FinQuiz - Curriculum Note, Study Session 11, Reading 36

8/17/2019 FinQuiz - Curriculum Note, Study Session 11, Reading 36

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Reading 36 Cost of Capital

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2. COST OF CAPITAL

The cost of capital is the minimum rate that must beearned on investment of a company or it is the rate ofreturn that is required by the suppliers of capital i.e.bondholders and owners as compensation for theircontribution of capital.

• Investing in projects with return > cost of capitaladd value to the company.

• Riskier the investment’s cash flows, greater will bethe cost of capital.

• Sources of capital include equity, debt and hybridinstruments (that share characteristics of debt andequity).

• Each source selected represents a component ofthe company’s funding and has a required rate ofreturn which is referred to as the component costof capital.

To evaluate investment opportunities, analysts are

primarily concerned with marginal cost of capital (i.e.cost to raise additional funds for the potential investmentprojects).

To calculate cost of capital:

1) Calculate Marginal cost of each of the varioussources of capital

2) Calculate a weighted average of these costs. Thisweighted average is called the Weightedaverage cost of capital (WACC). WACC is alsoknown as the marginal cost of capital (MCC)because it is the cost that a company incurs to

raise additional capital.

WACC = wdrd (1 – t) + wprp + were

where,

wd = proportion of debt that the company uses when it

raises new funds

r d = before-tax marginal cost of debt

t = company’s marginal tax rate

w p = proportion of preferred stock the company uses

when it raises new funds

r p = marginal cost of preferred stock

we = proportion of equity that the company uses when

it raises new funds

r e = marginal cost of equity

2.2 Weights of the Weighted Average

When a company has a target capital structure and itraises capital consistent with this target, then target

capital structure should be used to estimate weights ofthe weighted average.

An outsider e.g. an analyst does not know the targetcapital structure; thus, it can be estimated usingfollowing approaches:

1. In the absence of any explicit information abouta firm’s target capital structure, the company’scurrent capital structure can be assumed as thecompany’s target capital structure.• In current capital structure, each component isassigned weight according to its market value.

2. Estimate target capital structure by examiningtrends in the company’s capital structure orstatements by management regarding capitalstructure policy.

3. Estimate target capital structure using theaverages of comparable companies’ capital

structure. This method uses un-weighted,arithmetic average.

NOTE:

A debt-to-equity ratio D/E is transformed into a weighti.e. D / (D + E) as follows:

(D/E)/(1 + D/E)

2.3Applying the Cost of Capital to Capital

Budgeting and Security Valuation

• A company’s marginal cost of capital (MCC) mayincrease as additional capital is raised.

• In contrast, returns on company’s investmentopportunities may decrease as the additionalinvestments are made by a company.

This relationship is exhibited in the investment opportunityschedule (IOS) below.

Source: Figure 1, CFA® Program Curriculum,

Volume 4, Reading 36.

Practice: Example 3,


Practice: Example 1 & 2,



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• Marginal cost of capital schedule is upwardsloping.

• Investment opportunity schedule is downwardsloping.

Optimal capital budget: It refers to the amount of capitalraised and invested at which the marginal cost ofcapital intersects with the investment opportunityschedule i.e. where

MC of capital = Marginal return from investing

This implies that the firm should invest in all those projectswith IRRs>Cost of capital to maximize the value created.

• For an average-risk project, the opportunity costof capital is the company’s WACC. Thus, NPVs ofpotential projects of firm-average risk should becalculated using the marginal cost of capital forthe firm.

• If the systematic risk of the project is aboveaverage, a discount rate greater than the firm’sexisting WACC should be used.

•

If the systematic risk of the project is belowaverage, a discount rate less than the firm’sexisting WACC should be used.

Limitations of WACC: When a company uses WACC inthe calculation of the NPV of a project, it assumes thatwhen additional capital is raised to finance newprojects, the cost of capital will be unchanged, i.e.:

• The proportion of debt and equity remainunchanged i.e. a company will have a constanttarget capital structure throughout its useful life.

• The operating risk of the firm is unchanged.•

The financing is not project specific i.e. it has thesame risk as the average-risk of the company.

Marginal cost of capital is used by analysts in securityvaluation using different discounted cash flow valuationmodels i.e.

• If cash flows are cash flows to the company’ssuppliers of capital (i.e. free cash flow to the firm),the analyst uses WACC to find the PV of theseflows.

• If cash flows are cash flows to the company’sowners (i.e. free cash flow to equity or dividends),the analyst uses the cost of equity capital to find

the PV of these flows.

3. COST OF THE DIFFERENT SOURCES OF CAPITAL

Due to differences among sources of capital, eachsource of capital has a different cost. Differencesinclude seniority, contractual commitments andpotential value as a tax shield.

3.1 Cost of Debt

The cost of debt is the required return on company’sdebt e.g. bonds or bank loans.

Approaches to estimate cost of debt:

1) Yield-to-Maturity Approach: The required return ondebt can be estimated by computing the yield-to-maturity on the existing debt.

For example

N = 50; PMT = 45; FV = 1000; PV = -908.72; CPT I/Y = 5%;

YTM = 5(2) = 10%

2)

Debt-rating Approach: When a reliable currentmarket price for a company’s debt is not available,the cost of debt can also be estimated using thecurrent rates, based on the bond rating we expectwhen we issue new debt e.g. based on company’sdebt rating,

• Before-tax cost of debt is estimated by using theyield on comparably rated bonds i.e. with samedebt rating and similar maturity.

• In bond markets, this approach is referred to asmatrix pricing.

Important: The cost of debt is NOT the coupon rate of abond.

• Interest expense on a firm’s debt is tax-deductible,so the pre-tax cost of debt must be reduced bythe firm’s marginal tax rate to get an after-tax costof debt capital.

After-tax cost of debt = kd(1 – firm’s marginal tax rate)• The pre-tax and after-tax capital costs are equal

for both preferred stock and common equitybecause dividends paid by the firm are not tax-deductible.

• Debt rating and yields are also affected by debtseniority and security.

3.1.3) Issues in Estimating the Cost of Debt

In case of fixed rate security, analysts can easily observeyields of the company’s existing debt or market yields ofdebt of similar risk. However, for a floating-rate security, itis quite difficult to estimate cost of debt because cost of




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floating-rate security depends on both current yields andfuture yields.

• In this case, average cost can be estimated usingthe current term structure of interest rates and termstructure theory.

3.1.3.2 Debt with Option-like Features

To estimate cost of debt with option-like features,

• If the company already has debt outstanding withoption-like features, the analyst may simply use theYTM on such debt.

• If it is believed that the future debt will include orexclude few option features, the analyst canmake market value adjustments to the current YTMto reflect the value of such additions and/ordeletions.

3.1.3.3 Nonrated Debt

When the company has nonrated debt, cost of debt

can be estimated using a company’s “ synthetic” debtrating based on financial ratios. However, this method isinaccurate because debt ratings are based on

• Financial ratios, and• Information regarding particular bond issue andthe issuer.

3.1.3.4 Leases

If the company uses leasing as a source of capital, thecost of these leases should be included in the cost ofcapital. The cost of leasing is similar to that of thecompany’s other long-term debt.

3.2 Cost of Preferred Stock

In the case of nonconvertible, noncallable preferredstock:

• Preferred stock generally pays a constant dividendeach period.

• Dividends are expected to be paid every periodforever (i.e. fixed rate perpetual preferred stock).

PP = Dp / r p

where,P p = current preferred stock price per share

D p = preferred stock dividend per share

r p= cost of preferred stock

Thus,

rP = Dp/Pp NOTE:

Preferred dividends are not tax-deductible, so there is notax adjustment for the cost of preferred equity.

3.3 Cost of Common Equity

The cost of common equity (r e) (or the cost of equity), isthe rate of return required by company’s common

shareholders on the equity capital that is retained by acompany. Common equity can be increased in twoways:

i. Through retained earnings.ii. Through the issuance of new shares of stock.

Estimating the cost of equity capital is more difficult thanestimating the cost of debt capital due to uncertainty offuture cash flows with respect to the amount and timing.

The cost of equity can be estimated using the followingmethods:

• Capital asset pricing model• Dividend discount model• Bond yield plus risk premium method

NOTE:

The pre-tax and after-tax capital costs are equal forcommon equity because dividends paid by the firm orthe return on equity capital are not tax-deductible.

3.3.1) Capital Asset Pricing Model Approach

E (Ri) = RF + βi [E (RM) – RF]

where,

RF = Risk-free asset *

β i = sensitivity of stock return to changes in the

market return**

E (RM ) = expected return on the market

E (RM ) – RF = expected market risk premium

NOTE:

* A risk free asset refers to an asset that has no defaultrisk. A common proxy for the risk-free rate is the yieldon a default-free government debt instrument.Generally, risk-free rate should be selected accordingto the duration of projected cash flows e.g. for a

project with an estimated useful life of 10 years, rateon the 10-year Treasury bond can be used as risk-freerate.

** beta is estimated relative to an equity market index;therefore, market premium estimate used hererepresents an estimate of the equity risk premium(ERP).

• This approach involves estimating average rate ofreturn of a company’s market portfolio and theaverage rate of return for the risk-free asset in thatcountry using historical data.




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• Assuming an unchanged distribution of returnsthrough time, the arithmetic mean represents anunbiased estimate of the expected single-period equity risk premium; but for multiple periods,geometric mean is preferred to use.

Limitations of the historical premium approach:

1) Stock index’s risk level may change over time.

2)

Risk aversion of investors may change over time.3) Estimates are sensitive to the method of

estimation and the historical period used.

CAPM is a single factor model; thus, it does not take intoaccount all risks e.g. inflation, business-cycle, interestrate, exchange rate, and default risks. Thus, we can useMultifactor model that incorporates factors thatrepresent other sources of price risk i.e. macroeconomicfactors and company-specific factors. In general, it isexpressed as:

E (Ri) = RF + βi1 (Factor risk premium)1 + βi2 (Factor risk

premium)2

+…..+βi j

(Factor risk premium) j

where,

β i j = stock i’s sensitivity to changes in the jth factor

(Factor risk premium) j = expected risk premium for the jth

factor

3.3.2) Dividend Discount Model Approach

where,

r e = cost of equity

D1 = expected dividend for the next period

P0 = current market value of the stock

g = expected growth rate of dividends

D1/ P0 = forward annual dividend yield

Ways to estimate growth rate:

1) Using forecasted growth rate from a published sourceor vendor.

2) Using a relationship between growth rate, retentionrate and ROE i.e.

g = (1 - dividend payout ratio) × Historical return onequity

g = (1 -

) × ROE

g = retention rate × ROE

Survey Approach to estimate equity risk premium: In thisapproach, equity risk premium is estimated by asking apanel of finance experts for their estimates and takingthe mean response.

3.3.3) Bond Yield plus Risk Premium Approach

This approach is based on the fact that cost of capital ofriskier cash flows > cost of capital of less risky cash flows.Thus,

re =r d + Risk Premium

• Risk premium represents compensation foradditional risk associated with stock of thecompany relative to bonds of the same company.

• Unlike equity risk premium (cost of equity – risk-freerate), here

Risk premium = cost of equity – company’s cost of debt

• This premium can be estimated by using historicalspreads between bond yields and stock yields.

• In developed country markets, it is in the range of3%-5%.

4. TOPICS IN COST OF CAPITAL ESTIMATION

4.1 Estimating Beta and Determining a Project Beta

Company’s stock beta can be estimated using a marketmodel regression where company’s stock returns (R i) areregressed against market returns (Rm) over T periods.

t = 1, 2, …T.

where,

= estimated intercept= estimated slope of the regression, represents anestimate of beta.

Issues with estimated beta:

• Estimated beta is sensitive to the method ofestimation and data used.

• Estimated beta is sensitive to estimation periodused. There is trade-off between data precision




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obtained by using longer estimation period andcompany-specific changes which are betterreflected using shorter estimation periods.o Longer estimation periods can be used for

companies with long and stable operatinghistory.

o Shorter estimation periods can be used forcompanies experiencing significant structuralchanges in the recent past.

•

Periodicity of return interval (i.e. daily, weekly ormonthly): It has been observed that betaestimated using smaller return intervals (i.e. dailyreturns) have smaller standard errors.

• Selection of an appropriate market index: Betaestimate is affected by the choice of marketindex.

• Use of a smoothing technique: Historical beta isadjusted by some analysts to reflect tendency ofbeta to revert to 1.

• Adjustments for small-capitalization stocks: Small-capitalization stocks are considered to havegreater risk and generate greater returns relativeto larger capitalization stocks over the long-run.

Therefore, betas of small-capitalization companiesshould be adjusted upward.

Stock return data for publicly traded companies isreadily and easily available; therefore, beta for publiclytraded companies can be easily estimated.

It is difficult to estimate beta for:

a) Companies that are not publicly traded.b) Projects that are not average or typical project of

a publicly traded company.

Factors affecting beta of a company or project:1) Business risk include:

i. Sales risk i.e. risk related to uncertainty ofrevenues of a company. It is affected by elasticityof demand for the product, cyclicality ofrevenue, competition structure in the industry.

ii.

Operating risk i.e. risk related to operating coststructure of a company. It is affected by relativemix of fixed and variable operating costs i.e.greater the fixed operating costs, greater theuncertainty of income and cash flows fromoperations.

2) Financial risk: It is related to uncertainty of net incomeand net cash flows associated with use of financingthat has a fixed cost i.e. debt and leases.

• Greater the use of financial leverage, greater thefinancial risk.

Pure-play method: When a project’s risk is different fromthat of the firm’s average project, the beta of acompany or group of companies that are exclusively inthe same business as the project can be used to

estimate the project’s required return. Pure-play methodinvolves the following steps:

1) Estimate the beta for a comparable company orcompanies i.e. company with similar business risk.

• This beta is referred to as levered beta βL, comparable .

2) Un-lever the beta to get the asset beta using the

marginal tax rate and debt-to-equity ratio of thecomparable company.

• This beta is referred to as un-levered beta βU,comparable.

• This beta represents the company’s asset risk.

, ,

3) Re-lever the beta using the marginal tax rate anddebt-to-equity ratio of the firm considering the projectto incorporate project’s financial risk.

• This beta is referred to as levered beta βL, project.

, ,

NOTE:

4.2 Country Risk

Beta does not accurately incorporate country risk ofcompanies in developing nations. Thus, to reflect the

increased risk associated with investing in a developingcountry, a country equity premium or country spread isadded to the market risk premium when using theCAPM.

Approaches to estimate country spread:

1) Country spread can be estimated using a sovereignyield spread i.e.

Sovereign yield spread = Government bond yield of thecountry denominated in thecurrency of a developed

Practice: Example 9, 10 & 11,



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country – Treasury bond yieldon a similar maturity bond inthe developed country

2) Another approach to estimate country spread is asfollows:

Country equity premium =Sovereign yield spread ×(Annualized S.D of Equityindex / Annualized S.D ofsovereign bond market interms of the developedmarket currency)

• Greater the S.D (or volatility) of equity marketindex, greater the country equity premium, all elseconstant.

Cost of equity = Ke= RF + β[(E(RM)-RF) + CRP]

where,

CRP = Country Risk Premium

3)

Using country credit ratings to estimate the expectedrates of returns for countries that have credit ratingsbut do not have equity markets. It involves followingsteps:

• Estimating reward to credit risk measures for alarge sample of countries which have both creditratings and equity markets.

• Applying this ratio to countries without equitymarkets based on country’s credit rating.

4.3 Marginal Cost of Capital Schedule

The marginal cost of capital (MCC) refers to the cost ofthe last new dollar of capital (additional capital) raisedby a company. Cost of capital (WACC) increases asmore and more capital is raised i.e.

• As a firm raises additional debt, the cost of debtincreases to reflect additional financial risk e.g.

due to restriction in a bond covenant regardingissuing additional debt with similar seniority asexisting debt, a company have to issue less seniordebt (e.g. subordinated bonds) or have to issueequity which would have a higher cost.

• Issuing new equity is more expensive than usingretained earnings due to flotation costs.

• MCC also increases due to deviation from thetarget capital structure.

NOTE:

When a company that is solely financed with commonequity raises additional capital via debt, then due to taxadvantages, company’s WACC will decrease asadditional capital is raised.

As more and more capital is raised by a company, costof different sources of financing increases. Hence,typically, MCC schedule is upward sloping.

Break point: It is the amount of capital at which cost ofone of the components of the capital changes. A breakpoint is calculated as:

Breakpoint =

4.4 Flotation Costs

Investment banks assist companies in raising new equitycapital. They assist in

• Setting the price of the issue, and• Selling the issue to the public.

The costs of these services provided by the investmentbanks are referred to as “flotation costs”.

• The amount of flotation costs is generally quite lowfor debt and preferred stock (often 1% or less ofthe face value).

• For common stock, flotation costs can be as highas 25% for small issues, for larger issue they will bemuch lower.

These costs must be accounted for in the company’sWACC. There are two ways to do so:

a) By adjusting the cost of capital of a firm i.e.

When flotation costs are in monetary terms or per sharebasis:

where,

f = flotation cost in monetary terms or per share basis.

When flotation costs are in terms of % of the share price:

where, f = flotation cost as % of issue price.






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Limitation of method:

This method is inaccurate because it involves adjustingPV of the future cash flows by a fixed percentage.

Advantages:

• This method is useful when specific projectfinancing cannot be easily identified.

• It helps to demonstrate how costs of financing a

company change as its internally generatedequity (R/E) exhaust and a company needs toraise externally generated equity (new stockissues).

b) By adjusting the initial project cost: The correct way toaccount for flotation costs is by adjusting initial projectcost. It involves:

i. Estimating the dollar amount of the flotation costassociated with the project, and

ii. Adding that cost to the initial cash outflow for theproject.

Example: Suppose

• Initial cash outlay = $60,000• Cash inflows each year = $1,000• Tax rate = 40%• r d before tax = 5%• r e = 10%• Wd = 40% and We = 60%.• Debt =24,000 and Equity = 36,000.•

Flotation costs = 5% of new equity capital = 5% ×(36,000) = $1,800.

Thus,

WACC= 7.2%PV of cash inflows = $69,591

If flotation costs are not tax deductible:

NPV = $69,591 – $60,000 – $1,800 = $7,791

If flotation costs are tax deductible:

NPV = $69,591 – $60,000 – $1,800 (0.60) = $8,511

Practice: End of Chapter Practice

Problems for Readin 36.

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FinQuiz - Curriculum Note, Study Session 11, Reading 36