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Chapter 15

Chapter 15. Required Returns and the Cost of Capital. 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.

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Chapter 15

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  1. Chapter 15 Required Returns and the Cost of Capital

  2. 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.

  3. Required Returns and the Cost of Capital • Creation of Value • Overall Cost of Capital of the Firm • Project-Specific Required Rates • Group-Specific Required Rates • Total Risk Evaluation

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

  5. Cost of Capital • The cost of capital (COC) is the rate of return the firm must earn to maintain its market value and attract investors • projects with return > COC will improve the firm’s value • projects with return < COC will harm the firm’s value

  6. 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).

  7. Cost of Capital COC is estimated • on an after-tax basis • at a point in time • based on expected future values • holding business and financial risk fixed

  8. Cost of Capital • Target capital structure is the optimal mix of debt and equity financing for the firm • most firms seek to maintain a desired mix of debt and equity funding • each new chunk of capital should fit with the overall mix

  9. Cost of Capital • A firm is currently faced with an investment opportunity. Assume the following: • Because it can earn 7% on the investment of funds costing only 6%, the firm undertakes the opportunity.

  10. Cost of Capital • Imagine that one week later a new investment opportunity is available • In this instance, the firm rejects the opportunity, because the 14% financing cost is greater than the 12% expected return. • Is this action in the best interests of its owners?

  11. Cost of Capital • No—it accepted a project yielding a 7% return and rejected one with a 12% return. • Is there a better way? • Yes: the firm can use a combined cost, which over the long run would provide for better decisions. • By weighting the cost of each source of financing by its target proportion in the firm’s capital structure, the firm can obtain a weighted average cost that reflects the interrelationship of financing decisions.

  12. Cost of Capital • Assuming that a 50–50 mix of debt and equity is targeted, the weighted average cost in this example would be 10% [(0.50 x 6% debt) + (0.50 x 14% equity)]. • This outcome is clearly more desirable. • With this cost, the first opportunity would have been rejected (7% IRR < 10% weighted average cost), and the second one would have been accepted (12% IRR > 10% weighted average cost).

  13. Concept of Cost of Capital • Wren Manufacturing is considering projects 263 and 264. The basic variables surrounding each project using the IRR decision technique and the resulting decision actions are summarised in the following table.

  14. Concept of Cost of Capital • a Evaluate the firm’s decision-making procedures, and explain why the acceptance of project 263 and rejection of project 264 may not be in the owners’ best interest. • b If the firm maintains a capital structure containing 40% debt and 60% equity, find its weighted average cost using the data in the table. • c Had the firm used the weighted average cost calculated in part b, what actions would have been taken relative to projects 263 and 264? • d Compare and contrast the firm’s actions with your findings in part c. Which decision method seems more appropriate? Explain why.

  15. Concept of Cost of Capital • a. The firm is basing its decision on the cost to finance a particular project rather than the firm’s combined cost of capital. This decision-making method may lead to erroneous accept/reject decisions. • b. ka = wiki + wpkp + wsks •  ka = 0.40 (7%) + 0.60(16%) •  ka = 2.8% + 9.6% •  ka = 12.4% • 

  16. Concept of Cost of Capital • c. Reject project 263. Accept project 264. • d. Opposite conclusions were drawn using the two decision criteria. The overall cost of capital as a criterion provides better decisions because it takes into consideration the long run interrelationship of financing decisions

  17. Sources of finance • The four sources of long-term funds for the business firm: • debt, • preference share capital, • ordinary share equity capital and • retained earnings.

  18. Sources of finance • This is important!! • The specific cost of each source of financing is the after-tax cost of obtaining the financing today, i.e. the marginal cost of raising the next dollar of funding • It is not the historically based cost reflected by the existing financing in the firm’s accounting records • Only the cost of debt needs to be adjusted for tax. • Why do we not adjust the cost of preference shares and equity for tax? • Because dividends are paid from tax-paid profits. Therefore, the cost of these is an after-tax cost

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

  20. Cost of Debt • Cost of Debt is the required rate of return on investment of the lenders of a company. • Where P0 = current market price • Pt = maturity value at time t I = interest payment in $ • After tax cost is: • ki = kd(1 – T)

  21. Determination of the Cost of Debt Assume that Basket Wonders (BW) has $1,000 par value zero-coupon bonds outstanding. BW bonds are currently trading at $385.54 with 10 years to maturity. BW tax bracket is 40%. $0 + $1,000 $385.54 = (1 + kd)10

  22. Determination of the Cost of Debt (1 + kd)10 = $1,000 / 385.54 = 2.5938 (1 + kd) = (2.5938) (1/10) = 1.1 kd= 0.1 or 10% ki = 10% ( 1 – .40 ) ki = 6%

  23. Cost of debt • Du Chen Corporation is selling $10 million of 20-year, 9% coupon (stated annual interest rate) bonds, each with a face value of $1,000. • Similar-risk bonds earn returns greater than 9% so the firm must sell the bonds for $980 to compensate for the lower coupon interest rate. • The flotation costs paid to the investment banker are 2% of the face value of the bond (2% × 1000), or $20. • The net proceeds to the firm from the sale of each bond are therefore $960 ($980 – $20).

  24. Cost of debt • To solve this, we need a financial calculator or a spreadsheet. However there is a Yield to Maturity (YTM) formula that gives an good approximation answer: • kd = [I + (1,000 – Nd)/n]/(Nd + 1000)/2 • Where I = the interest payment in $ • Nd = proceeds from the sale of the bond • n = number of periods until the bond maturity.

  25. Cost of debt • The cash flows are: • End of Year Cash flow • 0 $960 • 1-20 -$90 • -$1,000 • Using the YTM formula, the answer is:

  26. Cost of debt

  27. Cost of debt • Assuming a 30% tax rate and before-tax cost of 9.4%, • ki = 0.094 x (1 – 0.30) = 6.6% = after-tax cost • The explicit cost of long-term debt is less than the explicit cost of other forms of long-term financing, because of the tax-deductibility of interest.

  28. Cost of Preferred Stock • The cost of preference share capital (kp) is the ratio of the preference share dividend (Dp) to the firm’s net proceeds (Np) from the sale of preference shares •  kp = Dp / Np • Example: consider an 8.5% pref issue, at par = $2.00 a share with an issue cost of 11 cents per share •  kp = ($0.17) / ($1.89) = 9% • (Np = 2.00 – 0.11 = $1.89)

  29. Cost of Preferred Stock • Comparing the 9% cost of preference capital with the 6.6% cost of long-term debt (bonds) shows that preference capital is more expensive. The difference exists primarily because the cost of the debt (interest) is tax-deductible. • The cost of preference share capital already issued is the dividend (Dp) divided by the market value (P) of preference share capital • kp = Dp / P • If the market value of Du Chen Corporation’s preference share capital is $10 million, and preference dividend payable is $0.9 million, the return on its preference share capital is: • kp= $0.90/$10.00 = 9.0%

  30. Cost of Preferred Stock Cost of Preferred Stock is the required rate of return on investment of the preferred shareholders of the company. kP = DP / P0

  31. Determination of the Cost of Preferred Stock 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. kP = $6.30 / $70 kP = 9%

  32. Cost of Equity Approaches • Dividend Discount Model • Capital-Asset Pricing Model • Before-Tax Cost of Debt plus Risk Premium

  33. Dividend Discount Model The cost of equity capital, ke, is the discount rate that equates the present value of all expected future dividends with the current market price of the stock. D1D2D  P0 = + + . . . +  (1 + ke)1 (1 + ke)2 (1 + ke)

  34. Constant Growth Model The constant dividend growth assumption reduces the model to: ke = ( D1 / P0 ) + g Assumes that dividends will grow at the constant rate “g” forever.

  35. Determination of the Cost of Equity Capital 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. ke = ( D1 / P0 ) + g ke = ($3(1.08) / $64.80) + 0.08 ke = 0.05 + 0.08 = 0.13 or 13%

  36. Determination of the Cost of Equity Capital • Calculate Du Chen Corporation’s cost of ordinary share equity capital, ke. The market price, P0, of its shares is $5. The firm expects to pay a dividend, D1, of 40 cents at the end of the coming year, 2005. The dividends paid over the past 6 years (1999–2004) were:

  37. Determination of the Cost of Equity Capital • Calculate the growth rate of dividends: • 1999 div/2004 div = 29.7/38.0 = 0.7816 • = PVIFk,5 = 5% • Or • 2004 div/1999 div = 38.0/29.7 = 1.2794 • = FVIFk,5 = 5%

  38. Determination of the Cost of Equity Capital • Substituting D1 = $0.40, P0 = $5.00 and g = 5 per cent into the Equation results in the cost of ordinary equity: • ke = $0.40/$5.00 + 0.05 • = 0.08 + 0.05 • = 0.13 or 13%

  39. Growth Phases Model The growth phases assumption leads to the following formula (assume 3 growth phases): D0(1 + g1)t Da(1 + g2)t–a a b P0 =   + (1 + ke)t (1 + ke)t t=1 t=a+1  Db(1 + g3)t–b  (1 + ke)t t=b+1

  40. Capital Asset Pricing Model The cost of equity capital, ke, is equated to the required rate of return in market equilibrium. The risk-return relationship is described by the Security Market Line (SML). ke = Rj = Rf + (Rm – Rf)j

  41. Determination of the Cost of Equity (CAPM) Assume that Basket Wonders (BW) has a company beta of 1.25. Research by Julie Miller suggests that the risk-free rate is 4% and the expected return on the market is 11.4% ke = Rf + (Rm – Rf)j = 4% + (11.4% – 4%)1.25 ke = 4% + 9.25% = 13.25%

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

  43. Determination of the Cost of Equity (kd + R.P.) Assume that Basket Wonders (BW) typically adds a 2.75% premium to the before-tax cost of debt. ke = kd + Risk Premium = 10% + 2.75% ke = 12.75%

  44. Comparison of the Cost of Equity Methods Constant Growth Model 13.00% Capital Asset Pricing Model 13.25% Cost of Debt + Risk Premium 12.75% Generally, the three methods will not agree. We must decide how to weight – we will use an average of these three.

  45. Weighted average cost of capital • The WACC (ka) is determined by weighting the cost of each specific type of capital by its proportion in the firm’s capital structure •  ka = (ki x wi) + (kp x wp) + (ke x ws) • Note: (i) The sum of weights must equal one. • (ii) It is the after-tax cost of debt that is used.

  46. BW’s Weighted Average Cost of Capital (WACC) n  Cost of Capital = kx(Wx) WACC = 0.35(6%) + 0.15(9%) + 0.50(13%) WACC = 0.021 + 0.0135 + 0.065 = 0.0995 or 9.95% x=1

  47. Weighted average cost of capital • The costs of the various types of capital for Du Chen Corporation are: • Cost of debt, ki = 6.6% • Cost of preference capital, kp = 9.0% • Cost of new shares, ke = 14.0% • The company uses the following weights in calculating its WACC:

  48. Weighted average cost of capital

  49. Weighted average cost of capital • Source Weight Cost WACC • Debt 0.40 6.6% 2.6% • Pref capital 0.10 9.0 0.9 • Ord equity 0.50 1 3.0 6.5 • Totals 1.00 10.0% • The WACC for Du Chen is 10%. • Assuming an unchanged risk level, the firm should accept all projects that earn a return greater than or equal to 10%

  50. Limitations of the WACC 1.Weighting System • Marginal Capital Costs • Capital Raised in Different Proportions than WACC

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