# CHAPTER 10 The Cost of Capital.

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CHAPTER 10 The Cost of Capital

Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite Risk Adjustments WACC with Flotation Costs

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

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

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

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

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%

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

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

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

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%

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

NCC’s Cost of preferred stock: PP = \$100 \$10 Dividend F = 2.5%
Where: Dps = Preferred dividend PPS = Preferred stock price F = Flotation cost %

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

Funding with New Common Equity
Mature firms rarely issue new equity High flotation costs Negative signal to the market Downward pressure on stock price

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

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

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

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

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

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

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

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

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

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]

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

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%

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

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

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

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%

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

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%

NCC’s DCF Cost of Equity, rs
D1 = \$ P0 = \$ g = 7% rs = D1 P0 + g = D0(1+g) + g = \$2.40 \$32 + 0.07 = %

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

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

Final Estimate of rs Method Estimate Used by CAPM 14.6% 74% - 85% DCF
14.5% 16% rd + RP 14.7% Non-public Average

Flotation Costs for Equity re = Cost of New Equity
NCC: D1 = \$ P0 = \$ F = 12.5%

Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite Risk Adjusted WACC with Flotation Costs

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

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

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%

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

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

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

Estimating Weights

WACC

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

Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite Risk Adjusted WACC with Flotation Costs

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

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

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.

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

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

Huron Steel Example

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

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% %

Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite Risk Adjusted WACC with Flotation Costs

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

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% % % = %

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% % % = %

NCC’s WACC WACC Description WACC No New Issues 11.770% With New Debt
11.794% With New Debt & New Equity 12.394%

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

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

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

CHAPTER 10 The Cost of Capital