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CHAPTER 10 The Cost of Capital

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**Topics Cost of Capital Components WACC Debt Preferred Common Equity**

Composite Risk Adjustments WACC with Flotation Costs

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**Sources of Long-term Capital**

Long-Term Debt Preferred Stock Common Stock Retained Earnings New Common Stock rs rd rps rce re 10-3 3

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**WACC Weighted Average Cost of Capital**

WACC = wdrd(1-T) + wpsrps + wcers (10.10) Where: wd = % of debt in capital structure wps = % of preferred stock in capital structure wce = % of common equity in capital structure rd = firm’s cost of debt rps= firm’s cost of preferred stock rs = firm’s cost of equity T = firm’s corporate tax rate Weights Component costs

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Capital Components Capital components = sources of funding from investors Accounts payable, accruals, and deferred taxes ≠ sources of funding from investors Not included in calculation of the cost of capital Adjustments made when calculating project cash flows

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Cost of Debt Method 1: Ask an investment banker what the coupon rate would be on new debt 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 company’s outstanding debt

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

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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) rd AT = 11%( ) = 6.6% Use nominal rate

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**Flotation Costs on New Debt**

Flotation costs on debt usually low Frequently ignored “Project Financing” Adjusts project’s cash flows for flotation costs of debt Debt has specific claim on the project’s cash flows

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**Adjusting the Cost of Debt for Flotation Costs**

Where: M = Bond’s par value (face value) F = Flotation cost as a % N = Number of coupon payments T = Corporate tax rate INT = Dollars of interest per period rd(1-T) = after tax cost of debt adjusted for inflation

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**NCC’s Cost of Debt (rd) with Flotation Costs**

Calculator Solution , S. / %- = 3.34% NCC can issue 30-year bonds N = 60 11% annual coupon rate Coupons paid semiannually PMT = [(.11 x 1000)/2]*(1-.40) PMT = $33 Flotation cost = 1% PV = -1000(1-.01) = -990 Face value = M = 1000 Nominal after-tax cost of debt with flotation costs = 6.68%

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**Preferred Stock Flotation costs for preferred are significant**

Use net price Preferred dividends are not deductible No tax adjustment Use rps Nominal rps is used

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**NCC’s Cost of preferred stock: PP = $100 $10 Dividend F = 2.5%**

Where: Dps = Preferred dividend PPS = Preferred stock price F = Flotation cost %

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**Cost of Common Equity Two Ways to raise equity financing: Directly**

Issue new shares of common stock Indirectly Reinvesting earnings not paid out as dividends Use retained earnings

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**Funding with New Common Equity**

Mature firms rarely issue new equity High flotation costs Negative signal to the market Downward pressure on stock price

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**Cost of Retained 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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**Cost for Reinvested Earnings**

Opportunity cost: The return stockholders could earn on alternative investments of equal risk They 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

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**Three ways to determine the cost of equity, rs:**

1. CAPM: rs = rRF + (RM - rRF)β = rRF + (RPM)β 2. DCF: rs = D1/P0 + g 3. Own-Bond-Yield-Plus-Risk Premium: rs = rd + Bond RP

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**Three ways to determine the cost of equity, rs:**

1. CAPM: rs = rRF + (RM - rRF)β = rRF + (RPM)β 2. DCF: rs = D1/P0 + g 3. Own-Bond-Yield-Plus-Risk Premium: rs = rd + Bond RP

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**CAPM Cost of Equity - Steps**

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

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**Estimating rRF Common stock = long-term security**

T-Bills more volatile than T-Bonds Most analysts use the rate on a long-term (10 to 30 years) government bond as an estimate of rRF

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**Estimating RPM or RM Historical - Ibbotson & Associates**

1926-most recent year 6.5% arithmetic mean - if constant risk aversion 4.9 % geometric mean – best future estimate Ex Ante = Forward-Looking If market in equilibrium: Historical or analysts’ estimates Value Line or Reuters

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**RPM Estimate – #1 RPM = 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% % = 11.73% Problems: Past = future? Growth rates sensitive to period measured

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**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% % = 17.79% Problems: Earnings growth ≠ dividend growth 1-year growth rate ≠ long-term growth Analysts’ accuracy Differing analysts’ opinions

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**Estimating RPM (or RM) RPM = Equity risk premium RM RPM=RM- rRF**

Most analysts use a rate of 5% to 6.5% for the market risk premium RM S&P500 index return =proxy for the market return RPM=RM- rRF Brigham-Daves →RPM = [3.5, 6.5]

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**Estimating Beta - β Beta estimates vary Beta estimates are “noisy”**

Wide confidence interval Historical Beta 4-5 years/monthly or 1-2 years/weekly Adjusted Beta Fundamental Beta Multinational issues

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**NCC’s CAPM Cost of Equity**

rRF = 8% RPM = 6% β= 1.1 rs = rRF + (RM - rRF )β = 8.0% + (6.0%)1.1 = 14.6%

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**Three ways to determine the cost of equity, rs:**

1. CAPM: rs = rRF + (RM - rRF)β = rRF + (RPM)β 2. DCF: rs = D1/P0 + g 3. Own-Bond-Yield-Plus-Risk Premium: rs = rd + Bond RP

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**DCF Approach: Inputs Current stock price (P0) Current dividend (D0)**

Growth rate (g)

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**Estimating the Growth Rate**

The historical growth rate If you believe future = past The earnings retention model Analysts’ estimates: Value Line, Zack’s, Yahoo.Finance

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**Earnings Retention Model**

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

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**Earnings Retention Assumptions**

Retention rate is constant ROE on new investments is constant No new common stock will be issued The risk of future projects is very close to the risk of the overall firm

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**Using Analysts’ Forecasts**

Analysts’ estimate earnings growth = proxy for dividend growth Sometimes involve non-constant growth Develop a proxy constant rate Analysts’ Estimates for NCC: 10.4% annual growth for 5 years 6.5% growth after 5 years Analysts’ estimates usually best source g = 6.9%

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**NCC’s DCF Cost of Equity, rs**

D1 = $ P0 = $ g = 7% rs = D1 P0 + g = D0(1+g) + g = $2.40 $32 + 0.07 = %

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**Three ways to determine the cost of equity, rs:**

1. CAPM: rs = rRF + (RM - rRF)β = rRF + (RPM)β 2. DCF: rs = D1/P0 + g 3. Own-Bond-Yield-Plus-Risk Premium: rs = rd + Bond RP

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**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 RPM Produces ballpark estimate of rs Useful check

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**Final Estimate of rs Method Estimate Used by CAPM 14.6% 74% - 85% DCF**

14.5% 16% rd + RP 14.7% Non-public Average

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**Flotation Costs for Equity re = Cost of New Equity**

NCC: D1 = $ P0 = $ F = 12.5%

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**Topics Cost of Capital Components WACC Debt Preferred Common Equity**

Composite Risk Adjusted WACC with Flotation Costs

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**WACC Weighted Average Cost of Capital**

WACC = wdrd(1-T) + wpsrps + wcers (10.10) Where: wd = % of debt in capital structure wps= % of preferred stock in capital structure wce= % of common equity in capital structure rd = firm’s cost of debt rps= firm’s cost of preferred stock rs= firm’s cost of equity T = firm’s corporate tax rate Weights Component costs

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WACC Weights Weights =percentages of the firm that will be financed by each component If 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

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**NCC’s WACC Weighted Average Cost of Capital**

Component w r Debt (before tax) 0.30 11.0% Preferred Stock 0.10 10.3% Common equity 0.60 14.6% WACC = wDrD (1- T)+ wPsrPs + wcrs WACC =0.3(11%)(1-.40)+0.1(10.3%)+0.6(14.6%) WACC = 11.77%

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**Cost of Capital Issues Before-tax vs. After-tax Capital Costs**

Long- and short-term debt affected Historical Costs vs. Marginal Costs Target Weights vs. Annual Financing Choices Target Weights vs. Book Values

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**Estimating Weights for the Capital Structure**

Estimate the weights using current market values rather than current book values If market value of debt is not known: Usually reasonable to use the book values of debt, especially if the debt is short-term

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**Estimating Weights Given: The stock price is $50**

There are 3 million shares of stock $25 million of preferred stock $75 million of debt

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**Estimating Weights Vce = $50 x (3 million) = $150 million**

Vps = $25 million Vd = $75 million Total value = $150 + $25 + $75 = $250 million

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Estimating Weights

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WACC

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**Factors that influence a company’s WACC**

Market conditions Interest rates The market risk premium Tax rates Firm’s capital structure Firm’s dividend policy Firm’s investment policy Firms with riskier projects generally have a higher WACC

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**Topics Cost of Capital Components WACC Debt Preferred Common Equity**

Composite Risk Adjusted WACC with Flotation Costs

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Risk-Adjusted WACC The composite WACC reflects the risk of an average project undertaken by the firm Different divisions/projects may have different risks The division’s or project’s WACC should be adjusted to reflect the appropriate risk and capital structure

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**Divisional Risk and the Cost of Capital**

Rate of Return (%) Acceptance Region WACC WACC H Acceptance Region Rejection Region WACC F Rejection Region WACC L Risk Risk Risk L H

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**Using WACC for All Projects - Example**

What would happen if we use the WACC for all projects regardless of risk? Assume the WACC = 15% 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 shouldn’t 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.

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**The Risk-Adjusted Divisional Cost of Capital**

Estimate the cost of capital that the division would have if it were a stand-alone firm Requires estimating the division’s beta, cost of debt, and capital structure CAPM frequently used

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**Pure Play Method for Estimating Beta for a Division or a Project**

Find several publicly traded companies exclusively in project’s business Use average of their betas as proxy for project’s beta Hard to find such companies

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Huron Steel Example

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Subjective Approach Consider the project’s risk relative to the firm overall If project risk > firm risk Project discount rate > WACC If project risk < firm risk Project discount rate < WACC

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**Subjective Approach - Example**

Risk Level Discount Rate Very Low Risk WACC – 8% % Low Risk WACC – 3% % Same Risk as Firm WACC % High Risk WACC + 5% % Very High Risk WACC + 10% %

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**Topics Cost of Capital Components WACC Debt Preferred Common Equity**

Composite Risk Adjusted WACC with Flotation Costs

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Flotation Costs Flotation costs depend on the risk of the firm and the type of capital being raised Flotation costs: Highest for common equity Most firms issue equity infrequently Flotation costs frequently ignored when calculating WACC

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**NCC’s WACC With New Debt**

Component w r New Debt (after-tax) d 0.30 6.68% Preferred Stock ps 0.10 10.3% New Common equity c 0.60 14.6% WACC = wdrATd + wpsrps + wcre WACC = 0.3(6.68%)+0.1(10.3%) +0.6(14.6%) WACC = 2.004% % % = %

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**NCC’s WACC With New Debt & New Equity**

Component w r New Debt (after-tax) d 0.30 6.68% Preferred Stock ps 0.10 10.3% New Common equity c 0.60 15.6% WACC = wdrATd + wpsrps + wcre WACC = 0.3(6.68%)+0.1(10.3%) +0.6(15.6%) WACC = 2.004% % % = %

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**NCC’s WACC WACC Description WACC No New Issues 11.770% With New Debt**

11.794% With New Debt & New Equity 12.394%

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**Increasing Marginal Cost of Capital**

Externally raised capital flotation costs Increases the cost of capital Investors often perceive large capital budgets as being risky Drives up the cost of capital If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital

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**Increasing Marginal Cost of Capital**

% 16 15 14 WACC2 = % 13 WACC1 = 11.77% 12 External debt & equity 10 No external funds 9 8 500 700 Capital Required 61 48

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Four Mistakes to Avoid Current (YTM) vs. historical (Coupon rate) cost of debt Mixing current and historical measures to estimate the market risk premium Book weights vs. Market Weights Use Target weights Use market value of equity Book value of debt is a reasonable proxy for market value Incorrect cost of capital components Only investor provided funding

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CHAPTER 10 The Cost of Capital

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