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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