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Week 9 Lecture 9

Week 9 Lecture 9. Ross, Westerfield and Jordan 7e Chapter 15 Cost of Capital. Last Week. Expected Returns and Variances Single asset & Portfolios Using probabilities & Historical returns Principle of Diversification Systematic and Unsystematic Risk Beta CAPM SML Reward to Risk Ratio.

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Week 9 Lecture 9

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  1. Week 9Lecture 9 Ross, Westerfield and Jordan 7e Chapter 15 Cost of Capital

  2. Last Week.. • Expected Returns and Variances • Single asset & Portfolios • Using probabilities & Historical returns • Principle of Diversification • Systematic and Unsystematic Risk • Beta • CAPM • SML • Reward to Risk Ratio

  3. Chapter 15 Outline • Cost of Capital: Introduction • Cost of Equity • Costs of Debt • Cost of Preferred Stock • Weighted Average Cost of Capital • Divisional and Project Costs of Capital • Flotation Costs

  4. Why Cost of Capital Is Important • The return to an investor is the same as the cost to the company • Our cost of capital provides us with an indication of how the market views the risk of our assets • Knowing our cost of capital can also help us determine our required return for capital budgeting projects

  5. Required Return = Cost of Capital • The Required Rate of Return = Discount Rate = Hurdle Rate = Cost of Capital • Need to know the required return for an investment so we can compute the NPV and decide whether or not to take the investment • Need to earn at least the required return to compensate investors for their financing • Required return – from the investor’s point of view • Cost of capital – from the firm’s point of view

  6. Cost of Capital • The firm is financed by a mixture of equity and debt • Cost of Capital is a mix of Cost of Equity and Cost of Debt • These costs are determined by the market • The firm determines the mix, Debt/Equity (D/E) reflecting it’s target capital structure. • To calculate cost of capital: • Calculate cost of equity • Calculate cost of debt • Combine them

  7. Cost of Equity • The cost of equity is the return required by equity investors, the shareholders on their investment in the firm • Since this cost is not directly observable, it must be estimated • There are two main methods for determining the cost of equity: • Dividend Growth Model • CAPM

  8. Cost of Equity - DGM Approach • Start with the dividend growth model formula where g is constant: • Where: RE is the required return for shareholders, P0 is the current price, D0 is the current/last dividend, D1 is the next dividend • and rearrange to solve for RE: • Where D1/P0 is the dividend yield, and g is the growth rate of dividends

  9. DGM - Example 1 • Bentex Ltd. recently paid a dividend of 40 cents per share. This dividend is expected to grow at 6% per year indefinitely. If the current market price of Bentex shares is $6 per share, estimate its cost of equity. • D0 = $0.40, g = 6%, P0 = $6, RE = ? D1 = D0(1 + g) = $0.40(1.06) = $0.424 RE = (D1 / P0) + g= (0.424/6.00) + 0.06 = 0.1307, and thus the cost of equity is 13.07%.

  10. DGM – Example 2 • Suppose ABC company is expected to pay a dividend of $1.50 per share next year. There has been a steady growth in dividends of 5.1% per year. The current price is $25. What is the cost of equity? • D1 = $1.50, g = 5.1%, P0 = $25, RE = ?

  11. Example - Estimating the Dividend Growth Rate ‘g’ • One method for estimating the growth rate is to use the historical average Year Dividend Change Return% • 2000 1.23 - • 2001 1.30 (1.30 – 1.23) / 1.23 = 5.7% • 2002 1.36 (1.36 – 1.30) / 1.30 = 4.6% • 2003 1.43 (1.43 – 1.36) / 1.36 = 5.1% • 2004 1.50 (1.50 – 1.43) / 1.43 = 4.9% • Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1% • Another way is use analysts’ forecast

  12. Advantages and Disadvantages of Dividend Growth Model • Advantage: • easy to understand and use • Disadvantages • Only applicable to companies currently paying dividends • Assumes dividend growth is constant • Cost of equity is sensitive to growth estimate • Does not explicitly consider risk

  13. Cost of Equity - CAPM or SML Approach • Recall CAPM for any asset i is: • The CAPM cost of equity is: • Use the following information to compute our cost of equity • RE = Required return for shareholders • Rf = Risk-free rate • E(RM) – Rf = Market risk premium • E = Systematic risk of firm’s equity relative to the market

  14. CAPM - Example • Suppose our ABC company has an equity beta of 0.58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is the cost of equity capital? • βE = 0.58, Rf = 6.1%, E(RM) – Rf = 8.6% RE = 0.061 + 0.58(0.086) = 11.1% • What if the expected market return is 8.6%? • RE = 0.061 + 0.58(0.086 – 0.061) = 7.55%

  15. Advantages and Disadvantages of CAPM • Advantages • Explicitly adjusts for risk • Applicable to all companies • Disadvantages • Have to estimate the expected market risk premium, which does vary over time • Have to estimate beta, which also varies over time • We are using the past to predict the future, which is not always reliable

  16. Example – Cost of Equity • Suppose our company has a beta of 1.5. The market risk premium is expected to be 9% and the current risk-free rate is 6%. The market believes our dividends will grow at 6% per year and our last dividend was $2. The stock is currently selling for $15.65. What is the cost of equity? • Using CAPM: RE = 6% + 1.5(9%) = 19.5% • Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55%

  17. Cost of Preferred Stock • Reminders • Preferred stock pays a constant dividend • Dividends are expected to be paid forever • Preferred stock return = Perpetuity RP • P0 = D/Rp RP = D / P0 • Example: • Your company has preferred stock that has an annual dividend of $3. If the current price is $25, what is the cost of preferred stock? • 25 = 3/Rp therefore RP = 3 / 25 = 12%

  18. Cost of Debt • The cost of debt is the required return on our company’s debt • We usually focus on the cost of long-term debt or bonds • The required return is best estimated by computing the yield-to-maturity or YTM • The cost of debt is NOT the coupon rate • For publicly listed debt use YTM • If the firm has no publicly traded debt, use YTM on similar debt that is traded.

  19. YTM of Bond • In general: • Where • C is coupon interest payment, • RD is required market return or YTM, • Tis the number of periods left until repayment, • Fis face value. • Need to solve for RD

  20. Example – Cost of Debt • Gloss Ltd issued a 20-year, 12% bond 10 years ago. The bond is currently priced at $860, and pays interest annually. What is its cost of debt? • Excel solution gives RD = 0.1476, meaning that Gloss’s cost of debt is 14.76%.

  21. Example - Cost of Debt • Suppose a firm has a bond issue currently outstanding that has 25 years left to maturity and pays coupons semiannually. The coupon rate is 9% per year. The bond’s current price is $908.72 per $1000 bond. What is the cost of debt? • t = 25 years x 2 = 50; C = $90/2 = 45; • F = $1000; Bond Price or P = $908.75; • RD or YTM = ? • By trial and error semiannual yield = 5% • YTM = RD = 5% x 2 = 10%

  22. Weighted Average Cost of Capital • We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm. • WACC is the required return on our assets, based on the market’s perception of the risk of those assets • The weights are determined by how much of each type of financing we use WACC = wE*RE + wP*RP + wD*RD

  23. Capital Structure Weights • Notation • E = market value of equity = nr. of outstanding shares times price per share • P = market value of preference shares = nr. of outstanding preference shares times price per share • D = market value of debt = nr. of outstanding bonds times bond price • V = market value of the firm = E + P + D • Weights • wE = E/V = percent financed with equity • wP = P/V = percent financed with preference stock • wD = D/V = percent financed with debt • wE + wP + wD = 1

  24. Example – Weights & WACC Cost of debt= 5.7 %, Cost of equity= 14.0 % Cost of preference shares = 9.0 % Source of CapitalM.ValueWeight Long term debt $40 m 40% Pref. shares $10 m 10% Equity $ 50 m 50% Total 100 m 100 % WACC = (E/V)*RE + (P/V)*RP + (D/V)*RD = (0.5)*0.14 + (0.1)*0.09 + (0.4)*0.057 = 0.1018 WACC = 10.18% (Unadjusted)

  25. WACC – Adjusted • The company gets a tax deduction for interest on debt, reducing the effective cost of debt. • If TC is the corporate tax rate then the after tax cost of debt is RD*(1  TC), and the WACC adjusted for taxation effects is given by: • WACC = wE*RE + wP*RPS + wD*RD*(1  TC) or • WACC = (E/V)*RE + (P/V)*RPS +(D/V)*RD*(1  TC) • Previous example: If tax rate is 30%, then WACC = (0.5)*0.14 + (0.1)*0.09 + (0.4)*0.057(0.7) = 0.0950 or 9.5%.

  26. Equity Information 50 million shares $80 per share Beta = 1.15 Market risk premium = 9% Risk-free rate = 5% Debt Information $1 billion in outstanding debt (face value) Current quote = 110% Coupon rate = 9%, semiannual coupons 15 years to maturity Tax rate = 40% WACC - Extended Example (1) Step 1: Calculate cost of equity and cost of debt Step 2: Calculate the market value of each source of financing and the weights Step 3: Calculate the WACC adjusting for tax.

  27. WACC - Extended Example (2) • What is the cost of equity? • βE = 1.5, Rf = 5%, RM – Rf = 9%, RE = ? • RE = 5% + 1.15(9%) = 15.35% • What is the cost of debt? • t = 15y x 2=30; Price = $1100; C = $90/2 = 45; F = $1000; by trial & error semi yield = 3.9268 • RD = 3.927% x 2 = 7.854% • What is the after-tax cost of debt? • RD(1-TC) = 7.854(1-0.4) = 4.712%

  28. WACC - Extended Example (3) • What are the capital structure weights? • E = 50 million x $80 = $4 billion • D = $1 b x 110% = $1.1 billion Or $1 b/1000 = 1 million bonds issued 1 m bonds x $1100 = $1.1 billion • V = 4 + 1.1 = 5.1 billion • wE = E/V = 4 / 5.1 = 0.7843 • wD = D/V = 1.1 / 5.1 = 0.2157 • What is the WACC? • WACC = wE*RE + wD*RD*(1  TC) • WACC = 0.7843(15.35%) + 0.2157(4.712%) = 13.06%

  29. Finding the Weights from D/E • Suppose Belo Corp has a target D/E ratio of 0.33. Cost of Debt is 10% and cost of equity is 20%. If tax is 34%, what is WACC? • First calculate WE and WD. • If D/E = 0.33 what is E = ? D = ? • Assign any value to equity. E = 1 • D/1= 0.33 then D = 0.33 and V = 1.33 • E/V = 1/1.33 = 0.7519 and • D/V = 0.33/1.33 = 0.2481 • WACC = wE*RE + wD*RD*(1  TC) • WACC = 0.75 x 0.20 + 0.25 x 0.10 x (1-0.34) = 16.65%

  30. Finding D/E • If BHP has a WACC of 21.67% and the cost of equity is 29.2%, cost of debt is 10%, what is it’s target D/E ratio? Assume tax is 34%. • We know that E + D = V or WE + WD = 1 • We express one in terms of another: • WE = 1 - WD • And insert in WACC equation: • 0.2167 = WE x 0.292 + WD x 0.10 x (1-0.34) • 0.2167 = (1-WD) x 0.292 + WD x 0.10 x (1-0.34)

  31. Finding D/E (cont.) • 0.2167 = (1-WD) x 0.292 + WD x 0.10 x (1-0.34) • Solve for WD the only unknown variable: • 0.2167 = 0.292 – WD x 0.292 + WD x 0.066 • 0.2167 – 0.292 = – WD x 0.292 + WD x 0.066 • -0.0753 = -WD x (0.292 - 0.066) • 0.0753 = WD x 0.226 • WD = 0.0753/0.2260 = 0.333 • Therefore WE = 1 – WD, WE = 1- 0.333 = 0.667 • D/E = 0.333/0.667 = 0.5

  32. Table 15.1 Cost of Equity & Debt

  33. Table 15.1 WACC

  34. Useful Websites • Yahoo Finance • Share price • Beta • Book value per share • Analysts estimates • T-Bill rate • www.nasdbondinfo.com • Bond information • www.sec.gov • Company filings • www.valuepro.net

  35. Divisional and Project Costs of Capital • Using the WACC as our discount rate is only appropriate for projects that have the same risk as the firm’s current operations • If we are looking at a project that does NOT have the same risk as the firm, then we need to determine the appropriate discount rate for that project • Divisions also often require separatediscount rates

  36. Using WACC for All Projects - Example Project Req. Ret. IRR WACC A 20% reject 17% accept 15% B 15% accept 18% accept 15% C 10% accept 12% reject 15% • Assume the WACC = 15% • If we use the WACC for all projects regardless of risk • Accept A and B, reject C • If correct required return based on specific risk is used • Accept B and C, reject A

  37. Divisional and Project costs of capital • WACC is the appropriate discount rate only when the project is about the same risk as the firm. • Other approaches to estimating a discount rate: • divisional cost of capital—used if a company has more than one division with different levels of risk; • pure play approach—a discount rate that is unique to a particular project is used; • subjective approach—projects are allocated to specific risk classes which, in turn, have specified discount rates.

  38. Other Approaches • Pure Play Approach: • Look at companies in the same line of business as the new project • Calculate an average WACC for all the companies and use this rate as the discount rate of the new project • Subjective Approach: • Consider the project’s risk relative to the firm overall risk • If the project risk > firm risk, use a discount rate > WACC • If the project risk < firm risk, use a discount rate < WACC

  39. Flotation Costs • The required return depends on the risk, not how the money is raised • However, the cost of issuing new securities should not just be ignored either • Basic Approach • Compute the weighted average flotation cost • Use the target weights because the firm will issue securities in these percentages over the long term fA = (E/V)*fE + (D/V)* fD • where fA is the weighted average flotation cost, fE is the equity flotation cost proportion, and fD is debt flotation cost proportion. • True cost of project = Cost/(1-fA)

  40. Flotation Cost Example • A firm has a target structure that is 80% equity and 20% debt. The costs for raising equity are 20% and the cost of raising debt are 6%. If the firm needs $65 million for a new facility, what is the true cost after accounting for flotation costs? fA = (E/V)*fE + (D/V)* fD = 0.8*0.2 + 0.2*0.06 fA= 0.172 or 17.2% • If the flotation cost is 17.2%, and we need to raise $65 million net, the true cost of the facility would be: $65/(1 - fA) = 65/0.828 = $78.50 million • The firm needs to raise $78.5 million to account for flotation costs and to have $65 million left to invest. • Since 78.5/65 = 1.2077, this suggests that for every dollar required by the project, the firm must raise $1.2077 to finance its projects.

  41. Quick Quiz • What are the two approaches for computing the cost of equity? • What is the cost of debt? • How do you compute the after-tax cost of debt? • How do you compute the capital structure weights required for the WACC? • When is appropriate to use WACC as the discount rate for projects? • What is the proportion of E and D if we have a D/E ratio of 1.2

  42. End Chapter 15

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