CH10_338_lpk

CHAPTER 10The Cost of Capital

TopicsCost of Capital ComponentsDebtPreferredCommon EquityWACCCompositeRisk AdjustmentsWACC with Flotation Costs

Sources of Long-term Capital10-*rdrsrpsrcere

WACCWeighted Average Cost of CapitalWACC = wdrd(1-T) + wpsrps + wcers

Where:

wd = % of debt in capital structurewps = % of preferred stock in capital structurewce = % of common equity in capital structurerd = firms cost of debtrps= firms cost of preferred stockrs = firms cost of equityT = firms corporate tax rateWeightsComponent costs(10.10)

Capital ComponentsCapital components = sources of funding from investorsAccounts payable, accruals, and deferred taxes sources of funding from investorsNot included in calculation of the cost of capitalAdjustments made when calculating project cash flows

Cost of DebtMethod 1: Ask an investment banker what the coupon rate would be on new debtMethod 2: Find the bond rating for the company and use the yield on other bonds with a similar ratingMethod 3: Find the yield on the companys outstanding debt

NCCs Cost of Debt (rd)A 22-year, 9% semiannual coupon bond sells for $835.42Bond pays a semiannual coupon:rd = 5.5% x 2 = 11%Calculator Solution 44 , 835.42 S. 45 /1000 0 %- = 5.50%

Component Cost of DebtInterest is tax deductible, so the after tax (AT) cost of debt is: rd AT= rd BT(1 - T) rd AT= 11%(1 - 0.40) = 6.6%Use nominal rate

Flotation Costs on New DebtFlotation costs on debt usually lowFrequently ignored

Project FinancingAdjusts projects cash flows for flotation costs of debtDebt has specific claim on the projects cash flows

Adjusting the Cost of Debt for Flotation CostsWhere:M = Bonds par value (face value)F = Flotation cost as a %N = Number of coupon paymentsT = Corporate tax rateINT = Dollars of interest per periodrd(1-T) = after tax cost of debt adjusted for inflation

NCCs Cost of Debt (rd) with Flotation CostsNCC can issue 30-year bondsN = 60 11% annual coupon rateCoupons paid semiannuallyPMT = [(.11 x 1000)/2]*(1-.40)PMT = $33Flotation cost = 1%PV = -1000(1-.01) = -990Face value = M = 1000Calculator Solution 60 , 990 S. 33 /1000 0 %- = 3.34%Nominal after-tax cost of debt with flotation costs = 6.68%

Preferred StockFlotation costs for preferred are significantUse net pricePreferred dividends are not deductibleNo tax adjustmentUse rpsNominal rps is used

NCCs Cost of preferred stock: PP = $100 $10 Dividend F = 2.5%Where:Dps = Preferred dividendPPS = Preferred stock priceF = Flotation cost %

Cost of Common EquityTwo Ways to raise equity financing:DirectlyIssue new shares of common stockIndirectlyReinvesting earnings not paid out as dividends Use retained earnings

Funding with New Common EquityMature firms rarely issue new equityHigh flotation costsNegative signal to the marketDownward pressure on stock price

Cost of Retained EarningsEarnings can be reinvested or paid out as dividendsInvestors could buy other securities, earn a returnThus, there is an opportunity cost if earnings are reinvested

Cost for Reinvested EarningsOpportunity cost: The return stockholders could earn on alternative investments of equal riskThey could buy similar stocks and earn rs, or company could repurchase its own stock and earn rs rs = the cost of reinvested earnings = the cost of equity

Three ways to determine the cost of equity, rs: 1.CAPM: rs= rRF + (RM - rRF)= rRF + (RPM)2.DCF: rs = D1/P0 + g3.Own-Bond-Yield-Plus-Risk Premium:rs = rd + Bond RP

Three ways to determine the cost of equity, rs: 1.CAPM: rs= rRF + (RM - rRF)= rRF + (RPM)2.DCF: rs = D1/P0 + g3.Own-Bond-Yield-Plus-Risk Premium: rs = rd + Bond RP

CAPM Cost of Equity - StepsEstimate risk-free rate (rRF)Estimate market risk premium (RPM) or expected return on the market (RM)Estimate beta ()Substitute into CAPM

Estimating rRFCommon stock = long-term securityT-Bills more volatile than T-BondsMost analysts use the rate on a long-term (10 to 30 years) government bond as an estimate of rRF

Estimating RPM or RMHistorical - Ibbotson & Associates1926-most recent year6.5% arithmetic mean - if constant risk aversion4.9 % geometric mean best future estimateEx Ante = Forward-LookingIf market in equilibrium:

Historical or analysts estimatesValue Line or Reuters

RPM Estimate #1RPM = 11.73%rM Estimate (Reuters, Spring 2008)Dividend yield on S&P500 = 2.61%Dividend growth rate = 13.20%rM=[0.0261(1+.132)]+0.132=16.15%Forward-looking RPM:Long-term T-Bond rate = 4.42%16.15% - 4.42% = 11.73%Problems:Past = future?Growth rates sensitive to period measured

RPM Estimate #2 RPM = 17.79%rM Estimate (Spring 2008)Reuters S&P500 dividend yield = 2.61%Yahoo Earnings growth rate = 19.1%rM=[0.0261(1+.191)]+0.191=22.21%Forward-looking RPM:22.21% - 4.42% = 17.79%Problems:Earnings growth dividend growth1-year growth rate long-term growthAnalysts accuracyDiffering analysts opinions

Estimating RPM (or RM)RPM = Equity risk premiumMost analysts use a rate of 5% to 6.5% for the market risk premiumRM S&P500 index return =proxy for the market returnRPM=RM- rRFBrigham-Daves RPM = [3.5, 6.5]

Estimating Beta - Beta estimates varyBeta estimates are noisy Wide confidence interval Historical Beta4-5 years/monthly or 1-2 years/weeklyAdjusted BetaFundamental BetaMultinational issues

NCCs CAPM Cost of Equity rs = rRF + (RM - rRF )= 8.0% + (6.0%)1.1 = 14.6%rRF = 8% RPM = 6% = 1.1

DCF Approach: InputsCurrent stock price (P0)Current dividend (D0)Growth rate (g)

Estimating the Growth RateThe historical growth rate If you believe future = pastThe earnings retention modelAnalysts estimates: Value Line, Zacks, Yahoo.Finance

Earnings Retention ModelNCC Data:ROE = 14.5%Dividend payout ratio = 52%Retention ratio = 100% - dividend payoutRetention rate = 100% - 52% = 48%Retention growth rate:g = ROE x (Retention rate) g = (14.5%) x 0.48 = 7%

Earnings Retention AssumptionsRetention rate is constantROE on new investments is constantNo new common stock will be issuedThe risk of future projects is very close to the risk of the overall firm

Using Analysts ForecastsAnalysts estimate earnings growth= proxy for dividend growthSometimes involve non-constant growthDevelop a proxy constant rateAnalysts Estimates for NCC:10.4% annual growth for 5 years6.5% growth after 5 yearsAnalysts estimates usually best sourceg = 6.9%

NCCs DCF Cost of Equity, rsD1 = $2.40 P0 = $32 g = 7%

The Own-Bond-Yield-Plus-Risk-Premium Method: rd = 11%, RP = 3.7% rs= rd + RP rs= 11.0% + 3.7% = 14.7%

This RP CAPM RPMProduces ballpark estimate of rs Useful check

Final Estimate of rs

Flotation Costs for Equityre = Cost of New Equity NCC: D1 = $2.40 P0 = $32 F = 12.5%

TopicsCost of Capital ComponentsDebtPreferredCommon EquityWACCCompositeRisk AdjustedWACC with Flotation Costs

WACCWeighted Average Cost of CapitalWACC = wdrd(1-T) + wpsrps + wcers

Where:

wd = % of debt in capital structurewps= % of preferred stock in capital structurewce= % of common equity in capital structurerd = firms cost of debtrps= firms cost of preferred stockrs= firms cost of equityT = firms corporate tax rateWeightsComponent costs(10.10)

WACC Weights Weights =percentages of the firm that will be financed by each componentIf possible, always use the target weights for the percentages of the firm that will be financed with the various types of capital NCC: 30% debt, 10% Preferred, 60% Equity

NCCs WACCWeighted Average Cost of Capital

WACC =0.3(11%)(1-.40)+0.1(10.3%)+0.6(14.6%)WACC = 11.77%WACC = wDrD (1- T)+ wPsrPs + wcrs

Cost of Capital IssuesBefore-tax vs. After-tax Capital CostsLong- and short-term debt affectedHistorical Costs vs. Marginal CostsTarget Weights vs. Annual Financing ChoicesTarget Weights vs. Book Values

Estimating Weights for the Capital StructureEstimate the weights using current market values rather than current book valuesIf market value of debt is not known:Usually reasonable to use the book values of debt, especially if the debt is short-term

Estimating Weights Given:The stock price is $50 There are 3 million shares of stock$25 million of preferred stock$75 million of debt

Estimating Weights Vce = $50 x (3 million) = $150 millionVps = $25 millionVd = $75 millionTotal value = $150 + $25 + $75 = $250 million

Estimating Weights

Sheet1

ValueWeight

Stock price$50$150,000,00060%

Share O/S3,000,000

Preferred Stock$25,000,000$25,000,00010%

Debt$75,000,000$75,000,00030%

Total Firm$250,000,000100%

Sheet2

Sheet3

WACC

Sheet1

Tax Rate =40%ValueWeightCost ofTax EffectWACC

Capital

Stock price$50$150,000,00060%14.60%8.76%

Share O/S3,000,000

Preferred Stock$25,000,000$25,000,00010%10.30%1.03%

Debt$75,000,000$75,000,00030%11.00%60%1.98%

Total Firm$250,000,000100%11.77%

Sheet2

Sheet3

Factors that influence a companys WACCMarket conditionsInterest ratesThe market risk premiumTax ratesFirms capital structure Firms dividend policyFirms investment policy Firms with riskier projects generally have a higher WACC

Risk-Adjusted WACCThe composite WACC reflects the risk of an average project undertaken by the firmDifferent divisions/projects may have different risksThe divisions or projects WACC should be adjusted to reflect the appropriate risk and capital structure

Divisional Risk and the Cost of Capital Rate of Return (%) WACC Rejection Region Acceptance Region Risk WACCH WACCL WACCF 0 RiskL RiskH Acceptance RegionRejection Region

Using WACC for All Projects - ExampleWhat would happen if we use the WACC for all projects regardless of risk?Assume the WACC = 15%

Sheet1

Required

Return

20%

15%WACC

10%

5%

05%10%15%20%IRR

Sheet2

RequiredDecision

ProjectReturnIRRIf 15%Risk Adj

A20%17%AcceptReject

B15%18%AcceptAccept

C10%12%RejectAccept

Sheet3

The Risk-Adjusted Divisional Cost of CapitalEstimate the cost of capital that the division would have if it were a stand-alone firm Requires estimating the divisions beta, cost of debt, and capital structureCAPM frequently used

Pure Play Method for Estimating Beta for a Division or a ProjectFind several publicly traded companies exclusively in projects businessUse average of their betas as proxy for projects betaHard to find such companies

Huron Steel Example

Sheet1

Huron Steel Company

Riskfree rate =7%

Market risk premium =6%

DivisionBetaCOC% Bus

Steel1.113.60%70%

Barge1.516.00%20%

Distrib0.510.00%10%

Overall1.1213.72%

Sheet2

Sheet3

Subjective ApproachConsider the projects risk relative to the firm overallIf project risk > firm riskProject discount rate > WACCIf project risk < firm riskProject discount rate < WACC

Subjective Approach - Example

Flotation CostsFlotation costs depend on the risk of the firm and the type of capital being raisedFlotation costs:Highest for common equityMost firms issue equity infrequentlyFlotation costs frequently ignored when calculating WACC

NCCs WACC With New Debt WACC = wdrATd + wpsrps + wcre

WACC = 0.3(6.68%)+0.1(10.3%) +0.6(14.6%)WACC = 2.004% + 1.03% + 9.36% = 11.794%

NCCs WACC With New Debt & New EquityWACC = wdrATd + wpsrps + wcre

WACC = 0.3(6.68%)+0.1(10.3%) +0.6(15.6%)WACC = 2.004% + 1.03% + 9.36% = 12.394%

NCCs WACC

Increasing Marginal Cost of CapitalExternally raised capital flotation costsIncreases the cost of capitalInvestors often perceive large capital budgets as being riskyDrives up the cost of capitalIf external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital

500700%Capital RequiredWACC1 = 11.77%WACC2 = 12.394%89101213141516Increasing Marginal Cost of Capital61No external fundsExternal debt & equity

Four Mistakes to AvoidCurrent (YTM) vs. historical (Coupon rate) cost of debtMixing current and historical measures to estimate the market risk premiumBook weights vs. Market WeightsUse Target weightsUse market value of equityBook value of debt is a reasonable proxy for market valueIncorrect cost of capital componentsOnly investor provided funding

CHAPTER 10The Cost of Capital

*Ask students which projects would be accepted if they used the WACC for the discount rate? Compare 15% to IRR and accept projects A and B.

Now ask students which projects should be accepted if you use the required return based on the risk of the project? Accept B and C.

So, what happened when we used the WACC? We accepted a risky project that we shouldnt have and rejected a less risky project that we should have accepted. What will happen to the overall risk of the firm if the company does this on a consistent basis? Most students will see that the firm will become riskier.48

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