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- 1. CHAPTER 1 The Cost of Capital 1
- 2. The Goal of the Firm The goal of a firm’s financial management is to maximize the market value. Market value is measured by common stock prices in corporations. Thus market value maximization would imply maximizing the price of common stock. 2
- 3. Maximizing Market Value Risk Financial Decisions MARKET VALUE 1) Financing Decisions 2) Investment Decisions Return 3
- 4. Balance Sheet ASSETS Debt Current Liabilities L.T. Debt (Bonds) + Preferred Stock + Common Equity Common Stock Retained Earnings
- 5. Why is it important to calculate the firm’s cost of capital correctly? A firm uses its cost of capital to determine if its investments are profitable. To make the right amount of investment, the firm’s cost of capital has to be calculated correctly. 5
- 6. Why is it important to calculate the firm’s cost of capital correctly? Assume that a firm miscalculates its cost of capital to be less than its true cost of capital. The firm would invest in many non-profitable projects and it would lose equity in the long run. 6
- 7. Why is it important to calculate the firm’s cost of capital correctly? Assume that a firm miscalculates its cost of capital to be more than it actually is. It would not invest in many profitable projects and it would become less competitive in the long-run. 7
- 8. What types of long-term capital do firms use? Long-term debt Preferred stock Common equity 8
- 9. Capital Components Capital components are sources of funding that come from investors. Accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the cost of capital. 9
- 10. Before-Tax vs. After-Tax Capital Costs Firms should incorporate the tax effects in the cost of capital. They should focus on the after-tax costs. Only the cost of debt is affected because interest is a tax-deductable expense. 10
- 11. Historical (Embedded) Costs vs. New (Marginal) Costs The cost of capital is used primarily to make decisions which involve raising and investing new capital. So, we should focus on marginal costs. 11
- 12. 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 debt, if it has any. 12
- 13. COST OF DEBT (ISSUING BONDS) Pb Pb BOND The Firm rd BT (Cost of Debt) The Investor INT, M = rd BT (Yield to Maturity) (no flotation cost is assumed) 13
- 14. FLOTATION COSTS Flotation cost is small for bonds compared with preferred stock and common stock. There is no flotation cost if the issue is privately (directly) placed. 14
- 15. Financial Calculator A financial calculator can make the cost of capital and capital budgeting calculations easier. The financial calculator I would recommend is: Texas Instruments BA II PLUS. 15
- 16. A 15-year, 12% semiannual bond sells for $1,153.72. What’s rd BT? 0 rd BT = ? -1,153.72 INPUTS 1 2 60 60 30 N OUTPUT ... 60 + 1,000 -1153.72 60 I/YR 30 PV 1000 PMT FV 5.0% x 2 = rd BT = 10% 16
- 17. What’s rd BT using PV tables? 0 rd BT = ? -1,153.72 1 2 30 ... 60 60 60 + 1,000 VB = (INT/2)(PVIFAr/2,2n) + (M)(PVIFr/2,2n) $1,153.72 = ($60)(PVIFA5% ,30) + ($1,000)(PVIF5%,30) $1,153.72 = ($60)(15.3725) + ($1,000)(0.2314) The percentage is exact. No interpolation is needed. Annual Cost of Capital: rd BT = 5% x 2 = 10% 17
- 18. Finding the YTM of the Bond with Excel A 1 interest rate (rate): B ? = 5.00% 2 number of periods (nper): 30 3 payment (pmt): 60 4 present value (pv): 5 future value: -$1,153.72 $1,000 Formula for Cell B1 = Rate(nper,pmt,pv,fv) Values entered into Cell B1 = Rate(B2,B3,B4,B5) 18
- 19. Component Cost of Debt Interest is tax deductible, so the after tax (AT) cost of debt is: rd AT = rd BT(1 – T) = 10% (1 – 0.40) = 6% Flotation costs small, so ignore. 19
- 20. COST OF PREFERRED STOCK Pnet = Pps (1 - F) Pps PREFERRED STOCK The Firm rps = Dps / Pnet The Investor Dps rps = Dps / Pps (Yield) (Cost of Preferred Stock) (Cost of P.S. financing) > (Yield) 20
- 21. Cost of preferred stock: Pps = $116.95, Div=10%, Par = $100, F = 5% Use this formula: rps = Dps Pps (1 – F) = = 0.1 ($100) $116.95 (1 – 0.05) $10 $111.10 = 0.09 = 9.0% 21
- 22. Cost of Preferred Stock Flotation costs for preferred stock are significant, so are reflected. Use net price. Preferred dividends are not tax deductible, so no tax adjustment. 22
- 23. What are the two ways that companies can raise common equity? By retaining earnings that are not paid out as dividends. By issuing new shares of common stock. 23
- 24. Why is there a cost for retained earnings? Earnings can be reinvested or paid out as dividends. Investors could buy other securities, earning a return. Thus, there is an opportunity cost if earnings are reinvested. 24
- 25. Cost for Retained 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. So, rs, is the cost of reinvested earnings and it is the cost of common equity. 25
- 26. Three ways to determine the cost of retained earnings 1. CAPM: rs = rRF + (rM – rRF) b = rRF + (RPM) b 2. DCF: rs = D1/P0 + g 3. Own-Bond-Yield + Judgmental Risk Premium: rs = rd + JRP 26
- 27. Comparing the Three Methods In practice, most firms use the CAPM to estimate the cost of equity capital. Many firms use the DCF method. Some firms estimate the cost of equity capital by adding a risk premium to their bond interest rate. 27
- 28. CAPM Cost of Retained Earnings: rRF = 5.6%, RPM = 6%, b = 1.2 rs = rRF + (RPM ) b = 5.6% + (6.0%)1.2 = 12.8% 28
- 29. Issues in Using CAPM Most analysts use the rate on a long-term (10 to 20 years) government bond as an estimate of rRF. 29
- 30. Issues in Using CAPM Most analysts use a rate of 3.5% to 6% for the market risk premium (RPM) Estimates of beta vary, and estimates are “noisy” (they have a wide confidence interval). 30
- 31. Beta Estimation Estimating Beta from Historical Returns Beta is the expected percent change in the excess return of the security for a 1% change in the excess return of the market portfolio. Consider Cisco Systems stock and how it changes with the market portfolio.
- 32. Monthly Returns for Cisco Stock and for the S&P 500, 1996–2009
- 33. Scatterplot of Monthly Returns for Cisco Versus the S&P 500, 1996–2009
- 34. Beta Estimation for Cisco As the scatterplot on the previous slide shows, Cisco tends to be up when the market is up, and vice versa. We can see that a 10% change in the market’s return corresponds to about a 20% change in Cisco’s return. Thus, Cisco’s return moves about two for one with the overall market, so Cisco’s beta is about 2.
- 35. DCF Approach: Cost of Retained Earnings D0 = $3.12; P0 = $50; g = 5.8% rs = D1 P0 +g= D0(1 + g) P0 +g = $3.12 (1.058) + 0.058 $50 = 6.6% + 5.8% = 12.4% 35
- 36. Estimating the Growth Rate Use the historical growth rate if you believe the future will be like the past. Obtain analysts’ estimates: Value Line, Zacks, Yahoo!Finance. Use the earnings retention model, illustrated on next slide. 36
- 37. Earnings Retention Model Suppose the company has been earning 15% on equity (ROE = 15%) and has been paying out 62% of its earnings. If this situation is expected to continue, what’s the expected future g? 37
- 38. Earnings Retention Model Growth from earnings retention model: g = (Retention rate)(ROE) = (1 – Payout rate)(ROE) = (1 – 0.62)(15%) = 5.7% This is close to g = 5.8% given earlier. 38
- 39. Own-Bond-Yield + Judgmental Risk Premium: rd = 10%, JRP = 3.2% rs = rd + Judgmental risk premium = 10.0% + 3.2% = 13.2% This judgmental risk premium ≠ CAPM equity risk premium, RPM. Produces ballpark estimate of rs. Useful check. 39
- 40. Average of the Three Methods Brigham and Ehrhardt suggest that the average of the three methods can be used in estimating the cost of equity capital. 40
- 41. What’s a reasonable final estimate of rs? Method Estimate CAPM 12.8% DCF 12.4% rd + JRP 13.2% Average 12.8% 41
- 42. Determining the Weights for the WACC The weights are the 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. 42
- 43. Estimating Weights for the Capital Structure If you don’t know the targets, it is better to estimate the weights using current market values than current book values. If you don’t know the market value of debt, then it is usually reasonable to use the book values of debt, especially if the debt is short-term. 43
- 44. Estimating Weights: A Numerical Example Suppose the stock price is $50, there are 3 million shares of stock, the firm has $25 million of preferred stock, and $75 million of debt. 44
- 45. Estimating Weights: A Numerical Example Vs = $50 (3 million) = $150 million Vps = $25 million Vd = $75 million Total value = $150 + $25 + $75 = $250 million 45
- 46. Estimating Weights: A Numerical Example ws = $150/$250 = 0.6 wps = $25/$250 = 0.1 wd = $75/$250 = 0.3 The target weights for this company are the same as these market value weights, but often market weights temporarily deviate from targets due to changes in stock prices. 46
- 47. What’s the WACC using the target weights? WACC = wd rd (1 – T) + wps rps + ws rs = 0.3 (10%) (1 − 0.4) + 0.1 (9%) + 0.6 (12.8%) = 10.38% ≈ 10.4% 47
- 48. What factors influence a company’s WACC? Uncontrollable factors: Market conditions, especially interest rates. The market risk premium. Tax rates. Controllable factors: Capital structure policy. Dividend policy. Investment policy. Firms with riskier projects generally have a higher cost of equity. 48
- 49. Is the firm’s WACC correct for each of its divisions? No! The composite WACC reflects the risk of an average project undertaken by the firm. Different divisions may have different risks. The division’s WACC should be adjusted to reflect the division’s risk and capital structure. 49
- 50. The Risk-Adjusted Divisional Cost of Capital Estimate the cost of capital that the division would have if it were a stand-alone firm. This requires estimating the division’s beta, cost of debt, and capital structure. 50
- 51. 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. 51
- 52. Divisional Cost of Capital Using CAPM Target debt ratio = 10% rd = 12% rRF = 5.6% Tax rate = 40% betaDivision = 1.7 Market risk premium = 6% 52
- 53. Divisional Cost of Capital Using CAPM Division’s required return on equity: rs = rRF + (rM – rRF) bDiv. = 5.6% + (6%) 1.7 = 15.8% WACCDiv. = wd rd(1 – T) + wsrs = 0.1 (12%) (0.6) + 0.9 (15.8%) = 14.94% ≈ 14.9% 53
- 54. Division’s WACC vs. Firm’s Overall WACC? Division WACC = 14.9% versus company WACC = 10.4%. “Typical” projects within this division would be accepted if their returns are above 14.9%. 54
- 55. What are the three types of project risk? Stand-alone risk Corporate risk Market risk 55
- 56. How is each type of risk used? Stand-alone risk is easiest to calculate. Market risk is theoretically best in most situations. However, creditors, customers, suppliers, and employees are more affected by corporate risk. Therefore, corporate risk is also relevant. 56
- 57. A Project-Specific, Risk-Adjusted Cost of Capital Start by calculating a divisional cost of capital. Use judgment to scale up or down the cost of capital for an individual project relative to the divisional cost of capital. 57
- 58. Cost of Issuing New Common Stock When a company issues new common stock they also have to pay flotation costs to the underwriter. Issuing new common stock may send a negative signal to the capital markets, which may depress stock price. 58
- 59. THE COST OF FINANCING WITH A NEW COMMON STOCK ISSUE (re) Pn = Po (1 - F) The Firm Po COMMON STOCK re = [D1 / Po(1-F)] + g Dt , g (Cost of Common Stock) re > rs The Investor rs = (D1 / Po) + g (Yield) 59
- 60. Cost of New Common Equity: P0 = $50, D0 = $3.12, g = 5.8%, F = 15% re = D0 (1 + g) P0 (1 – F) +g $3.12 (1.058) + 5.8% = $50 (1 – 0.15) = $3.30 $42.50 + 5.8% = 13.6% 60
- 61. COST OF DEBT (Issuing Bonds with Flotation Costs) Pn = Pb - F Pb BOND The Firm rd BT (Cost of Debt) The Investor INT, M > rd BT (Yield to Maturity) (flotation cost is assumed) 61
- 62. Cost of Debt with Flotation Costs: A Numerical Example Cost of New 30-Year Debt: Par = $1,000, Coupon = 10% paid annually, F = 2% Using a financial calculator: N = 30 PV = 1,000 (1 – 0.02) = 980 PMT = (0.10)(1,000)(1 – 0.4) = 60 FV = 1,000 Solving for I/YR: rd AT = 6.15% 62
- 63. Four Mistakes to Avoid Current vs. historical cost of debt Mixing current and historical measures to estimate the market risk premium Book weights vs. Market Weights Incorrect cost of capital components 63
- 64. Current vs. Historical Cost of Debt When estimating the cost of debt, don’t use the coupon rate on existing debt, which represents the cost of past debt. Use the current interest rate on new debt. 64
- 65. Estimating the Market Risk Premium When estimating the risk premium for the CAPM approach, don’t subtract the current long-term T-bond rate from the historical average return on common stocks. For example, if the historical rM has been about 12.2% and inflation drives the current rRF up to 10%, the current market risk premium is not 12.2% – 10% = 2.2%! 65
- 66. Estimating Weights Use the target capital structure to determine the weights. If you don’t know the target weights, then use the current market value of equity. If you don’t know the market value of debt, then the book value of debt often is a reasonable approximation, especially for short-term debt. 66
- 67. Capital components are sources of funding that come from investors. Accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the WACC. We do adjust for these items when calculating project cash flows, but not when calculating the WACC. 67

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