Capital Budg résumé.pdf

8/13/2019 Capital Budg rsum.pdf

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Capital BudgetingSummary

January 2013


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Introduction

Capital Budgeting= process of analyzing different investment opportunities and to choose thegood one (the one that will be able to maximize the value of the company).

Corporate Finance!deals with all the decisions that a business can make and that could have

an impact on the firm value. A corporate finance decision is any decision

that affects the finance of the company.

Balance Sheet of the firm:

Net working capital=current assets current

liabilities

Business Firm= firm that is publicly traded >< private firm

Objective: Value creation:

! Stock price maximization! Firm value maximization! Stockholder wealth maximization


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Corporate Finance in 4 questions:1. In what long-lived assets should the firm invest?

!capital budgeting/investing decisions2. How can the firm raise cash for its required capital expenditures?

!financing decisions and capital structure3. How should short-term operating cash flows be managed?

!timing of cash flows and short-term financing decisions4. How should the distribution of cash to shareholders be managed?

!dividend policy and stock repurchases

How to value real assets?!Real investments= expenditures that generate cash in the future and, asopposed to financial investments (like stocks and bonds), are not financial

instruments that trade in the financial markets.(!explained later in Module 2)

!Corporations create value for their shareholders by making good real

investment decisions.

!We can value real assets using the tracking portfolio approach(Module 2):

Market value of the real investments = tracking the real assets cash flows with

a portfolio of financial assets.

!Market price of the project:Financial managers should use a market-based approach to value assets,

whether valuing financial assets (like stocks and bonds) or real assets (likefactories and machines). We have to go to the financial market where wecan find the price.

!Present value (PV)of a project = market price of a portfolio of tradedsecurities that tracks the future cash flows of the proposed project

(= discounted cash flow of the real investment)

!" !!"!

!!! !!!

!Net present value criterion:A project creates value for a corporation if:

!"#$!"!"#$%&!"'!"!!!!"#$%&'! !"#$!"!"#$%&!"'!"!!"#$%"&'"!"!"#$#%"$& !""#$"

!!!"!"#$%&!!!!"#$%&!!!"#$#%&!"I can invest in real asset or financial asset: the one that will cost the less

will be the most appropriate.

!To obtain a PV: discount the estimated future cash flows of a project at

an appropriate rate of return (discount rate).


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!Appropriate discount: discount = rate of return of the appropriate

tracking portfolio.


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Module 1: Fundamentals of Discounting

1. Time-value-of-money concept

Relationship between $1 today and $1 in the future:Ex: a firm is contemplating investing $1 million in a project that is expectedto

pay out $200,000/year for 9 years. Should the firm accept the project?

!We need to know the relationship between a dollar today and a dollar in

the future.

Compounding and discounting:

Discount: to know thevalue today from a

future investment !

know !!and not !!:

!! !!!

!! ! !!!

Compound: to get thefuture value. The money

will generate interests

but also interests on

interests:!! ! !!!!! ! !!!

Simple interest: !! ! !! ! !!! !!!(here I will not reinvest the interests I receive from investing in an asset)

Net Present Value criterion:Ex 4.2: Uncertainty & Valuation:

A firm speculates in modern paintings. The manager is thinking of buying an

original Picasso for $400,000 with the intention of selling it at the end of oneyear. He expects that the painting will be worth $480,000 in one year. Therelevant cash flows are depicted in Figure 4.3. Of course, this is only an

expectation. Suppose the guaranteed interest rate granted by banks is 10%.

Should the firm purchase the piece of art?

Year 0: $400,000Year 1: $480,000

If r=10%: !!""""" !!"####

!!!!!!!! ! !"!"# ! !!risk free, there is a net present value!

!invest!


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If r=25%: !!""""" !!"####

!!!!!!"!!! !!not invest in the project!

2. Basics of capital budgeting

Different issues need to be addressed:! What to value?

!We should evaluate the future cash flows that are generated from the

asset that is being valued (hypothesis and assumptions).

!cash flows !income or earnings numbers

! Discount rates = rate of return that discounts future cash flows to the present.! General formulae that derive present values.

CASH FLOWS OF REAL ASSETS

3. Cash Flows of real assets

Cash Flows of the project= cash flows generated by the real assets of theproject + cash flows from financial subsidies that the project manages to

garner (ex: tax subsidy associated with debt financing).

Incremental cash flows to the firm = cash flows of the firm with the project cash flows of the firm without the project.

!In computing the NPV of a project, only cash flows that are incremental to

the firm should be used.

!These CF are the changes in the firms CF that occur as a direct

consequence of accepting the project.

Ex: 2 scenarios: Flyway Air is thinking of acquiring a fleet of new-fuel-savingjets. The airline will have the following CF if it doesnt acquire the jets:

If it does acquire the jets, its CF will be:

!What are the incremental cash flows of the project?


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!Incremental CF = (80-100)+(180-40)+(110-120)+(130-100) = 140

4. Estimating the cash flows to the firm Unlevered cash flows= cash flows generated directly from the real assets of

the projects of firm.

!Financing cash flows! = associated with (1) issuance or retirement of debtand equity, (2) interest or dividend payments, and (3) any interest-based tax

deductions that stem from debt financing.

Why not taking into account the financing cash flows?

Asset EquityDebt

!Deriving unlevered CF from the accounting CF statement:

The increase (or decrease) in cash reported near the bottom of a firms cash

flow statement represents the difference in the cash (+cash equivalents)

position of the firm for 2 consecutives balance sheets = Accounting CF !Unlevered CF !

5. Deriving unlevered CF from the accounting CF statementAccounting CF(US GAAP)

= operating CF = CF from operations interest and taxes

+ investing CF = CF from investing activities

+ financing CF = CF from financing activities

Unlevered CF

(US GAAP)

= operating cash inflow+ investing cash inflow (which is usually negative)

+ debt interest

- debt interest tax subsidy

(IFRS)

= net CF from operating activities

+ net CF from investing activities (which is usually negative)

- debt interest tax subsidy


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(EBIT)

= EBIT

+ depreciation and amortization

- change in working capital

- capital expenditures+ sales of capital assets

- realized capital gains

+ realized capital losses

- EBIT !tax rate

Working capital= current assets current liabilities= accounts receivable + inventories accounts payable

accrued expenses + other operating activities investment

in working capital reduces cash

Computing unlevered CF from EBIT:Pretax CF= EBITDA increase inworking capital

Taxes= EBIT x rate (ici: 40%)

!Unlevered CF= Pretax CF Taxes

6. Cash flow forecasts Creating pro-forma forecasts of financial statements:

Cash flows forecasts: usually derived from forecasts of financial statements.Forecasts should be made about the income statement, CF statement and

the balance sheet assets and liabilities.

The Sale forecastwill drive forecasts over many items on the incomestatement and the balance sheet.

!Trends based on past performance, firms plans for future products,

competitive position of the firm, general trends affecting the industry (ex:

attraction of substitute product).

Financing forecasts:The firms decisions on financing will have a major effect on the financial

statement: the net amounts of debt and equity that the firm will issue are

major assumptions.


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Interest rate forecasts:!should reflect the average interest rate that we expect the firm to be

paying on its indebtedness during the forecast period.

Expense forecasts:

! Fixed costs: more of the same approach! Variable costs: % of sales !the cost of good sold and the level of

inventory are often direct function of sales !% driven by past

experience !multiple scenario analysis.

" EBIT = sales forecast cost of sales forecast" Interest expense = function of the expected future average interest

rate and the expected future debt outstanding

" Earnings/EBT = EBIT interestCapital investment forecasts:

New PPE (net)= old PPE + capital investments depreciation sales of assets

If we assume that sales of assets are negligible, a reasonable assumption for a

growing firm is:

Capital investments= new PPE old PPE + depreciation

Financing cash flow:Paying off debt !cash outflow

Borrowing!cash inflow

Payments of dividends !cash outflow

Sale of equity !cash inflow

Buying equity back !cash outflow

Cash:Many firms use a minimum of 15 to 30 days worth of sales around in cash and

cash equivalents.

Trade receivable and inventories: % of sales technique

Current liabilities(trade and other payables, accrued expenses): % of salestechnique

Deferred taxes forecast: function of the forecast of PPE (logical since the bulkof deferred taxes arise from depreciation differences and since depreciation

is tied to investment in PPE).

Property, plant and equipment (PPE):Several methods:

1) Direct method: forecast expenditures + old PPE estimate of nextyears depreciation expense and equipment sales

2) More of the same method: old PPE depreciation expense for thecoming year

3) % of sales


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DISCOUNTING/COMPOUNDING CASH FLOWS

7. Discounting and compounding Multi-period setting:

When r is the interest rate (or rate of return per period) and all interests (profit)

is reinvested, an investment of !!at date 0 has a future value at date t of:

!! ! !!!!! !!!

The date 0 value of an amount !!, paid at date t, also known as the present

value or discounted value, comes from rearranging this formula:

!! !!!

!!! !!!

8. Time

Computing the time to double your money:How many periods will it take your money to double if the rate of return perperiod is 4%?

!!!! ! !!!!! !!!"!! ! ! ! !"!!!

!"!!!!"!! !"!!"#!"#$%&'

9. Compound (future) value

The value of an investment over multiple periods when interest (profit) isreinvested:


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Implicit interest compounding:Compound interest rates reflect the interest that is earned on interest.

Compound interest arises whenever interest earnings are reinvested in the

account to increase the principal balance on which the investor earns future

interest.

What about securities that never explicitly pay interest, and thus have no

interest or profit to reinvest?

!To see how to apply compound interest formulae when interest (or profit)

cannot be reinvested, consider a zero-coupon bond (=bond that promises a

single payment at a future date).

With a date 0 price !!and a promise to pay a face value of 100 at date !and nothing prior this date, the yield (rate of return) on the bond can still be

quoted in compound interest terms:

!"" ! !!!! ! !!!! ! !

!""

!!

!

!

! !

10.Present (discounted value)

Determining the present value of a cash flow stream:Compute the present value of the unlevered cash flows of the example

computed in page 7. Recall that these cash flows were 96,000"at the end ofeach of the first 5 years and 56,000"at the end of years 6 to 8. Assume that

the discount rate is 10%/year.

!!" !!"###

!!!!!!

!"###

!!!!!!!!!!!

!"###

!!!! !

!"###

!!!! !

!"###

!!!! !

!"###

!!!! ! !"#!!"#$

11.Present & Future value

Value additivity:Present values (or discounted values) and future values obey to the principle

of value additivity:

Present (future) value of many cash flows combined = sum of their

individual present (future) values.


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DISCOUNT RATES

12.Discount rates

Single-period returns and their interpretation:Over a single period, a return is simply the profit over initial investment:

! !

!! ! !!

!!

!!: investment value at date 1

!!: investment value at date 0

Prices determine rates of return: !! ! !!!!!

!" !! ! !!!!! !!(use this formula to have to real r)

13.Present/future value & inflation

! Nominal discount rates !!"#$!%&(find it in the financial market)! Nominal cash flows !!! Real cash flows or inflation-adjusted cash flows !!!"

(adjusted for the inflation)

!!!"!

!!

!! ! !!!

! Real discount rates:!!"#$ !

!! !!"#$!%&

! ! !! !

Cours de marchs financiers 2e:

" #$%& '()* +) '),+)-),. / 0)*%1 23.),% +$,4 %, -2,+) 5$'6$1.7 4$,4 '148%)7 4$,41,6*$.12,7 29 .2%4 *)4 '(4%*.$.4 4)'$1),. 02,,%4 ). 0)'.$1,4:

" #$%& +) '),+)-),. ,2-1,$* ; / .$%& '()* +% '),+)-),. '< = .$%& +>1,6*$.12,$,.1015( ? @

! ! ! ! !!! !!!!! ! !!

A')*$.12, $55'2&: +>B'C1,D E14F)'G

!Inflation can have an impact on interest rate and on nominal CF!

Discounting nominal cash flows at nominal discount rates or inflation-

adjusted cash flows at the appropriately computed real interest rates

generates the same present value. #


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14.Annualized rates

Interest rates on all investments tend to be quoted on an annualized basis.

! The rate quoted on a mortgage with monthly payments = 12 X themonthly interest paid per unit of principal

! Annualized quoted interest rates with the same r but !compoundingfrequencies mean different things !need to convert each rate to the

same compounding frequency!

15.Equivalent rates

Convert annualized rates into equivalent rates:A 16% annuallycompounded rate means that $1 invested at the beginningof the year has a value of $1.16 at the end of the year.

However, a 16% compounded semi-annuallybecomes an 8% over a 6-monthperiod. At the end of 6 months, one could reinvest the $1.08 for another 6

months and the $1.08 would have grown to $1.1664 by the end of the year,i.e. an equivalent annually compounded rate of 16.64%.!!!!" ! !!!"!!!!" ! !!!""#!

Translating annualized interest rates with !compounding frequenciesinto interest earned per period:

Finding equivalent rates with !compounding frequencies:If the compounding frequency is !times a year and the annualized rate is !,

the amount accumulated from an investment of PV after !years is:

!! ! !"! ! !!

!

!"

If there is a continuouscompounding, so that !becomes infinite, the formulahas the limiting value:

!! ! !"!!!"


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Ex: an investment of $1 that grows to $1.1 at the end of one year is said to

have a return of 10%, annually compounded.

What are the equivalent semiannually and continuously compounded rates

of growth for this investment?

!!!

! ! !!!

!

!

and !!

! ! !!"

Ex of the 16% compounded semi-annually with the formula:

!! ! !! !!!!!"

!

!

! !!!""#

GENERALIZING THE PRESENT VALUE FORMULAE

16.Generalizing the present value formulae

Perpetuity:!" !

!

!

If !is the discount rate per period, the present value of a perpetuity withpayments of !each period commencing at date 1 is ! !.

The value of a perpetuity:Ex: in 1752, the British government decided to consolidate all of its debt into

one perpetuity that paid a 3.5% coupon. The bond, which is known as a

consol, still exists today except that its coupon has now changed to 2.5%

payable.

Assuming that the discount rate on the bond is 5% per annum, what is the

value of the bond today?

!!" !!!!

!!!"! !"#

Computing the value of a complex perpetuity:Ex: What is the value of a perpetuity with payments of 2 every half-year

commencing one-half-year from now if ! !10%/year with annual

compounding?

!voir dia 53 (notes fabienne)


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Annuities:A standard annuity has payments of !from date 1 to date !!

A standard annuity can be viewed as the difference between 2 perpetuities.

If !is the discount rate per period, the present value of an annuity with

payments commencing at date 1 and ending at date !is:

!" !!

!

!! !

! ! ! !

! !" ! !

! ! !

!!! !!!

!

Computing annuity payments:Ex: Flavio hast just borrowed 100,000 from his professor to pay for his doctoral

studies. He has promised to make payments each year for the next 30 years

to his professor at an interest rate of 10%.

What are his annual payments?

!!" ! !""!!!!/ ! ! !!!/ ! ! !"

!Using the formula above: ! !!""!!!!

!!!"#! !"#!!"#

Growing perpetuities & annuities:Growing perpetuity= perpetual cash flow stream that grows at a constantrate !over time:

Growing annuity= same that growing perpetuity except that the cash flows

terminate at date !.

The value of a growing perpetuity with initial payment of !dollars one period

from now is:

!" !!

!! !

(!constant growth rate)

A growing annuity is like the difference between 2 growing perpetuities:

!" !!

!! !!!

!!! !!!

!! ! !!!


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(!growing growth rate)

Growing perpetuity & the dividend discount model:When dividends are assumed to be growing at a constant rate, the stocksprice per share is:

!! !!"#!

!! !

!"#!: next years forecasted dividend per share

!: discount rate

!: dividend growth rate

Growing perpetuity:Ex of valuing a share of equity:

Agfa is an imaging technology firm that is listed on NYSE Euronext. For the last

four years, it paid a gross dividend of "0.50/year. Assume that next year, Agfa

will pay a dividend of "0.50 and that this will grow thereafter by 7% per

annum forever. If the relevant discount rate is 10%, how much should you pay

for Agfa equity?

!The per share value is: !" !!!!

!!!!!!!"! !"!!"#

Exercises: voir cours


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Module 2: Valuing real assets using the tracking

portfolio approach

1. Real investments

= expenditures that generate cash in the future and, as opposed to financial

investments (like stocks and bonds) are not financial instruments that trade in

the financial markets.

Corporations create value for their shareholders by making good real

investment decisions.

2. Valuing real investments

A. Net Present Value (NPV) rule for evaluating real projectsB. The DCF method and the NPV ruleC. Drawbacks in the DCF method

A. Net Present Value criterion:

Financial managers should use a market-based approach to value assets,

whether valuing financial assets (like stocks and bonds), or real assets (like

factories and machines).

Present Value (PV)of a project = the market price of a portfolio oftraded securities that tracks the future cash flows of the proposed

project (= discounted cash flows of the real investment)

Projects cash flow=expected free cash flows from the project =incremental cash flows to the firm.

!Synergies and other interactions between the new project and the

firms existing projects/products.

Net Present Value (NPV) of an investment project:!the projects PV (the value of a portfolio of financial instrument

llllithat tracks the projects future cash flows)

!the cost of implementing the project.

The financial assets in the tracking portfolio are the zero point on the NPV

measuring stick, as the real assets are always measured in relation to them:


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Value creation if NPV > 0Value destruction if NPV < 0

Project valuation with NPV:If cost of adopting a project < PV of tis future cash flows !financing theproject by selling short this tracking portfolio leaves surplus cash in the firm

today.

Risk-free project valuation with NPV:When perfect tracking is possible:

adopt the project when NPV is positive = creation of wealth through

arbitrage.

!Arbitrage opportunities between the markets for real assets and

financial assets

!It makes all financial assets zero-NPV investments!In efficient markets, financial securities are fairly priced while

bargains exist in the market for real assets.

On the financial markets, we can find zero-coupon bonds selling for $0.93 per

$ of face value

All riskless projects can have their future cash flows tracked with a portfolio of

zero-coupon bonds. Shorting the tracking portfolio thus offsets the future cashflows of the project.

For a project with riskless cash flows, the NPV is the same as the discountedvalue of all present and future cash flows of the project.


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Tracking portfolio with risky projects:If the project could be spun off and sold as a separate entity !the firm

create value by taking all real investment projects that cost less than what

the project can generate from the sale of stock in the project.

When aperfect trackingis possible: a portfolio that perfectly tracks the cash

flows of a risky project exists only in certain circumstances (ex: oil well, copper

mine).

When only an imperfect trackingis feasible (most cases): there will be some

tracking error: difference between the CF of the tracking portfolio and the CF

of the project.

Example of a perfect tracking:

If !! ! !": the future CF of the project can be perfectly tracked by a $10

million investment: (a) $5 million in a risk-free rate (worth $5.3 million one year

from now) and (b) $5 million in the market portfolio.

Since a portfolio of financial assets worth $10 million tracks the CF of the

casino, the value of the casinos future CF is $10 million.!We dont even need to know the expected market return or the risk-free

return to value the project #

If one were discounting the casinos expected CF to obtain a present value,the appropriate discount rate must equal the discount rate for the tracking

portfolios expected CF, that is a weighted average of the expected return,

where the weights correspond to the respective portfolio weights on the

market () and risk-free asset (1-) in the tracking portfolio.

Whenever a tracking portfolio for the future cash flows of a project generates

tracking error with zero systematic (or factor) risk and zero expected value,the market value of the tracking portfolio = the PV of the projects future cash

flows.

Example of imperfect tracking:

! The mix of the market portfolio and the risk-free asset that best tracks theproject is the one that minimizes the variance of the tracking error.

! Valuation requires a tracking portfolio with the same expected futurecash flows as that of the real asset it tracks. The difference between the

tracking portfolios future value and the casinos CF has an expectedvalue of 0.


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! The tracking error represents unsystematic or diversifiable risk. Whenevertracking error has no systematic (or factor) risk and has 0 expected value,

it has 0 PV and can be ignored.

Tracking portfolios with an expected tracking error of zero:The tracking error must consist entirely of unsystematic or firm-specific risks.

!Asset pricing models like CAPM or APT: the models generate substantial

tracking error because of the restrictive composition of their tracking portfolio

but with 0 present value.

$ Imperfect tracking: the Capital Asset Pricing Model (CAPM):Efficient frontiers and capital market lines:

o A chaque instant, les investisseursdoivent choisir parmi les centaines

dinstruments de placement.

o Un nombre infini de portefeuillespeuvent tre forms partir de 2

ou + dactifs. Ainsi, si on dcide decrer tous ces portefeuilles, de

calculer le rendement et le risque

de chacun, et de reprsenterchaque combinaison dans un

espace risque-rendement, on

obtient toutes les combinaisonspossibles de portefeuilles.

Cet ensemble est reprsent par

laire ombre de la figure suivante.

Frontire efficiente = ensemble de

tous les portefeuilles efficients(offrant le meilleur rapport risque-

rendement) : courbe du haut. Tous les portefeuilles au-dessus sont prfrables.

Ceux sa gauche ne peuvent tre considrs des fins dinvestissement puisquils sont lextrieur de lensemble des possibilits.

Ceux sa droite ne sont pas souhaitables, puisque leur rapport risque-rendement est infrieur celui des portefeuilles efficients.

Point A : market portfolio.

Bta :

2 composantes de linvestissement :

% Risque diversifiable (spcifique)% Risque systmatique (de march)

" Risque diversifiable : rsulte dvnements incontrls et alatoires propres lentreprise(grves, procs,). Eliminable, diversifiable.

" Risque systmatique : li des facteurs qui affectent lensemble des investissements et qui nesont pas propres un instrument donn.Il ne peut tre limin par la diversification. Non liminable, non diversifiable.

Risque total = risque non diversifiable + risque diversifiable

Tout investisseur peut rduire ou pratiquement liminer le risque diversifiable en grant unportefeuille diversifi de titres.

Bta= outil permettant de mesurer le risque du march non diversifiable (systmatique).


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" La diversification consiste minimiser le risque diversifiable en choisissant des instruments dontle rendement nvolue pas dans le mme sens.

" Le bta est utilis dans le modle du CAPM pour dterminer le rendement quun investisseurrationnel est en droit dexiger dun actif en particulier.

" Le bta relve le comportement de la valeur dun titre face aux fluctuations du march : + lavaleur du titre est sensible aux mouvements du march, + le bta est lev.

"

il se calcule en fonction de la relation entre les rendements du titre et le rendement du marchou du portefeuille de march.

" le bta dun actif !est obtenu en normalisant la covariance entre cet actif et le march M :

!! !!"#!!!!!!!

!!!!

!!

NB : !"# ! !!Il mesure la liaison qui existe entre lactif et le march en donnant aussi la contribution delactif dans le risque total du march.

!!!! ! !

!

!!!

# Bta mesure le risque du march (systmatique ou non diversifiable) dun titre.# Bta du march = 1# Bta dun actif sans risque = 0# Bta des titres positif ou ngatif# Titres dont le bta > 1 plus ractifs aux fluctuations du march (plus risqus)# + le bta dun titre est lev, + son risque systmatique est lev, + son rendement exig ou

espr est grand.

CAPM= modle utilisant le bta afin dtablir un lien formel entre les notions de risque et derendement.Partant du bta comme mesure de risque non diversifiable, le modle dvaluation des actifs

financiers dfinit le rendement requis ou exig selon :

!! ! !! ! !!!!! ! !!!

!!: Rendement exig de linvestissement i (expected return)!!: Taux sans risque (risk-free asset)!!: Bta pour linvestissement i (risk)!!

: Rendement du march (expected return of tangency portfolio)!!! !!: risk premium

Droite de march (SML = Security Market Line) :reprsentation graphique de la relation linaire duCAPM, pour chaque niveau de risque non

diversifiable, elle donne le rendement exig par

linvestisseur.

If =0 : expected return on a stock = risk-free

rate (Rf)

If =1 : expected return on a stock = expected

return on the market (!!

)Beta of security = responsiveness of a security to the market portfolio.

You will every time go back to the SML.

!It is

mispriced

Q: Price is too low!sell it and price

will go up again


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A : price is too low !I have to undertake the projectAll the projects > line !invest !

All the projects < line !NO invest !

Risk-free investment:Risk-free= without default risk AND without interest risk!

!0-coupon treasury bills?Problems:

! Default risk for some states !0! If the project has !expected CF! Short-term risk-free rate

B. The Discounted Cash Flow (DCF) method and the NPV rule:

To find the present value of next periods cash flow using the risk-adjusted

discount rate method:

1. Compute the expected future cash flow ! ! ;2. Compute the beta of the return of the project ;3. Compute the expected return of the project by substituting the beta

calculated in step 2 into the tangency portfolio risk-expected return

equation;

4. Divide the expected future cash flow in step 1 by one + the expectedreturn from step 3:

!" !!!!!

!! !! ! !!!! ! !!!

Ex: using the cost of capital to value a non-traded subsidiary:

Inputs: HSCC has a of 1.2 against the tangency portfolio risk-free annualrate is 9%; tangency portfolio annual average return of 19%


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The tracking portfolio method is implicit in the risk-adjusted discount rate

method:

Ex: Hilton Hotel/casino:

! expected CF: $11.3 million! of the project: 0.5! expected market return: 20%, risk-free rate: 6%

!Appropriate discount rate:

0.06+0.5(0.2-0.06)=0.13 = 13%

NB: calcul du :

Tracking portfolio:

! !!"##"$%!!!

! !"#

! !!"##"$%!!! ! !"#!Somme: total value of the financial asset = 10 million!! ! !!!! ! !!!!!! !!!!! ! !!!

Discount the estimate future cash flows of a project at the rate of return of the

appropriate tracking portfolio of financial assets.

A manager should adopt a project if:

Cost of investing in the project


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!The CAPM and beta comparable method:

Beta comparable method: The effect of leverage oncomparisons

Right of the balance sheet can be viewed as

a portfolio of investments, with the weight on

debt as!

!!!and the weight on equity as !

!!!

A: Assets = a lot of projects

E: Equity = claim on the projects, they give money to finance the projects!! ! ! ! !

!! !!

!!!

!! !!

!!!

!!

!! ! !!!

!!! !

!

!!!

If the firm has risk-free debt !!! ! !

Case 1: firm issues risk-free debt: Risk measures:

!! !!

!!!!! !

!!!!!

!! !!

!!!! !

!

!!!!!

!!: increasing function of the beta of the assets !!.There is a strong assumption that debt is riskless.

If ! !: value of the bond !(= expected CF discounted at the interest rate)

!!"

!!!!

Case 2: firm issues short-term debt, but it doesnt alter the operations of the

firm:

Note on risk-free debt VS default-free debt:

! Risk-free debt !default-free debt! Default-free debt !risk-free debt

2 sources of risk associated with debt:! Interest rate risk: general changes in long-term interest rates! Credit risk: possibility of default

!!!return on the asset!!!return on debt!!!return on equity

!!! ! ! !!

!!!

and

!!! ! ! !!

!!!


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Long-term debt and long-term interest rates (bond yields). Asset valuesand long-term interest rates !effect on debt beta

Short-term debt and long-term interest rates !short-term default-freetends to have a beta near 0.

!Unlevering asset beta when debt has a positive beta:

!! !!

! ! !!! !

!

! ! !!!

!! ! ! !!

!!! !

!

!!!

Equity beta (!!) & firms leverage ratio:

Straight line first and then a curve line.

No default: !!!! !"#!! ! !! !!!!

If more leverage: equity will be more riskybecause more debt holders !claims on debt

>< less leverage: equity less risky

If default is possible, some debt holders wont

receive their claims.

G&T, 2ndedition, p382

Why should equity holders risk per dollar invested increase with leverage?

Here, the shareholders will only receive the total amount that is due to the debt holders !theyhave to share with debt holders and they will be paid first.

The leverage will magnify the decrease in the equity.

Cost of equity of a firm= expected return (!!) required by investors to inducethem to hold the equity: since the firms equity beta increases linearly with

leverage, the cost of equity should also increase as a function of the leverage

ratio, !!!:

!! ! !! !!

!!! ! !!


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Cost of debt, equity, and capital as a function of !!!:

G&T, 2ndedition,

p384

!!: no default risk at the beginning and then it increases (because with the leverage, debtincreases)

We want to compute the return on asset !!by using !!and !!(since we can find !!on thefinancial market).

!If the firms debt !(! !and ! !): risk per dollar of equity investment !(betaand standard deviation)

If beta of a non-listed firm !search for a firm with traded stocks that has

similar operations, compute the traded firms beta by regressing past stock

returns on the returns of a market proxy, and compute the expected return

for the non-traded firm using the comparable beta.

NB: the amount of debt financing a firm takes on can dramatically affect

equity betas !adjustments are necessary to make appropriate beta riskcomparisons:

A two step approach:

" Method 1:(1)Use a formula to convert the equity and debts betas of comparable

publicly traded firms to asset beta to undo the confounding effect of

leverage on equity beta.(2)Apply an asset pricing model to convert the asset beta to an asset

expected return which is then used as the risk-adjusted discount rate.

" Method 2:(1)Use an asset pricing model to convert the equity beta to an equity

expected return.

(2)Use a formula to convert the equity expected return (and sometimesthe debt return) of comparable publicly traded firms to an assetexpected return to undo the confounding effect of leverage on equity

beta. The asset expected return is then used as the risk-adjusted

discount rate.


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The CAPM, the comparison method, and adjusting for leverage:If an acquisition (or project) and its comparison firm(s) are financed

differently, it may be possible to adjust the comparison firms beta for the

difference in leverage ratios:

! Adjustments in the absence of taxes! Adjustments in the presence of taxes

The CAPM and leverage adjustments in the absence of taxes:

- Risk-free rate !!: 4%

- Market risk premium !!! !!: 8.4%

- CAPM holds

- All 3 firms provide equally good comparisons for Mariotts restaurant division.

We know that: !! !!

!!!!!

So:

Here we want to know the cost of capital of the restaurant.

!WACC:

!"## !!

! ! !!! !

!

! ! !!!

!Real price of the restaurant =!"

!!!!!!!discounted CF of restaurant

Compare the costs to the CF:Discount rate: objective of this exercise !we look at the market and look at the restaurants

that are at the same level as our restaurant = benchmarking.Real discount rate: simple average !if I think my company is more similar to Wendys I will give

Mc Donalds an other weight then Wendys !!proportions.

!Need to find the !!(WACC) of each restaurant (see above) and then make an average ofthese 3 WACCs.


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Adjusting the unlevered beta for cash:

The unlevered beta that we compute for a firm reflects both its operating

assets and the cash holdings of the firm:

!!"#$%$&$'!"#$%&'"!"#!"#!"#$ ! !!"#$%$&$'!!

!"#$

!"#$!"#$%&!"#$%


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B.2. The certainty equivalent method ( NOT FOR EXAM!)

Definition:

!With this method, the numerator of that ratio, the certainty equivalent cash

flow, is adjusted for risk and discounted at a risk-free interest rate in the ratios

denominator.

The certainty equivalent of a risky cash flow paid at future date !is the riskless

cash flow paid at date !that has the same present value as the risky cash

flow:

Difference between the certainty equivalent method and the risk-adjusted

discount rate method:

!simply a matter of where the risk adjustment occurs: the risk-adjusted

discount rate adjusts the denominator while the certainty equivalent method

adjusts the numerator for risk.

Identifying the certainty equivalent from models of risk and return:If!"!!!= the certainty equivalent of uncertain cash flow !!!!!= cash flow mean

Then, we can obtain a certainty equivalent by subtracting the product of the

cash flow beta and the tangency portfolio risk premium from the expected

cash flow:

!" ! ! ! ! ! !!!! ! !!!where ! !

!"#!!!!!!

!!

!

Certainty equivalent present value:The Present Value of next periods cash flow can be found by:

(1)computing !!!!, the expected future CF and the beta of the futureCF;

(2)subtracting the product of this beta and the risk premium of thetangency;

(3)dividing by !!! !"#$ ! !"##!"#$%&$!:

!" ! ! ! ! !!!!!

!!!!! !!


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Interpreting the cash flow beta:Cash flow beta= tracking portfolios dollar investment in the tangencyportfolio.

The tangency portfolio earns an extra expected return (a risk premium)because of systematic risk.

For an investment of !dollars in the tangency portfolio, the additional

expected cash flow (in dollar) from the projects systematic (or factor) risk is:

!!!! ! !!!

Subtracting !!!! ! !!!from the expected cash flow yields:

! ! ! !!!! ! !!!

!Cash flow that would be generated if the project had a cash flow beta of

zero or if the future cash flow were risk free.

Cash flow betas and return betas:In the risk-adjusted discount rate method, the return beta of the project = the

beta of a comparison financial security, which is a zero NPV investment.However:

The cash flow beta = the product of the projects PV with the return beta.

!To identify cash flow betas: estimate beta through scenarios.

Ex: the CAPM and the certainty equivalent method:

CAPM, scenarios, and the certainty equivalent method:

Evaluate the present value of the additional cash flow one year from now of

purchasing 10 new airline reservation computers. The new computers, whichare faster than the current ones in place, are expected to increase the

number of reservation each agent can handle. !! ! !!!"#$, CAPM holds:

The certainty equivalent formula and the tracking portfolio approach:

Hilton hotel casino project:

Tracking portfolio approach:

- Hilton project tracked by an investment of $5 million in the market portfolioand $5 million in a risk-free asset

- Risk premium of 14% (20%-6%)

- Risk-free rate of 6%


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Certainty equivalent method:

The amount invested in the tangency portfolio = the cash flow beta: $5

million. The certainty equivalent cash flow is: $11.3m - $5m x 0.14 = $10.6m

PV of the project: $10.6m/1.06 = $10m

Obtaining certainty equivalents with risk-free scenarios:The risk-free scenario method generates the certainty equivalent with a

typically conservative cash flow forecast under a scenario where all assets

are expected to appreciate at the risk-free rate.

A reasonable procedure for estimating the cash flows for the risk-free scenario

is to forecast the cash flow as a multiple of firm stock price and compute

what the price will be when stock appreciates at the risk-free rate.

If it is possible to estimate the expected future cash flow of an investment orproject under a scenario where all securities are expected to appreciate at

the risk-free return, then the present value of the cash flow is computed by

discounting the expected cash flow for the risk-free scenario at the risk-free

rate:

! ! !"#$%!"#!"#$!%!! ! ! ! !!!Regress the actual excess returns of any zero-NPV investment on the actualexcess return of the tangency portfolio:

!!

!! ! ! ! ! !!!

!! ! ! where ! ! ! !If ! ! !!! ! !! ! ! !! ! !!

! ! !"#$%!! ! !! ! !!So, when the return on the tangency portfolio = the risk-free return!all zero-

NPV investments are expected to appreciate at the risk-free rate.

In this risk-free scenario, a projects expected value is:

! ! !"#$%!"#$!"##!!"#$%&'( ! !! !! !!"! !" ! ! ! !"#$%!"#$!"##!"#$%&'(! !"#$%&'()! !"!!!!!

The only scenario where cash flow forecasts are needed is one in which all

securities are expected to earn the risk-free return.

In the risk-free (pessimistic) scenario, the investors expect the stock held byshareholders in the managers own firm and the stock in all other firms in theindustry to appreciate at !! !

It is easier to estimate the future cash flow of the project than to estimate

both its expected value over all scenarios and its covariance with the

tangency portfolio.


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Computing certainty equivalents from prices in financial markets:The forward price represents the certainty equivalent of the uncertain future

price rather than its expected value.

B.3. DCF: which method to use?

! Discounting an expected CF at a risk-adjusted discount rate: if tradedsecurities exist for companies that have the same line of business as the

project.

! Discounting a certainty equivalent CF at a risk-free rate: if its notpossible to identify the beta risk of comparison securities and when

forward prices exist for commodities that are fundamental to the

profitability of the project.


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C. Drawbacks in the DCF method

Pitfalls in the comparison method:! Project betas !firm betas:New projects may have higher beta risk than the firms mature projects:

project with high operating leverage, growth option or large R&D investment.

A project may also be less risky than the firm as a whole.

! Growth opportunities are usually the source of high betas:When a firms value is largely generated by its perceived ability to develop

new profitable projects growth opportunities or growth options one must

be cautious about using it as a comparison firm for a project, even one of its

own.

Ex: firm with high P/E ratio, firms in newer industries, etc.

! Multiperiod risk-adjusted discount rates:Multiperiod valuation problems have been viewed as simple extensions of the

one-period analysis:

Approach used by practitioners:

(1)estimate the equity beta from a comparison firm using historical data;(2)compute the expected return using an appropriate asset pricing

model;

(3)adjust for leverage (and taxes) to obtain a cost of capital;(4)use the cost of capital as a single discount rate for each period.

Pitfalls in using the practitioner approach: a single cost of capital tends to

misvalue cash flows." Riskless cash flow: term structure of interest rates. A single discount

rate would undervalue the near-term cash flows and overvalue the

cash flows more distant in the future.

" Risky cash flow: tracking portfolios composition needs to be adjustedover time.

CF horizon & beta risk:

Betas vary with the cash flow horizon >< financial analysts who implement

the risk-adjusted discount rate method almost always use the same beta

for every cash flow in a cash flow stream.

CF horizon & risk-free rate:

No theoretical reason to select a short-term risk-free rate over a long-termrisk-free rate, or vice versa. Whether its better to include long-term risk-free

bond or a short-term risk-free bond in the tracking portfolio depends on

which bond generates a better tracking portfolio (i.e. a tracking error withPV closest to 0).

!While technically correct, the short horizon CAPM-based method of

valuing a riskless long-horizon cash flow has substantial tracking error.

! Empirical failures of the CAPM:Size, book-to-market or momentum effects in stock returns: market-to-book

ratio, firm size and firm momentum are better determinants of a stocks future

expected rate of return than market betas or factor betas.


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!In this case: use a set of firms with similar size and market-to-book ratio as

comparison firms.

! What if no comparable line of business exists?For some real assets, there is no suitable comparison line of business in which

to search for the components of a tracking portfolio.!Advanced corporate finance topics!

! DCF method is biased against long-term projects because it ignores manyaspects of long-term investment projects that cannot easily be quantified.

! It also ignores that the adoption of an investment project generates futureinvestment opportunities that often are quite valuable.

- New opportunities due to economics of scope are ignored

- Indirect CF are ignored

-

!Advanced corporate finance topics!


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Module 3: Some alternative investment rules

1.

Properties of the NPV rule:

Why use NPV?Present values and Net present values have the value additivity property:2 future CF streams, when combined, have a value that is the sum of the PV

of the separate CF streams.

!This value additivity property is closely linked to the principle of no

arbitrage.

" Implications of value additivity for project adoption and cancellation:

" Implications of value additivity when evaluating mutually exclusiveprojects:

Given a set of investment projects, each with positive NPV, one should select

the project with the largest positive NPV if allowed to adopt only one of the

projects: adopting the project with the cash flows that have the largest NPV

generates the largest NPV of the firms aggregated cash flows.

Ex: Mutually exclusive projects and NPV:

The law firm of Jacob&Meyer is small and has the resources to take on only 1

of 4 cases. The CF for each of the 4 legal projects and their NPV discounted

at the rate of 10%/period are given below. Which is the best project?

Cost of adopting 1 of 2 mutually exclusive projects, each with positive NPV =

the forgone cash flows of the other project.


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!Answer:

These CF are calculated as the CF of the firm with the project the CF of the

firm without any of the 4 projects:

Problems using the NPV rule:

" Using NPV with capital constraints:The amount of capital the firm can devote to new investments is limited.

!Profitability index

The NPV rule says that one should select projects for which:

!"

!!!

! ! !"!! ! !and

!"

!!!

! ! !" !! ! !Ex of profitability index:

There is a capital constraint of 10,000 in the initial period. The 2 scalableprojects available for investment are projects B and C. The cash flows, NPVs

at 10%, and profitability indexes are given below.

!Which is the betterproject?

10 project B (1000x10) 9,000x10 = 90,000

10,000 to invest2 project C (5000x10) 15,000x2 = 30,000

!!" !!!

!!!!

!!

!!!!!!!!

!NPV role: !"# ! !" ! !! ! !(should be always like this) ! !"!!!

! ! ! !"#$%&'(%)%&* !"#$%!!!!!"#$%&'!"#$!!"!#!$%!"#$%&'$"&!

Project B:

!" !!!

!!!!!!"!!

!!!! ! !"!!!!!!"# ! !"!!!! ! !!""" ! !!!!!!!"#$!"#$% ! !""""

!"""! !"

Project C:

!" !!!

!!!!!!"!!

!!!! ! !"!!!!!!"# ! !"!!!! ! !!""" ! !"!!!!!!"#$!"#$% ! !""""

!"""! !

!We choose project B because highest profitability index (C is penalized because of the high

investment).

(total value if you invest 10,000)


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" Using NPV to evaluate projects that can be repeated over time:Ex of evaluating projects with !lives:

2 types of canning machines, A and B, can be placed only in the same

corner of a factory. Machine A, the old technology, has a life of 2 periods.

Machine B costs more to purchase but produce cans faster. However,machine B has a life of only 1 period. The delivery and setup of each

machine takes place one period after initially paying for it. Immediately upon

the setup of either machine, positive cash flows begin to be produced.

The CF from each machine and the NPVs of their CF at a discount rate of 10%

are:

It appears that machine A is a

better choice Is it true?

!NO!B machines NPV > A machine NPV

2. Internal rate of return (taux interne de rentabilit)

Definition:IRR for a cash flow stream !!!!!!! !!!at dates !!!!! !!respectively = interest

rate !that makes the NPV of a project equal 0.

!That is the !that solves:

! ! !! !!!

!! !!

!!

!!! !!!!!!

!!

!! ! ! !! !"#!

Intuition for the IRR method:The IRR method compares the IRR of a project with a hurdle rate to determine

whether the project should be taken.

When cash flows are riskless, the hurdle rate is always the risk-free rate of

interest.

For risky projects, the hurdle rate (= projects cost of capital) may reflect a risk

premium.

Hurdle rate= discount rate that makes the PV of the tracking portfolio CFsequal to its market price = rate of return I will earn in the financial market.


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Numerical iteration of the IRR:Trial-and-error procedure

If a project has cash flows only at year 0 and year 1, we have:

! !!!

!!

! !

Cash flow pattern:A latercash flow stream starts at date 0 with a negative CF and then, atsome future dates, begins to experience positive cash flows for the remaining

life of the project.

An earlycash flow stream starts at date 0 with a series of positive cash flowsand all negative cash flows occur only after the last positive CF.

o Later CF stream: similar to a cash flow pattern for investing !wheninvesting, high rates of return are good: accept the project if:

!"" ! !"#$%&!"#$o Early CF stream: similar to borrowing !when borrowing, its better to

have a low rate than a high rate: accept the project if:!"" ! !"#$%&!"#$

An IRR calculation and a comparison with NPV:Clachers Snooker Emporium is considering whether to recover its snooker

tables, which will generate additional business. The projects cash flows,

which occur at dates 0,1,2 and 3, are assumed to be riskless and are

described by the following table:

If the yields of riskless zero-coupon bonds maturing at years 1,2 and 3 are 8%,

5% and 6%/period, find the NPV and IRR of the cash flows.

Hurdle rate:If the IRR is applicable, the appropriate hurdle rate for comparison with theIRR is that which makes the sum of the discounted future cash flows of the

project equal to the selling price of the tracking portfolio of the future cash

flows !The analyst has to compute the PV of the project in order to compute

the appropriate hurdle rate!


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Hurdle rate of a riskless project:Long-maturity bonds have !yields to maturity than short-maturity riskless

bonds !the appropriate hurdle rate should be !for evaluating riskless cash

flows occurring at !time periods.

A unique IRR with later CF streams:Refer to the Clachers Snooker project, how does the IRR compare with the

hurdle rate for the project?

A unique IRR with early CF streams:Consider the cancellation of the project immediately after Clachers Snooker

made the adoption decision. In other words, the decision was not to recoversnooker tables following the earlier decision to recover them.

!What are the cash flows from cancelling the project? How does the IRR

compare with the hurdle rate?

Multiple IRR:Ex: Strip Mine is considering a project with the cash flows described in the

following table:

!Compute the IRR of this project?

NPV for cash flows as a function of discount rates:

G&T, p327


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An example where no IRR exists:A group of statisticians is thinking of taking a 2-period leave from their

academic positions to form a consulting firm for analyzing survey data from

polls in political campaigns. The project has cash flows described by the

following table:

!Compute its IRR?

NPV for cash flows as a function of discount rates:

G&T, p328

Mutually exclusive projects and the IRR:When selecting one project from a group of alternatives, the NPV rule

indicates that the project with the largest positive NPV is the best project.

!Dont select the project with the largest NPV !!

Ex: Consider a firm with 2 projects, each with a discount rate of 2%/period.

The following table describes their cash flows, NPVs and IRR:

!Given that the firm must select only

1 project, should it use A or B?

Mutually exclusive projects and the appropriate IRR-based procedure:The appropriate IRR-based procedure for evaluating mutually exclusive

projects is similar to that used for the NPV rule.

!Subtract the cash flows of the next best alternative. If one is lucky and the

difference in the CF streams of the 2 projects have an early or later signpattern, one can choose which of the 2 projects is better.

CF of project A CF of project B:


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!There is only one sign reversal and a later CF !Project A better than

project B because the 5.56% IRR > 2% hurdle rate.

Multiple internal rates:How multiple IRR arise from mutually exclusive projects?

!The project with the largest IRR is generally not the project with the highest

NPV !not the best among a set of mutually exclusive projects.

Ex: NASA must select 1 of 3 commercial projects for the next space shuttle

mission. Each of these projects has industrial spin-offs that will pay off in the

next 2 years.

Cash flows, NPV, internal rates of return of the projects:

!Which project shouldNASA select?

3. Using NPV for other corporate decisions:

Laying off workers as an investment decision:Ex: Ace Farm is currently suffering from a slowdown in sales and temporary

overstaffing. The company can save "600,000 ("0.6million) at the end of eachof the next 3 years if it cuts its workforce by 25 individuals. In 4 years, however,

it expects that its market will improve and that it will have to hire 25

employees. It estimates that the cost of hiring and training workers is

"100,000/employee, or "2.5million for the 25 employees. If the discount rate is

10%, should Ace temporarily cut its workforce?

!Incremental cash flows associated with the layoffs:

! !"# !!"

!

!!

!!!!!"

!

!!

!!!! !

!"!

!!

!!!! !

!"!

!!

!!!! ! !"#$!

Cutting product price as an investment decision:Ex: assume that Local Beers currently sells about 10,000 cases of beer/month

in the UK, which is 15% of the beer market. Management is considering a

temporary price cut to attract a larger share of the market. If they choose to

lower beer prices from 4 to 3.8 a case, Local Beers will expand its market by

50%. The CFO estimates that the beer costs 3.5/case, so that the companywould be making 5000/month with the higher price but only 4500/month


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with the lower price. However, the company plans to stick with the lower

price for 2 years and then raise it to 3.9/case. Management believe that at

this higher price they still will be able to keep their new customers for the

subsequent 2 years, allowing Local Beers to generate a monthly CF of

6000/month in years 3 and 4.

If the discount rate is 1%/month, should prices be lowered?

!Incremental cash flows:

(on passe de 5000/mois au plus haut prix 4500!-500 les 2 premires annes. Puis on

remonte le prix pour les 2 annes suivantes !ongagne 6000/mois au lieu de 5000 !+1000)

! !"# !!!""

!!!"!!!""

!!!"!!!!

!!""

!!!"!"!

!"""

!!!"!"!

!"""

!!!"!"!!!

!"""

!!!"!" ! !"!!"#

4. Alternative investment rules

The accounting rate of return criterion:This criterion evaluates projects by comparing the projects return on assets.

The accounting rate of return is then compared with some hurdle rate.

However, accounting profits are often very different from the cash flows

generated by a project.

!Popular but incorrectprocedure!

The payback method:!it evaluates projects based on the number of years needed to recover the

initial capital outlay for a project.

Major problem: it ignores cash flows that occur after the project is paid off.

!Popular but incorrectprocedure!



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Module 4: Valuing real assets with corporate

taxes

1. Impact of financing on real asset valuation

No corporate taxes: Corporate taxes:

NB: position of shareholders riskier than position of debt holders who are paid

first if bankruptcy !!! ! !!

No corporate taxes: if we raise the part of debt, the financial structure will be

riskier. But the return on assets !!will be constant.If corporate taxes: !!wont be constant.(voir notes et graphes fabienne)

!Valuing real asset with corporate taxes:

! The Adjusted Present Value (APV) method:calculates the NPV of the all-equity-financed project and adds the

value of the tax (and any other) benefits of debt.

! The Weighted Average Cost of Capital (WACC):accounts for any benefits of debt by adjusting the discount rate.

Adjusted present value (APV) method:

!generates PV by:

(1)forecasting a projects unlevered cash flows;(2)valuing the cash flows in step 1, assuming that the project is financed

entirely with equity;(3)adding to the value obtained in step 2 the value generated as a result

of the tax shields and other subsidies from the projects debt financing.


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o Components:

Unlevered cash flows:

Hypothesis: the after-tax cash flows generated directly by the real assets of

the project or firm are unaffected by the amount of debt financing the firmuses.

!Unlevered CF = after-tax cash flows of the project or firm under the

assumption that the project or firm is financed entirely with equity.

Cost of capital for an all-equity financed or unlevered firm:

The appropriate risk-adjusted discount rate for a projects future CF when the

CF has the same risk as the overall firm is the firms cost of capital.

!Unlevered cost of capital

!!"= the expected return on the equity ofthe firm if the firm is financed entirely with equity.

Comparison approach & cost of capital:

To value an all-equity-financed project when the comparison firm has debt

financing, its necessary to calculate the required rate of return on the

comparison firms equity in the hypothetical case of a comparison firm that is

all equity financed.

!Unlevering equity betas

o Levered firm with deductible debt interest:

o How debt financing and taxes affect the risks of various componentsof the firms balance sheet?

Beta (or expected return) of the assets is the portfolio-weighted average ofthe betas (or expected returns) of the unlevered assets and debt tax shields:

!! !!"

! ! !!!" !

!"

! ! !!!"

!! !

!"

! ! ! !!" !

!"

! ! ! !!"


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o Hamadas model:Key assumptions:

(1)The debt is perpetual !it is either a perpetuity or consists of rolled overshort-term debt positions;

(2)The debt is default-free and pays the risk-free rate;(3)The face value of the debt and the tax rate dont change over time.

Static perpetual risk-free debt:

- Firms debt tax shield:

!!! !!!!!!

!!

- Values for !"and !"? Hamadas model:

!" ! !!! ! !" ! ! ! ! ! !!!

- Impact on asset betas:

!! !! ! ! ! !!!

! ! !!!"

Equity betas and asset betas:

!! ! !!!

!

!!

We know that:

!! !! ! ! ! !!!

! ! !!!"

!!! ! ! !!

!

!!!!!!!

!!!!!" ! ! ! ! ! !!

!

!!!"


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Comparison method:

When debt tax shields exist, its the betas and required rates or return of the

unlevered assets of comparison firms (and not their assets) that are perceived

as being similar to those of the project being valued.

How one could value a project using a risk-adjusted discount rate estimated

from the stock returns of comparison firms?

!Unlevering equity betas: !!" !!!

!! !!!!!

!

!Substituting !!"into a risk-expected return formula gives the desired

unlevered cost of capital.

Ex of Mariott:

!Estimate the unlevered

cost of capital for Mariotts

restaurant division?

!Assume !! ! !"! !! ! !! ! !!!"!!! ! !"#, CAPM holds

!Risk-free debt, all 3 firms provide equally good comparisons for Mariott.

G&T, p466

o Projects debt capacity:Projects debt capacity= marginal amount by which a firms debt capacityincreases as a direct result of taking on the project.

The notion that the debt tax shield creates value suggests, TACRE, that firms

should be financed with enough debt to eliminate their tax liabilities.

Limits and costs of debt financing: probability of bankruptcy, frictions in the

capital markets.!Debt capacity restricted by the management.


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Dynamic VS static debt capacity:

A project may initially be financed entirely with internal funds but become

debt financed at a later date when the firm finds it more convenient or less

costly to issue debt.

!The dynamic sequence of debt financing must be taken into account indetermining the corporate tax subsidy.

What determines debt capacity?

!Trade-off between the benefits of debt (tax-advantage of interest

deductions) and the disadvantages of debt (bankruptcy costs).

o The APV and the risk-adjusted discount rate method: risk-free debt taxshields:

Ex: G&T p470. United technologies (UT) is considering a project that has a cost ofcapital of 14% if its financed entirely with equity. The project is expected to generate

unlevered CF in the next 4 years as follows:

Since the project generates large tax deductions in the first 2 years, UT will initially

finance the project exclusively with equity. However, at the start of year 3 the firm willrepurchase some of its equity and borrow $2billion to finance the project for the last 2

years. The borrowing (and discount) rate at this time will be 8%/year and the

corporate tax will be 34%.

!PV of the project?

The tax savings from debt wont be risk-free and shouldnt be discounted at

the risk-free rate if the firms financing plans are flexible or if there is a chance

that the firm may not be able to generate CFs large enough to take full

advantage of the interest tax shield.

Ex: G&T p471


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Weighted average cost of capital (WACC):

!generates PV by:

(1)estimating a projects expected unlevered cash flows;(2)valuing the expected cash flows in step 1 by discounting them at a

single risk-adjusted discount rate that varies with the degree of debt

financing that can be attributed to the project.

o Adjusted discount rate:

!"## ! !!!! !!! !! !! !!

!!: market value of equity over market value of all financing!!: debt

!expected return on equity to investors, !!

!expected return on debt to investors, !!!expected after-tax cost of debt to the firm, !! ! ! !!

o WACC Components:! Expected return paid by the firm to its shareholders= expected return

received by the equity holders.! Expected return paid by the firm to its bondholders!expected return

received by investors.

!The tax deductibility of interest implies that the cost of debt financing to a

corporation may be less than the rate of return on a firms debt received by

the firms debt holders.

! Cost of equity financing: this rate of return can be determined in many ways.Typically, one uses expected return formulas from the CAPM or dividend

discount model. With the CAPM, equity betas are estimated from historical

return data.

! Cost of debt financing:1. Default-free debt: yield to maturity.

Practitioners typically assume that the firms pretax cost of debt is the

yield to maturity of the firms debt.

!the yield to maturity provides a fairly accurate estimate of a firms

pretax cost of debt when the debt is highly rated and not callable or

convertible.

2. Risky debt: promised yield or expected return?If risky debt: promised return on the debt (=yield to maturity) > debts

expected return: because of the possibility of default.


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" Expected return of risky debt !!:Method 1: Substract expected losses owing to default from thepromised yield to generate the pretax cost of debt financing.

Ex: promised yield on a high-yield bond may be 14%. 4% of these

bonds default in a given year with the bond holders recovering

about 60% of their original investment:!!!"!!"# ! !!!"! !!"# ! !!!!"#

Method 2: Use CAPM to calculate the expected return of the debt!estimated betas for junk debt range from about 0.3 to about 0.5.

!Determining the costs of debt and equity when the project is adopted:

For a firm, the relevant pretax cost of debt capital or the cost of equity

capital = the expected rate of return of the respective sources of capital atthe time the firm decides to adopt the project(rather than the actual cost

that the firm incurred to obtain the funds).

Ex:

o Effect of leverage on a firms WACC:" No tax:

If no tax: the WACC of a firm is independentof how it is financed.!WACC is the same as the unlevered cost of capital, identical to the

expected return of assets:

!! !

!

! ! !!! !

!

! ! !!!

" WACC, cost of equity and cost of debt VS D/E with NO taxes:

G&T, p481


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" Debt interest corporate tax deduction:

With corporate taxes: the WACC declineswith an increase in debt because,relative to all-equity financing, part of the cost of financing is borne (soutenu)

by the government:

!

! ! !!! ! !! !

!

! ! !!!

Substituting in:!"## ! !!!! !!! !! !! !!

!"## ! !! ! !

! ! !!!!!

When debt interest is tax deductible, the WACC will decline as the firmsleverage ratio (D/E) increases.

!Expected return on assets is a portfolio-weighted average of the expected

returns of the unlevered assets and the debt tax shield (Hamadas model):

!! ! !! !!!

! ! !!!" !

!!!

! ! !!!

!Substituting this in the WACC formula:

!"## ! !!"

!! !!

!

! ! !

" Effect of leverage on the WACC with corporate taxes:Ex: G&T p482

" WACC, cost of equity and cost of debt VS D/E with corporate taxes:

G&T p483


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o Evaluating individual projects:The appropriate discount rate for a particular project must reflect the risk and

debt capacity of the project rather than the risk and debt capacity of the

firm as a whole.

! Riskless project, riskless financing: riskless CFs and financing consisting of debtwith tax-deductible interest payments !compare the projects proceeds

with its financing costs + debt tax shield.

! Riskless project, risky equity financing: risk-free project financed by an equityoffering!the risk-free rate is still the appropriate marginal, or incremental,

cost of raising capital for the project.

Marginal cost of capital= amount by which the firms total cost of financingwill increase/decrease if it raises additional amount of capital to finance the

project.The marginal cost of capital for the project reflects the risk of the project (and

not the risk of the firm as a whole).

The marginal weighted average cost of capital:Ex: G&T p486

" Computing a projects WACC from comparison firms:The comparison firm must have the same risk profile as the project beingvalued.

The project must:

(1)have the same beta;(2)contribute the same proportion as the entire firm to the firms debt

capacity.The WACC of the comparison firm can be used to discount the expected real

asset cash flows of the project.

WACC vs APV?!Using WACC:

! Conceptually easier;! Used more widely by analysts;! It assumes that the firm continuously monitors the value of its debt and

adjusts the debt to keep the ratio of debt to equity (D/E) constant;


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! If the project leverage is changing, WACC shouldnt be constant!better to assume that the rate of return on the firms assets is constant

rather than the WACC;

! Specific to the project.

!Using APV:

! It categorizes the sources of value and thus lets a manager make aninformed decision about the economic profitability of a project vs

other sources of value coming from financing and growth;

! It works well for projects, in which the firm knows the level of debt;! Its also straightforward to value subsidized financing which is often

missed in a WACC analysis;

! APV is particularly suited to complicated tax situations:Ex: A project that initially has a great deal of nondebt tax deductions

because of accelerated depreciation write-offs or tax credits for R&Dexpenses.

!Phase 1: low level of debt

Phase 2: substantial increase in the amount of debt

!the changes in the financing of the project cause its cost of capital

to change over time, which makes calculating the projects NPV with

the WACC method difficult.

Value creation for shareholders: firm value & wealth transfers:

o Cash flows to shareholders:3 sources of value creation for shareholders:

1) The PV of the projects unlevered CFs: main source of value from aninvestment project;

2) The PV of subsidies due to the financing of the project(ex: debt taxshield): projects financing can create value for the firm (reduction in

corporate taxes linked to debt financing, debt financing at reduced

rates);

3) Transfers to shareholders from existing debt holders: selection of high-risk projects, etc.

o Value creation to shareholders:

CFs to shareholders !CFs to the firm:

Selecting a project based on the total CFs of the real assets (which accrue to

the debt holders and the shareholders) maximizes the total value of the firmsoutstanding claims (debt+equity).


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This decision rule conflicts in some case with the objective of maximizing the

value of the firms equity: the adoption of positive NPV project can transfer

wealth from equity holders to debt holders, which adversely affects share

prices.

!Advanced corporate finance topics!


END.

Documents

Capital Budg résumé.pdf