However, because of difficulty to measure, sometimes, inpractice, they use (i) Revenue Weights; (ii) Profit Weights; or (iii)Book Value of Assets Weights.

    Last is the best because we can adjust for industry market-to-book ratio.

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !%"

    Multiple Divisions?

    ru=

    ValueDiv1

    FirmValueru

    Div1+

    ValueDiv2

    FirmValueru

    Div2+...+

    ValueDivN

    FirmValueru

    DivN

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    1) UNLEVER (old capital structure during estimation period)

    2) RELVER (future capital structure and cost of debt)

    3) Compute the WACC (future capital structure and cost of debt)

    Advanced Corporate Finance, Vasil Revishvili, [email protected] !%(

    Recap of Basic Technique

    rU =

    D(1! t)

    D(1! t)+ErD+

    E

    D(1! t)+ErE

    rE = r

    U+D(1

    !

    t)

    E[r

    U! r

    D]

    WACC=D

    D+ErD(1! t)+

    E

    D+ErE