Chapter 15 Required Returns and the Cost of Capital

Learning Objectives After studying Chapter 15, you should be able to: Explain how a firm creates value and identify the key sources of value creation. Define the overall “cost of capital” of the firm. Calculate the costs of the individual components of a firm’s cost of capital - cost of debt, cost of preferred stock, and cost of equity. Explain and use alternative models to determine the cost of equity, including the dividend discount approach, the capital-asset pricing model (CAPM) approach, and the before-tax cost of debt plus risk premium approach. Calculate the firm’s weighted average cost of capital (WACC) and understand its rationale, use, and limitations. Explain how the concept of Economic Value Added (EVA) is related to value creation and the firm’s cost of capital. Understand the capital-asset pricing model's role in computing project- specific and group-specific required rates of return.

Creation of Value Overall Cost of Capital of the Firm Project-Specific Required Rates Group-Specific Required Rates Total Risk Evaluation Creation of Value Overall Cost of Capital of the Firm Project-Specific Required Rates Group-Specific Required Rates Total Risk Evaluation Topics

Growth phase of product cycle Barriers to competitive entry Other -- e.g., patents, temporary monopoly power, oligopoly pricing Cost Marketing & price Perceived quality Superior organizational capability Industry Attractiveness Competitive Advantage Key Sources of Value Creation

Overall Cost of Capital of the Firm Cost of Capital is the required rate of return on the various types of financing. The overall cost of capital is a weighted average of the individual required rates of return (costs).

Type of Financing Mkt ValWeight Long-Term Debt $ 35M 35% Preferred Stock$ 15M 15% Common Stock Equity $ 50M 50% $ 100M 100% Market Value of Long-Term Financing

Cost of Debt Cost of Debt is the required rate of return on investment of the lenders of a company. Cost of Debt k i = k d ( 1 - T ) P 0 = Current market price I t = Interest payment at t P t = Principal payment at t k i = After-tax cost of debt k d = Before-tax cost of debt T = Marginal tax rate

Assume that Basket Wonders (BW) has $1,000 par value zero-coupon bonds outstanding. BW bonds are currently trading at $ with 10 years to maturity. BW tax bracket is 40%. Cost of Debt: Example $ = $0 + $1,000 (1 + k d ) 10

(1 + k d ) 10 = $1,000 / $ = (1 + k d ) = (2.5938) (1/10) = 1.1 k d =.1 or 10% k i = 10% ( ) k i 6% k i = 6% Cost of Debt: Example YearCash Flow 0 $ (385.54) 1 $ $ 1, irr=10.00%

Cost of Preferred Stock Cost of Preferred Stock is the required rate of return on investment of the preferred shareholders of the company. Cost of Preferred Stock k P = D P / P 0 k P = Cost of preferred stock D P = Stated annual dividend P 0 = Current market price

Assume that Basket Wonders (BW) has preferred stock outstanding with par value of $100, dividend per share of $6.30, and a current market value of $70 per share. k P = $6.30 / $70 k P 9% k P = 9% Cost of Preferred Stock: Example

A.Dividend Discount Model B.Capital-Asset Pricing Model C.Before-Tax Cost of Debt plus Risk Premium Cost of Equity Approaches

cost of equity capital The cost of equity capital, k e, is the discount rate that equates the present value of all expected future dividends with the current market price of the stock. A. Dividend Discount Model P 0 = Current market price D t = Dividend expected at t k e = Cost of equity capital

constant dividend growth assumption The constant dividend growth assumption reduces the model to: k e = ( D 1 / P 0 ) + g Dividend Discount Model: Constant Growth P 0 = Current market price D 1 = Dividend expected at t=1 k e = Cost of equity capital g = Dividend growth rate

Assume that Basket Wonders (BW) has common stock outstanding with a current market value of $64.80 per share, current dividend of $3 per share, and a dividend growth rate of 8% forever. k e = ( D 1 / P 0 ) + g k e = ($3(1+.08) / $64.80) +.08 k e.1313% k e = =.13 or 13% Cost of Equity Capital: Example (Constant Growth)

growth phases assumption leads to the following formula (assume 3 growth phases): The growth phases assumption leads to the following formula (assume 3 growth phases): Dividend Discount Model: Growth Phases P 0 = Current market price D t = Dividend expected at t k e = Cost of equity capital g = Dividend growth rate

The cost of equity capital, k e, is equated to the required rate of return in market equilibrium. The risk-return relationship is described by the Security Market Line (SML). B. Capital Asset Pricing Model R f = Risk-free rate R m = Expected return for market portfolio k e = Cost of equity capital β j = Beta coefficient (responsiveness to market)

Assume that Basket Wonders (BW) has a company beta of Research by Julie Miller suggests that the risk-free rate is 4% and the expected return on the market is 11.2% k e = R f + (R m - R f )  j = 4% + (11.2% - 4%)1.25 k e 13% k e = 4% + 9% = 13% Cost of Equity (CAPM): Example

The cost of equity capital, k e, is the sum of the before-tax cost of debt and a risk premium in expected return for common stock over debt. C. Before-Tax Cost of Debt Plus Risk Premium k e = k d + Risk Premium* *Risk premium is not the same as CAPM risk premium

Assume that Basket Wonders (BW) typically adds a 3% premium to the before-tax cost of debt. k e = k d + Risk Premium = 10% + 3% k e 13% k e = 13% Cost of Equity (k d + R.P.): Example

13% Constant Growth Model13% 13% Capital Asset Pricing Model13% 13% Cost of Debt + Risk Premium13% Generally, the three methods will not agree. Comparison of the Cost of Equity Methods

Cost of Capital WACC =.35(6%) +.15(9%) +.50(13%) = =.0995 or 9.95% Weighted Average Cost of Capital (WACC)

1.Weighting System Marginal Capital Costs Capital Raised in Different Proportions than WACC Limitations of the WACC 2.Flotation Costs 2.Flotation Costs are the costs associated with issuing securities such as underwriting, legal, listing, and printing fees. a.Adjustment to Initial Outlay b.Adjustment to Discount Rate

Add Flotation Costs (FC) to the Initial Cash Outlay (ICO). Reduces Impact: Reduces the NPV Adjustment to Initial Outlay (AIO)

Subtract Flotation Costs from the proceeds (price) of the security and recalculate yield figures. Increases Impact: Increases the cost for any capital component with flotation costs. decreases Result: Increases the WACC, which decreases the NPV. Adjustment to Discount Rate (ADR)

A measure of business performance. It is another way of measuring that firms are earning returns on their invested capital that exceed their cost of capital. Specific measure developed by Stern Stewart and Company in late 1980s. Economic Value Added

EVA = NOPAT – [Cost of Capital x Capital Employed] Since a cost is charged for equity capital also, a positive EVA generally indicates shareholder value is being created. Based on Economic NOT Accounting Profit. NOPAT – net operating profit after tax is a company’s potential after-tax profit if it was all- equity-financed or “unlevered.” Economic Value Added

Initially assume all-equity financing. Determine project beta. Calculate the expected return. Adjust for capital structure of firm. Compare cost to IRR of project. Determining Project-Specific Required Rates of Return Use of CAPM in Project Selection:

Difficulty in Determining the Expected Return Locate a proxy for the project (much easier if asset is traded). Plot the Characteristic Line relationship between the market portfolio and the proxy asset excess returns. Estimate beta and create the SML. Determining the SML:

Project Acceptance and/or Rejection SML X X X X X X X O O O O O O O SYSTEMATIC RISK (Beta) EXPECTED RATE OF RETURN RfRf Accept Reject

1.Calculate the required return for Project k (all-equity financed). R k = R f + (R m - R f )  k 2. Adjust for capital structure of the firm (financing weights). Weighted Average Required Return = [k i ][% of Debt] + [R k ][% of Equity] Determining Project-Specific Required Rate of Return

Assume a computer networking project is being considered with an IRR of 19%. Examination of firms in the networking industry allows us to estimate an all-equity beta of 1.5. Our firm is financed with 70% Equity and 30% Debt at k i =6%. The expected return on the market is 11.2% and the risk-free rate is 4%. Project-Specific Required Rate of Return: Example

k e = R f + (R m - R f )  j = 4% + (11.2% - 4%)1.5 k e 14.8% k e = 4% % = 14.8% WACC 12.16% WACC =.30(6%) +.70(14.8%) = 1.8% %= 12.16% IRR 19%WACC 12.16% IRR = 19% > WACC = 12.16% Do You Accept the Project?

Determining Group-Specific Required Rates of Return Initially assume all-equity financing. Determine group beta. Calculate the expected return. Adjust for capital structure of group. Compare cost to IRR of group project. Use of CAPM in Project Selection:

Comparing Group-Specific Required Rates of Return Group-Specific Required Returns Company Cost of Capital Systematic Risk (Beta) Expected Rate of Return

Amount of non-equity financing relative to the proxy firm. Adjust project beta if necessary. Standard problems in the use of CAPM. Potential insolvency is a total- risk problem rather than just systematic risk (CAPM). Qualifications to Using Group-Specific Rates

Risk-Adjusted Discount Rate Approach (RADR) The required return is increased (decreased) relative to the firm’s overall cost of capital for projects or groups showing greater (smaller) than “average” risk. Project Evaluation Based on Total Risk

RADR and NPV Discount Rate (%) RADR – “high” risk at 15% (Reject!) RADR – “low” risk at 10% (Accept!) Adjusting for risk correctly may influence the ultimate Project decision. Net Present Value $000s

Probability Distribution Approach Acceptance of a single project with a positive NPV depends on the dispersion of NPVs and the utility preferences of management. Project Evaluation Based on Total Risk

Firm-Portfolio Approach B C A Indifference Curves STANDARD DEVIATION EXPECTED VALUE OF NPV Curves show “HIGH” Risk Aversion

Firm-Portfolio Approach B C A Indifference Curves STANDARD DEVIATION EXPECTED VALUE OF NPV Curves show “MODERATE” Risk Aversion

Firm-Portfolio Approach B C A Indifference Curves STANDARD DEVIATION EXPECTED VALUE OF NPV Curves show “LOW” Risk Aversion

 j =  ju [ 1 + (B/S)(1-T C ) ]   j : Beta of a levered firm.   ju : Beta of an unlevered firm (an all-equity financed firm). B/S:Debt-to-Equity ratio in Market Value terms. T C :The corporate tax rate. Adjusting Beta for Financial Leverage

Adjusted Present Value (APV) is the sum of the discounted value of a project’s operating cash flows plus the value of any tax-shield benefits of interest associated with the project’s financing minus any flotation costs. Adjusted Present Value APV = Unlevered Project Value + Value of Project Financing

Assume Basket Wonders is considering a new $425,000 automated basket weaving machine that will save $100,000 per year for the next 6 years. The required rate on unlevered equity is 11%. BW can borrow $180,000 at 7% with $10,000 after- tax flotation costs. Principal is repaid at $30,000 per year (+ interest). The firm is in the 40% tax bracket. NPV and APV Example

NPV to an all-equity-financed firm What is the NPV to an all-equity-financed firm? NPV = $100,000[PVIFA 11%,6 ] - $425,000 NPV = $423,054 - $425,000 NPV-$1,946 NPV = -$1,946 Basket Wonders NPV Solution

APV What is the APV? First, determine the interest expense. Int Yr 1($180,000)(7%) = $12,600 Int Yr 2( 150,000)(7%) = 10,500 Int Yr 3( 120,000)(7%) = 8,400 Int Yr 4( 90,000)(7%) = 6,300 Int Yr 5( 60,000)(7%) = 4,200 Int Yr 6( 30,000)(7%) = 2,100 Basket Wonders APV Solution

Second, calculate the tax-shield benefits. TSB Yr 1($12,600)(40%) = $5,040 TSB Yr 2( 10,500)(40%) = 4,200 TSB Yr 3( 8,400)(40%) = 3,360 TSB Yr 4( 6,300)(40%) = 2,520 TSB Yr 5( 4,200)(40%) = 1,680 TSB Yr 6( 2,100)(40%) = 840 Basket Wonders APV Solution

Third, find the PV of the tax-shield benefits. TSB Yr 1($5,040)(.901) = $4,541 TSB Yr 2( 4,200)(.812) = 3,410 TSB Yr 3( 3,360)(.731) = 2,456 TSB Yr 4( 2,520)(.659) = 1,661 TSB Yr 5( 1,680)(.593) = 996 PV = $13,513 TSB Yr 6( 840)(.535) = 449 PV = $13,513 Basket Wonders APV Solution

APV What is the APV? APV = NPV + PV of TS - Flotation Cost APV = -$1,946 + $13,513 - $10,000 APV$1,567 APV = $1,567 Basket Wonders NPV Solution

YearCash FlowLoan Bal.RepaymentInterestTS BenefitFlotation NPV=($1,946.21)$13, APV=$1,566.04