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Business Finance BA303 ♦ Fall 2012 Michael Dimond Risk and the costs of capital • When considering common equity, preferred equity and debt, the owners of these securities each bear a different level of risk. The higher the risk, the higher the rate of return will be. • Usually, this is what you expect: Rf < Kd < Kpfd < Ke and… inflation < Rf • What does this tell you about the return demanded by each type of investor? • What does that imply about the risk borne by each? • Real Rates, Risk Premium, etc. • Market efficiency (the EMH) Michael Dimond School of Business Administration More about risk and return • Risk is uncertainty. Not just success or failure, but to what extent will something be as expected? • It may be necessary to consider scenarios and weigh them based on their likelihood. For example: • The experts in your company predict the following results and probabilities: Scenario Return Very poor 0.75% 0.05 0.75 x 0.05 = 0.0375 Poor 1.25% 0.15 1.25 x 0.15 = 0.1875 8.5% 0.60 8.5 x 0.60 = 5.1000 Good 14.75% 0.15 14.75 x 0.15 = 2.2125 Very good 16.25% 0.05 16.25 x 0.05 = 0.8125 Average • What is the expected rate of return? Probability sum = 8.3500 • The weighted average is 8.35% Michael Dimond School of Business Administration More about risk and return • Variation or volatility is another form of uncertainty. • What is standard deviation? What does it represent? Michael Dimond School of Business Administration More about risk and return • How do the following assets compare to Stock X? Expected Return Std Deviation Stock X 12% 5% Stock A 12% 7% Stock B 10% 8% Stock C 14% 6% • When making a decision, which should you consider first? • Risk? • Return? • • • • Which has the lowest potential return? Which has the highest potential return? Which has the most uncertainty? What would be the Coefficient of Variation for each? • CoV = Std Deviation ÷ Return • What is Diversification? • Can all risk be diversified away? Michael Dimond School of Business Administration Determining Kd with YTM • Remember from valuing bonds that the “i” in the TVM relationship is the yield on a bond. • Yield is the rate of return demanded by investors in debt. • To find the Cost of Debt (Kd), solve for the yield of a bond. • Remember: Costs of capital are forward-looking numbers. It is what an investor will demand from future performance. • What does this mean for the cost of debt (Kd)? Michael Dimond School of Business Administration Determining Ke with the Dividend Growth Model • Ke is the required rate of return for equity investors “Cost of Equity” • We can derive this from the dividend discount model: P0 = D1/(r-g) :. (r-g) = D1/P0 :. r = D1/P0 + g • Since r is the required rate of return, Ke = D1/P0 + g • How do you test the answer you get? • What if you wanted to solve for the expected growth rate? • There is another way to find the cost of equity: CAPM Michael Dimond School of Business Administration Determining Ke with CAPM • Ke is the required rate of return for equity investors “Cost of Equity” • The CAPM (Capital Asset Pricing Model) is a formula used to compute Ke Ke = Rf + β(Rm – Rf) or Ke = Rf + β(MRP) • MRP is the Market Risk Premium MRP = Rm – Rf • Remember: Costs of capital are forward-looking numbers. It is what an investor will demand from future performance. • What does this mean for the cost of equity (Ke)? Michael Dimond School of Business Administration About beta • Beta (β) represents how well an asset’s return correlates with the return on the market • Correlation, not Causality • Beta measures sensitivity to economic inputs • Beta is the slope of the line showing the relationship of the data 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Mkt Return 16% 13% 7% 14% 12% -5% -9% -12% 4% 8% A Return 28% 22% 14% 18% 20% -2% 2% -8% 9% 13% 30% 25% 20% A Return 15% Linear (A Return) y = 1.0893x + 0.0637 10% 5% 0% -20% -10% 0% 10% 20% -5% -10% • What is the difference between Systematic and Unsystematic risk? • Can beta be zero? Can beta be negative? Michael Dimond School of Business Administration Can beta really be negative? What does a negative beta imply about the stock performance? What does a negative beta imply about Ke? Michael Dimond School of Business Administration Determining Kpfd with the Dividend Discount Model • The value of a perpetuity is how we price preferred equity: PVperp = CF/r :. Price = Dividend/Kpfd :. Price x Kpfd = Dividend :. Kpfd = Dividend / Price • So… If XYZ Company has 8% preferred stock with a $20.00 par value which is selling for $28.00, what would be the Cost of Preferred Equity? • 8% x 20.00 = 1.60 • 1.60 / 28.00 = 0.0571 = 5.71% Michael Dimond School of Business Administration Market Value vs Book Value • Investors have an opinion about the value of a company. A stockholder believes the price of stock is appropriate value, and this is different than what the balance sheet shows for the value of equity. • The balance sheet shows the book value. The market price determines the market value. • Example: Book Value • Example: Market Value (“Market Cap” or Market Capitalization) • P/B ratio Michael Dimond School of Business Administration WACC • Investors care about market value more than book value. • Costs of capital are used in making investing decisions. • :. If we wanted to know the overall cost of capital for a company (the cost of equity and the cost of debt combined), we would use a weighted average of the percentages, and weight them based on the market values. • The Weighted Average Cost of Capital is called the WACC. WACC = we x Ke + wd x Kd (1-t) • If there is preferred stock, we just expand the formula: WACC = wpfd x Kpfd + we x Ke + wd x Kd (1-t) Michael Dimond School of Business Administration Weights of Equity & Debt • The weight is the proportion of that type of capital compared with the total capital in the firm. • What is the weight of each type of capital below? • Equity = E = $600MM • Debt = D = $300MM • Preferred Stock = Pfd = $100MM • • • • Total Capital = TC = 600+300+100 = 1,000 We = E/TC = 600/1,000 = 0.60 Wd = D/TC = 300/1,000 = 0.30 Wpfd = Pfd/TC = 100/1,000 = 0.10 • Note: the sum of the weights always equals 1.00 Michael Dimond School of Business Administration Determining the WACC • You may need to compute the WACC from information presented like this: • ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125. • What is the best approach to solving this problem? Michael Dimond School of Business Administration Break a complicated problem into smaller pieces • ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125. • Find the market values • • • • MVe = $27.50 x 1MM = $27.5MM MVd = 10MM ÷ 1,000 (assumed FV) x $1,125 = $11.25MM MVpfd = $125 x 10,000 = $1.25MM TC = $27.5MM + $11.25MM + $1.25MM = $40.0MM • Find the weights & tax shield • • • • We = 27.5 ÷ 40.0 = 0.6875 Wd = 11.25 ÷ 40.0 = 0.2813 Wpfd = 1.25 ÷ 40.0 = 0.0313 (1-t) = (1 - 0.34) = 0.66 Michael Dimond School of Business Administration Break a complicated problem into smaller pieces • ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125. • Find the different costs of capital • Kd : Solve for the yield find i, where: n=10x2, PV=-1125, FV=1000, PMT=0.085x1000÷2 [i=3.3800] :. Kd = 2x3.38% = 6.76% • Ke : Use the Dividend Discount Model or the CAPM (based on data available) Ke = r = D1/P0 + g Ke = [(1.80 x 1.07) / 27.50] + 0.07 = 0.1400 :. Ke = 14.00% • Kpfd : Find the return on a non-growing perpetuity Kpfd = r = D1/P0 = (0.09 x 100)/125 = 0.0720 :. Kpfd = 7.20% Michael Dimond School of Business Administration Determining the WACC • From there, put the pieces of the formula in place, then work through the formula in steps • • • • WACC = wpfd x Kpfd + we x Ke + wd x Kd x (1-t) WACC = 0.0313 x 0.072 + 0.6875 x 0.14 + 0.2813 x 0.0676 x 0.66 WACC = 0.0023 + 0.0963 + 0.2813 x 0.0446 WACC = 0.0023 + 0.0963 + 0.0126 WACC = 0.1112 = 11.12% 0.0446 is the After-Tax Cost of Debt • By parsing the problem, you avoid errors • Try another example: • XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25 Michael Dimond School of Business Administration Determining the WACC • Try another example: • XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25 • Market Values & Weights • • • • MVe = $18,750,000 MVpfd = $ 880,000 MVd = $10,890,000 TC = $40,520,000 we = 0.7095 wpfd = 0.0217 wd = 0.2688 1.0000 a • Tax Shield = (1 – t) = (1 - 0.35) = 0.65 Michael Dimond School of Business Administration Determining the WACC • Try another example: • XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25 • Costs of Capital • Ke = Rf + β(Rm – Rf) = 0.0315 +1.25(0.1038-0.0315) = 0.1219 = 12.19% • Kpfd = Dividend / Price = 9.25/110 = 0.0841 = 8.41% • Kd = Find YTM where i is semiannual and… n = 24 semiannual, PV = -1,100, FV = 1,000, PMT = 41.25 semiannual i = 3.5021 :. YTM = 7.0043% or 0.0700 Michael Dimond School of Business Administration Determining the WACC • From there, put the pieces of the formula in place, then work through the formula in steps • • • • WACC = wpfd x Kpfd + we x Ke + wd x Kd x (1-t) WACC = 0.0217 x 0.0841 + 0.7095 x 0.1219 + 0.2688 x 0.0700 x 0.65 WACC = 0.0018 + 0.0865 + 0.2688 x 0.0455 WACC = 0.0018 + 0.0865 + 0.0122 WACC = 0.1005 = 10.05% Michael Dimond School of Business Administration Real life is more complicated • Equity can come from retained earnings or from new investment. • New issues of stocks and bonds come with flotation costs, price adjustments, etc. which must be factored in. • Growth rates are rarely stated, so they must be computed. Michael Dimond School of Business Administration Kd with flotation cost • ABC Company is in the 40% tax bracket and can sell 15-year bonds ($1,000 par) paying annual interest of 12%. Market rates are slightly below that for bonds of this rating, so the bonds will sell for $1,100. To issue the bonds, ABC will have flotation costs of $30 per bond. Find Kd. • • • • • n = 15 years (annual) i = ?? Solve for YTM (annual) PMT = 12% x 1,000 (annual) outflow PV = 1,100 – 30 (expected proceeds less flotation costs) inflow FV = 1,000 outflow • • • • i = 11.0252 YTM = 11.03% Kd = 11.03% Kd (After-tax) = 11.03% x (1-0.40) = 6.62% Michael Dimond School of Business Administration Kpfd with flotation cost • XYZ Company is issuing preferred stock with an 8% dividend and a $120 par value. The shares will sell for $129.60 and have flotation costs of $7.20 per share. What is the cost of preferred equity? • • • • • • Par = 120.00 Dividend = 8% x 120 = 9.60 Selling price = 129.60 Flotation costs = 7.20 Net proceeds = 129.60 – 7.20 = 122.40 Kpfd = 9.60 / 122.40 = 0.0784 = 7.84% Michael Dimond School of Business Administration Ke with flotation cost • ABC Company is considering a SEO (Seasoned Equity Offering). Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. The planned dividend per share is $1.45 for the coming year, and they expect the growth of dividends to follow the same average growth it has for the past 5 years. Historic annual DPS are: • • • • • 2008 2009 2010 2011 2012 2.12 2.30 2.60 2.92 3.10 • What is their Cost of Equity for the SEO? • Ke = D1 / P0 + g… but what is g? Michael Dimond School of Business Administration Ke with flotation cost – finding the growth rate • Historic annual DPS for the last 5 years are: • • • • • 2008 2009 2010 2011 2012 2.12 2.30 2.60 2.92 3.10 • Growth can be found by solving for the CAGR (Compound Annual Growth Rate) • • • • (3.10/2.12) = 1.46 1.46 ^ (1/4) = 1.0997 (a 5-year sample means we see 4 years of compounding) CAGR = 1.0997 – 1 = 0.0997 – 9.97% g = 9.97% Michael Dimond School of Business Administration Ke with flotation cost • ABC Company is considering a SEO (Seasoned Equity Offering). Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. The planned dividend per share is $1.45 for the coming year, and they expect the growth of dividends to follow the same average growth it has for the past 5 years. Historic annual DPS are: • • • • • 2008 2009 2010 2011 2012 2.12 2.30 2.60 2.92 3.10 • What is their Cost of Equity for the SEO? • Ke = D1 / P0 + g • Ke = 1.45 / P0 + 0.0997 … what should we use for P0? Michael Dimond School of Business Administration Ke with flotation cost • Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. • Net Proceeds will be 48.22 – 1.00 – 2.86 = 44.36 • What is their Cost of Equity for the SEO? • Ke = D1 / P0 + g • Ke = 1.45 / 44.36 + 0.0997 = 0.1324 = 13.24% • What if they used Retained Earnings instead of issuing new stock? • Ke = 1.45 / 48.22 + 0.0997 = 0.1298 = 12.98% • Why is the cost of equity higher for new stock than for retained earnings? • What would happen if a company always issued new stock instead of funding growth from retained earnings? Michael Dimond School of Business Administration