the basics of cost of capital

7/21/2019 The Basics of Cost of Capital

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THE BASICS OF COSTOF CAPITAL

PGP TERM III

IIM INDORE


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THE AGENDA

WACC

Cost of Capital Components

Debt

Preferred

Common Equity

Component Weights


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CAPITAL COMPONENTS

Capital components are sources of funding that comefrom investors.

Accounts payable & accruals are not sources offunding that come from investors, so they are not includedin the calculation of the cost of capital.

We do adjust for these items when calculating thecash flows of a project, but not when calculating the cost

of capital.


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SHOULD WE FOCUS ON BEFORE-TAX

OR AFTER-TAX CAPITAL COSTS?

Tax effects associated with financing can be incorporatedeither in capital budgeting cash flows or in cost of capital.

Most firms incorporate tax effects in the cost of capital.Therefore, focus on after-tax costs.

Only cost of debt is affected.

Preferred Dividends are not tax-deductible


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SHOULD WE FOCUS ON HISTORICAL(EMBEDDED) COSTS OR NEW(MARGINAL) COSTS?

The cost of capital is used primarily to make decisionswhich involve raising and investing new capital. So, weshould focus on marginal costs.


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WACC

WACC = [(D/V) kd (1-t)] + [(E/V) ke]

D = Proportion of Debt in the total Value

E = Proportion of Equity in the total Value

V = E + D

kd = Cost of Debt

t = Coporate Tax RateKe = Cost of Equity

Weights in WACC are market value weights


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COST OF DEBT

Expected return on a traded, long-term fixed-rate obligation of acredit quality that corresponds to the capital structure ratios builtinto the WACC Formula

Method 1: Ask an investment banker what the coupon rate would beon new debt. NoteIt will not be the same as the embedded / historical rate

Method 2: Find the bond rating for the company and use the yield

on other bonds with a similar rating.Method 3: Find the yield on the companys debt, if it has any.

Method 4: Synthetic Ratings


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A 15-YEAR, 12% SEMIANNUAL BOND SELLS

FOR $1,153.72. WHATS RD?

60 60 + 1,00060

0 1 2 30

i = ?

n = 30 PV = -1153.72 Coupon -60 FV= 10005.0% x 2 = rd = 10%

-1,153.72...


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COMPONENT COST OF DEBT

Interest is tax deductible, so the after tax (AT) cost of debt is:

rd AT = rd BT * (1 - T) = 10% *(1 - 0.40) = 6%.

Use nominal rate.

Flotation costs small, so ignore.


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COST OF EQUITY


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WHAT ARE THE TWO WAYS THAT

COMPANIES CAN RAISE COMMON EQUITY?

Directly, by issuing new shares of common stock.

Indirectly, by reinvesting earnings that are not paid out as dividends

(i.e., retaining earnings).

Why is there a cost for reinvested earnings?

Earnings can be reinvested or paid out as dividends.

Investors could buy other securities, earn a return.

Thus, there is an opportunity cost if earnings are reinvested.


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OPPORTUNITY COST

Opportunity cost: The return stockholders could earn on alternativeinvestments of equal risk.

They could buy similar stocks and earn rs

So, rs, is the cost of reinvested earnings and it is the cost of equity.


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THREE WAYS TO DETERMINE THE

COST OF EQUITY, RS:

1. CAPM rs = rRF + b(rM - rRF)

2. DCF rs = D1/P0 + g.

3. Own-Bond-Yield-Plus-Risk Premium rs = rd + RP.


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APPROACH 1: THE CAPM


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COST OF EQUITY: CAPM

Req. returns = Riskless rate + Risk-premium

CAPM defines expected returns as:

Expected returns = Riskless rate + Beta x (Market risk premium)

Marginal investor: A well diversified investor that is most likely totrade next the only risk that he or she perceives in an investment is risk that cannot be

diversified away (i.e, market or non-diversifiable risk)

The only risk for which she earns a risk premium for: systematic risk

Not-so-well diversified / Non-diversified investors?


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rRF = 7%, RPM = 6%, b = 1.2. rs = rRF + (rM - rRF )b.

= 7.0% + (6.0%)1.2 = 14.2%.

WHATS THE COST OF EQUITYBASED ON THE CAPM?


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RISK FREE RATE

Risk free: actual return = expected return No default risk

No reinvestment risk

Returns on Government Security Yield to Maturity on a long term Treasury bond

Long-term for a going concern, else the maturity should meet theprojected cash flow period Match the duration of the analysis to the duration of the risk free rate

Most analysts use the rate on a long-term (10 to 20 years)government bond as an estimate of rRF.

Currency choices, and nominal vs. real rates consistent with cashflows


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MARKET RISK PREMIUM

Risk Premium: Measures extra returns for making an average risk investment rather than risk-

free investment Function of risk aversion of an investor volatility and risk associated with

underlying economy

Pratt and Grabowski (2008) Range for MRP of 3.5% to 6 %, point estimate of 5 % as of 2007

Fernandez, Aguirreamalloa and Linares (2013) MRP in India based on a survey as on June 2013 8.5%

Risk free rate 6.9 % for India

Survey on MRP for other countries as well in the same paper

Some analysts derive estimates from historical data on US Stock andbond returns published by Ibbotson Intl.


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MARKET RISK PREMIUM

Estimating Risk premium: Historical premium

Time period used: Estimation as back as 1926, 50 yrs, 20 yrs, 10 yrs

Longer term rates are better, however, investor risk aversion might havechanged

Choice of risk-free security

Geometric averages Vs. arithmetic averages

Implied premiums

Value = Expected dividends next period / (Required return on equityExp. Growth rate in dividends)

Mistake to avoid: Historical data for market returns, andcurrent long-term bond yield


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BETABetas: Risk that an investment adds to a market portfolio

Regression method Historical data

Estimation period, observation frequencies

Market Index

Consistency between the target capital structure in theWACC and the degree of leverage present in the estimate

period used for computing equity beta Un-lever the historical beta and re-lever using target capital structure


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BETA (CONTD.)

Fundamental Beta: Intuitive underpinnings of betas Type of business; operating leverage; financial leverage

Financial Leverage:

Estimates of beta vary, and estimates are noisy (they have a wide

confidence interval).

)).1(1(E

Dt

UL


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BETA

Using betas from a sample of comparable publicly traded firms

Estimation of Bottom-up betas:

Identify the business linesEstimate unlevered (asset) beta for comparable public firms in each line

Estimate weighted average of unlevered betas

Estimate levered beta by current market value of debt and equity


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COST OF EQUITY FOR NON-

DIVERSIFIED INVESTORSMarginal investor non diversified

Bottom-up beta using public firms will understate risk

Adjust for total risk rather than market risk

squaredR

BetaMarketBetaTotal


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APPROACH 2: THE DCF APPROACH TODETERMINING THE COST OF EQUITY


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DCF APPROACH: ESTIMATING THE

GROWTH RATE

1. Use the historical growth rate if you believe the future will be likethe past.

2. Obtain analysts estimates: Thomson Reuters, Bloomberg, ValueLine

3. Use the earnings retention model, illustrated on next slide.

4. An approach used for calculating the cost of new equity (UsingPrice per share net of floatation costs)


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EXPECTED FUTURE GROWTH

Suppose the company has been earning 15% on equity (ROE = 15%)and retaining 35% (dividend payout = 65%), and this situation isexpected to continue.

Whats the expected future g?


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RETENTION GROWTH RATE

g = ROE * (Retention rate)

g = 0.35* (15%) = 5.25%.

This is close to g = 5% given earlier.


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COULD DCF METHODOLOGY BE APPLIED IF GIS NOT CONSTANT?

YES, non-constant g stocks are expected to have constant g at some

point, generally in 5 to 10 years.But calculations get complicated.


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APPROACH-3 TO ESTIMATINGTHE COST OF EQUITY


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FIND RS USING THE OWN-BOND-YIELD-PLUS-RISK-PREMIUM METHOD.

rd = 10%, RP = 4%.

This RP CAPM RPM

.

Produces ballpark estimate of rs. Useful check.

rs = rd + RP

= 10.0% + 4.0% = 14.0%


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WHATS A REASONABLE FINAL

ESTIMATE OF RS?

Method Estimate

CAPM 14.2%

DCF 13.8%

rd + RP 14.0%

Average 14.0%


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NOTE ON WACC

Weights in WACC Market value weights

Target Capital Structure -Weights should represent the long-term targetcapital structure rather than current capital structure

Consistent rates to be used in deriving cost of equity and WACC

Tax Rate

Marginal vs. Effective Tax rates Firms that are non-taxpayers for extended periods, appropriate tax rate

could be low or zero


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WEIGHT FOR DEBT

Market value of debt

If you dont know the market value of debt

Approach A: It is usually reasonable to use the book values of debt Approach B: Convert book value debt into market Value Debt

Treat the entire debt as one coupon instrument;

Coupon = interest expenses on all debt;

FV= total debt; maturity= weighted average maturity of debt;

discount rate= current cost of debt


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ESTIMATING WEIGHTS CONTD.

Suppose the stock price is $50, there are 3 million shares of stock,the firm has $25 million of preferred stock, and $75 million of debt.

Vce = $50 (3 million) = $150 million.Vps = $25 million.

Vd = $75 million.

Total value = $150 + $25 + $75 = $250 million.

wce = $150/$250 = 0.6

wps = $25/$250 = 0.1

wd = $75/$250 = 0.3


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WHATS THE WACC?

WACC = wd

rd

(1 - T) + wps

rps

+ wce

rs

= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)

= 1.8% + 0.9% + 8.4% = 11.1%.


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COST OF PREFERRED STOCK


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WHATS THE COST OF PREFERRED STOCK?

%.0.9090.010.111$

10$

00.2$10.113$

100$1.0

n

ps

psP

Dr

Current price of Perpetual Pref. Stock = $113.10

10% Quarterly dividend, Par = $100; F = $2.


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PICTURE OF PREFERRED

2.50 2.50

0 1 2rps = ?

-111.1

...

2.50

.50.2$

10.111$

PerPer

Q

rr

D

%.9)4%(25.2%;25.210.111$

50.2$)( NompsPer rr


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NOTE:

Flotation costs for preferred are significant: Use net price.

Preferred dividends are not deductible, so no tax adjustment.Just rps.

Nominal rps is used.


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IS PREFERRED STOCK MORE OR LESS RISKY TOINVESTORS THAN DEBT?

More risky; company not required to pay preferred dividend.

However, firms want to pay preferred dividend. Otherwise, (1) cannot

pay common dividend, (2) difficult to raise additional funds


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WHY IS YIELD ON PREFERRED LOWER THAN RD?

Corporations own most preferred stock, because 70% of preferred dividendsare nontaxable to corporations.

Therefore, preferred often has a lower Before-tax yield than the Before-Tax

yield on debt.The After-Tax yield to investors and After-Tax cost to the issuer are higher onpreferred than on debt, which is consistent with the higher risk of preferred.


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EXAMPLE:

rps = 9% rd = 10% T = 40%

rps, AT = rps - rps (1 - 0.7)(T)

= 9% - 9%(0.3)(0.4) = 7.92%

rd, AT = 10% - 10%(0.4) = 6.00%

A-T Risk Premium on Preferred = 1.92%


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ESTIMATING HURDLE RATES FORFIRMS IN MULTIPLE BUSINESSES/ DIVISIONS / PROJECTS


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SHOULD THE COMPANY USE THE COMPOSITEWACC AS THE HURDLE RATE FOR EACH OF ITS

DIVISIONS?

NO! The composite WACC reflects the risk of an average project undertakenby the firm.

Different divisions may have different risks.

The divisions WACC should be adjusted to reflect the divisions risk andcapital structure.


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WHAT PROCEDURES ARE USED TO DETERMINETHE RISK-ADJUSTED COST OF CAPITAL FOR APARTICULAR DIVISION?

Estimate the cost of capital that the division would have if it were astand-alone firm.

This requires estimating the divisions beta, cost of debt, andcapital structure.


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METHODS FOR ESTIMATING BETA FOR ADIVISION OR A PROJECT

1. Pure play. Find several publicly traded companies exclusively inprojects business.

Use average of their betas as proxy for projects beta.Hard to find such companies.

Follow the estimation of Bottom-up betas discussed earlier

2. Accounting beta. Run regression between projects ROA and S&Pindex ROA.

Accounting betas are correlated (0.5 0.6) with market betas.But normally cant get data on new projects ROAs before thecapital budgeting decision has been made.


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FIND THE DIVISIONS MARKET RISK AND COSTOF CAPITAL BASED ON THE CAPM, GIVEN

THESE INPUTS:

Target debt ratio = 10%.

rd = 12%.

rRF = 7%.

Tax rate = 40%.

betaDivision = 1.7.

Market risk premium = 6%.


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Beta = 1.7, so division has more market risk than average.

Divisions required return on equity:

rs= rRF + (rM rRF)bDiv.

= 7% + (6%)1.7 = 17.2%.

WACCDiv. = wdrd(1 T) + wcrs

= 0.1(12%)(0.6) + 0.9(17.2%)

= 16.2%.


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HOW DOES THE DIVISIONS WACC COMPARE

WITH THE FIRMS OVERALL WACC?

Division WACC = 16.2% versus company WACC = 11.1%.

Typical projects within this division would be accepted if their returns are

above 16.2%.


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DIVISIONAL RISK AND THE COST OFCAPITAL

Rate of Return(%)

WACC

Rejection Region

Acceptance Region

Risk

L

B

A

HWACCH

WACCL

WACCA

0 RiskL RiskA RiskH


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TO SUM UP:

COST OF EQUITY

A single business firm & project risk similar to the firm

Cost of equity of the firm

Multiple business firm, each business has different risk profile Bottom-up beta for each business

If project risk is consistent with the corresponding business, use respectivebusiness-line/division beta

Independent projects which are large investments compared tothe firm And the risk profile is different from the firm

Independent cost of capital

Bottom-up beta


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TO SUM UP: COST OF DEBT

Project

characteristics Cost of Debt Debt Ratio

1 Small; cash flowssimilar to firm

Firm's CoD Firm's D/E

2 Large; CF different

to firm

CoD of comparable

firms

Avg D/E of

comparables

3 Large; Stand alone CoD of Project (Based

on actual or synthetic

ratings)

D/E of project


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ADDITIONAL ISSUES


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1. When a company issues new common stock they

also have to pay flotation costs to the underwriter.2. Issuing new common stock may send a negative

signal to the capital markets, which may depressstock price.

WHY IS THE COST OF INTERNAL EQUITY FROMREINVESTED EARNINGS CHEAPER THAN THE

COST OF ISSUING NEW COMMON STOCK?


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ESTIMATE THE COST OF NEW COMMONEQUITY: P0=$50, D0=$4.19, G=5%, ANDF=15%.

g

FP

gDre

)1(

)1(

0

0

%.4.15%0.550.42$

40.4$

%0.515.0150$

05.119.4$


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ESTIMATE THE COST OF NEW 30-YEAR DEBT:PAR=$1,000, COUPON=10%PAID ANNUALLY,

AND F=2%.

N = 30

PV = 1000(1-.02) = 980

PMT = -(.10)(1000)(1-.4) = -60

FV = -1000

Solving for I: 6.15%


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COMMENTS ABOUT FLOTATION COSTS:

Flotation costs depend on the risk of the firm and the type of capitalbeing raised.

The flotation costs are highest for common equity. However, since most

firms issue equity infrequently, the per-project cost is fairly small.We will frequently ignore flotation costs when calculating the WACC.


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FOUR MISTAKES TO AVOID

1. When estimating the cost of debt, dont use thecoupon rate on existing debt. Use the currentinterest rate on new debt.

2. When estimating the risk premium for the CAPMapproach, dont subtract the current long-term T-bond rate from the historical average return oncommon stocks.

(More ...)


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For example, if the historical rM has been about 12.2% and inflationdrives the current rRF up to 10%, the current market risk premium isnot 12.2% - 10% = 2.2%!

(More ...)


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3. Dont use book weights to estimate the weights forthe capital structure.

Use the target capital structure to determine theweights.

If you dont know the target weights, then use the

current market value of equity, and never the bookvalue of equity.

If you dont know the market value of debt, then thebook value of debt often is a reasonable

approximation, especially for short-term debt.

(More...)


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4. Always remember that capital components aresources of funding that come from investors.

Accounts payable, accruals, and deferred taxesare not sources of funding that come frominvestors, so they are not included in thecalculation of the WACC.

We do adjust for these items when calculatingthe cash flows of the project, but not whencalculating the WACC.

the basics of cost of capital

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