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Chapter 12

Chapter 12. The Cost of Capital. Chapter Overview Recall a capital budgeting decision looks like this: Invest only if NPV > 0 We know which CFs to use Total CF = OCF – D NWC - NCS Now we need to figure out what R to use . A capital budgeting decision looks like this:

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Chapter 12

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  1. Chapter 12 The Cost of Capital

  2. Chapter Overview • Recall a capital budgeting decision looks like this: Invest only if NPV > 0 • We know which CFs to use • Total CF = OCF – DNWC - NCS Now we need to figure out what R to use 

  3. A capital budgeting decision looks like this: • Now we need to figure out what R to use: • R is the required return of the project • It is the amount investors need to earn • Based on the risk of the company’s business • consumer products, consumer durables, luxury goods… • Pay CFO, Get CF1 through CFN • Recall: If R < IRR, then NPV > 0 • R is the return the company’s investors require • The company’s cost= What the investors earn • The Cost of Capitalis the Required Return

  4. Chapter Overview • So only do a project if: The return is more than the cost • Same as saying the project has a positive NPV • But what is the cost of the capital to the company? • The cost of capital is what investors demand from the company • What do investors demand? • It depends on the investor: • Some investors buy the company’s STOCK • And they earn an expected return on the stock • How do we calculate E(R)? (CAPM) • Some investors buy the company’s BONDS • And they earn a yield to maturity (YTM) on the bond • How do we calculate YTM? • Some investors buy the company’s PREFERRED STOCK • And they earn a yield (RP) on the preferred stock • How do we calculate the return on preferred stock?

  5. Chapter Overview • Determine a firm’s cost of capital raised from selling ownership stakes • Return paid to stock or equity holders (RE) • Determine a firm’s cost of capital raised from borrowing money • Return paid to bond or debt holders (RD) • Determine a firm’s cost of capital raised from selling Preferred Stock • Return paid to preferred stock holders (RP) • Determine a firm’s Weighted Average Cost of Capital: • Average these costs by their balance-sheet weights: • Call it the Weighted Average Cost of Capital WACC = WERE + WDRD(1 - T) + WPRP (We’ll get to the “(1 – T)” part later)

  6. Chapter Outline • Discuss why WACC is the appropriate discount rate for projects • Calculate WACC: • Calculate the Cost of Equity (RE) • Calculate the Cost of Debt (RD) • Calculate the Cost of Preferred Stock (RP) • Calculate the Weights (Capital Structure) • WACC Example • Discuss alternatives for projects with different risks

  7. Why is the WACC used for Capital Budgeting? In other words: Why is the WACC the denominator for NPV calcs? Simple Capital Budgeting Problem: • Consider a 1 year project that costs $100 and pays $110 in 1 year • If the discounted future CFs of a project is greater than the cost Then the NPV > 0  Accept the project • If the discount rate is 5%  NPV = -$100 + $110/(1.05) = $4.76 Here’s another way to think about this project: • What is the IRR of this project? • 0 = -$100 + $110/(1.10)  The IRR = 10% • Or: What is the “return” on the $100 invested in this project? • R = ($110/$100) – 1 = 10%  The Return = 10% • If we require 5% and the return is 10%, then the project adds value • NPV > 0 means a project’s return is greater than the required return So how do we figure out the required return? 

  8. How Much Return Does a Project Require? • Assume (for now) that the project is the same as the company’s other projects • It’s has the same risk as the company’s existing business • What return do investors require on the company’s existing business? • It depends on the risk of that business • The riskier the business, the higher the return

  9. How Much Return (Continued) Here’s the key point: • The RETURNto investors is the same as the company’s COST • What the investor receives, the company pays Conclusion: • The appropriate discount rate is the investors’ required return • Which is based on the project’s risk • A project must earn atleast the required return to compensate investors for providing the money • If the project earns exactly the required return, then the NPV = 0 • If the project earns less, then investors are not being compensated for the risk they are incurring in that project • Then the NPV < 0 • So the company should not use the investors capital for that project

  10. Calculating the Cost of Capital The Required Return equals the Cost of Capital: • The Cost of Capital raised from selling ownership (Equity or Stocks) • The Cost is the Required Return on Equity = RE • The Cost of Capital raised from borrowing money (Debt or Bonds) • The Cost is the Required Return on Debt = RD • The Cost of Capital raised from selling Preferred Stock • The Cost Required Return on Preferred = RP • Each of these costs are weighted by the portion used to finance the company activities • This is the WACC and is used to calculate NPV WACC = WERE + WDRD(1 - T) + WPRP How do we calculate each of these terms

  11. Calculating the Cost of Equity (RE) • The cost of equity is the return required by equity investors given the risk of the cash flows from the firm • All the risk? The total risk? • Measured by the standard deviation of returns? (s) • NO! • Investors need only be compensated for the Market Risk! • Measured by Beta (b) • Calculate the cost of equity (which is equal to the required return) using the CAPM (or the Security Market Line equation) • The CAPM shows the expected return on a company’s equity is: E(R) = Rf + b[E(RM) – Rf] • The return expected by the investor is the same as the return required by the investor and therefore the cost of equity to the firm • RE = Rf + b[E(RM) – Rf]

  12. Calculating RE Using the CAPM • According to the CAPM, the cost of equity to the firm is: • RE = Rf + b[E(RM) – Rf] Example: • Suppose the company has an equity beta of 0.58 • The risk-free rate is 6.1% • The expected market risk premium is 8.6% • Calculate the cost of equity capital: RE = Rf + b[E(RM) – Rf] = 6.1% + 0.58(8.6%) = 11.1%

  13. Clicker Question: • A firm has an equity beta of 1.50 • The risk-free rate is 2% • The expected market risk premium is 8.60% • Calculate the firm’s cost of equity capital. • 6.60% • 8.60% • 9.90% • 11.90% • 14.90%

  14. Clicker Answer:

  15. Calculating RE Using the Div Growth Model • Another way to calculate RE is to start with the constant dividend growth rate model and solve for R (Really RE): P0 = D1/(RE – g) RE = D1/P0 + g Example: • A company is expected to pay a $1.50 dividend next year • There has been a steady growth in dividends of 5.1% per year and the market expects that to continue • The current price is $25 • Calculate the cost of equity capital: RE = D1/P0 + g = $1.50/$25 + 0.051 = 0.111 = 11.1%

  16. Clicker Question: • A company will pay a $4.95 dividend in one year • There has been a steady growth in dividends of 5% per year and the market expects that to continue • The current price is $50 • Calculate the cost of equity capital: • 6.60% • 8.60% • 9.90% • 11.90% • 14.90%

  17. Clicker Answer:

  18. Estimating the Dividend Growth Rate (g) • Estimate g using the historic average: Average Annual Dividend Growth = 4.73% So assume g = 4.73%

  19. Advantage and Disadvantages of Dividend Growth Approach: • Advantage • Easy to understand and use • Disadvantages • Only applicable to companies currently paying dividends • Not applicable if dividends aren’t growing at a reasonably constant rate • Extremely sensitive to the estimated growth rate – an increase in g of 1% increases the cost of equity by 1% • Does not explicitly consider risk

  20. Advantages and Disadvantages of the CAPM (or SML) Approach • Advantages • Explicitly adjusts for systematic risk • Applicable to all companies, as long as we can compute beta • 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 relying on the past to predict the future, which is not always reliable

  21. Calculating the Cost of Debt (RD) • The cost of debt to the company is the same as the ReturnRequiredby the lenders • Return Required is the Amount Earned • Determined by the price • The required return is essentially the Yield To Maturity (YTM) • The higher the required return (YTM), the lower the price • The lower the required return (YTM), the higher the price

  22. Required Return is YTM NOTthe Coupon Rate • Bond holders earn the YTM, not the coupon rate • The coupon rate was the required return when the bond was issued • At that time YTM = Coupon Rate • If the bond’s price has gone down, bond holders get the coupons plus the capital appreciation • If the Price < Par, then the YTM > Coupon Rate • If the bonds price has gone up, bond holders get the coupons less the capital appreciation • If the Price > Par, then the YTM < Coupon Rate

  23. Required Return is YTM Semi-Annual Coupon Bond Example: • A $1,000 face value bond that makes semi-annual payments has 15 years to maturity. The coupon rate is 8%. The price is $1,044.57. Calculate the return required by people holding this debt: • N = 30, PMT = $40, FV = $1,000, PV = -$1,044.57, I/YR = 3.75 • 3.75% is the Semi-Annual YTM • The Annualized YTM = 0.0375 x 2 = 7.50%. • Holders of this bond require a 7.50% return • If the price is $958.05: • N = 30, PMT = $40, FV = $1,000, PV = -$9,58.05, I/YR = 4.25 • The Annualized YTM is 8.50%

  24. Clicker Question: • A company has an outstanding bond with 4 years to maturity. The bond pays a 8% semi-annual coupon and is priced at 87% of par. • Calculate the return required by people holding this debt. • In other words: How much would the company have to pay to issue new debt? • In other words: What would be the coupon rate on new debt? • 6.10% • 8.00% • 12.20% • 12.31% • 16.00%

  25. Clicker Answer:

  26. Calculating the Cost of Preferred Stock (RP) • The cost of preferred stock to the company is the same as the returnrequiredby holders • Recall: • Preferred (generally) pays a constant dividend every period • Dividends are expected to be paid every period forever • So Preferred stock is a perpetuity Price: P0 = D/RP • Solve for RP: RP = D/P0 • Example: • A company has preferred stock with an annual dividend rate of 10.80% • Recall the dividend is quoted as a percentage of the par value of $100 • The current price is $90 • Calculate the cost of preferred stock: RP= $10.80/$90 = 12%

  27. Clicker Question: • A company has outstanding preferred stock that pays a 7.50% dividend. • The current price is $105 • Calculate the return required by people holding this preferred. • In other words: How much would the company have to pay to issue new preferred stock? • In other words: What would be the dividend rate on new preferred stock? • 7.14% • 7.50% • 8.50% • 9.14% • 105.00%

  28. Clicker Answer:

  29. The Weighted Average Cost of Capital • Use the individual costs of capital (RE, RD and RP) • To get the “average” cost of capital for the firm • The WACCis the required return on the assets employed in the firm’s projects • Based on • The market’s perception of the risk of those projects • And the way the firm chooses to finance the assets • Meaning the weights of equity, debt and preferred • The weights are determined by how much of each kind of financing the firm chooses

  30. WACC Notation • E = Market Value of Equity = # outstanding shares x price per share • D = Market Value of Debt = # outstanding bonds x bond price • P = Market Value of Preferred = # outstanding shares x price per share • V = market value of the firm = D + E + P • Weights • WE = E/V = percent financed with equity • WD = D/V = percent financed with debt • WP = P/V = percent financed with preferred

  31. Capital Structure Weight Calculations A firm’s assets are financed with: • 10,000 shares of common stock at market value of $20 per share • Bonds outstanding with a total market value of $140,000 • 750 shares of preferred stock at a market value of $80 per share Calculate the Capital Structure Values: • E = 10,000 x $20 = $200,000 • D = $140,000 • P = 750 x $80 = $60,000 • V = E + D + P = $20,000 + $140,000 + $60,000 = $400,000 Calculate the Weights: • WE = $200/$400 = 0.50 • WD = $140/$400 = 0.35 • WP = $60/$400 = 0.15

  32. Clicker Question: A firm’s assets are financed with: • 100,000 shares of common stock with a market value or $10 • $1.2 million of outstanding bonds • 4,000 shares of preferred stock with a market value of $110 Calculate the Capital Structure Weights:

  33. Clicker Answer:

  34. Taxes and the WACC What really matters is the after-taxcost of capital • Interest expense (the cost of debt) reduces the company’s taxes • If the cost of debt (RD) is 8% • And the Tax rate is 35% • Then the firm can deduct 35%(8%) = 2.8% of the 8% cost of debt from its taxes • Its after-tax cost of debt is (1 – 35%)(8%) = 5.2% • WACC accounting for the after-tax cost of Debt: WACC = WERE + WDRD(1 - T) + WPRP

  35. Taxes and the WACC Note that when we calculated a project’s CFs: CF = OCF – DNWC – NCS OCF = (Sales – Costs)(1 – T) + Dep x T OCF = (Sales – FC – VC)(1 – T) + Dep x T • We did not account for INTEREST EXPENSE as a cost. • We will account for it now as a FINANCING EXPENSE • Not included as a cost or OPERATING EXPENSE • Included as part of the WACC • So Interest Expense is included in the WACC • But NOT Included as part of the operations

  36. 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 price = 110% of par Coupon rate = 9%, semi-annual coupons 15 years to maturity Tax rate = 40% (No Preferred Stock) WACC Example

  37. WACC Example Continued • Cost of equity (RE): • RE = RF + b[E(RM) - Rf]= 5 + 1.15(9) = 15.35% • Cost of debt (RD): • N = 30; PV = -1100; PMT = 45; FV = 1000; I/Y = 3.9268 • RD = 3.927(2) = 7.854% • Capital structure weights: • E = 50 million ($80) = 4 billion • D = 1 billion (1.10%) = 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 • WACC: • WACC = 0.7843(15.35%) + 0.2157(7.854%)(1 - 0.4) = 13.06% This is the discount rate for the company’s proposed projects

  38. Recap: Table 12.1 Page 400

  39. What if the Project is NOT the same? • WACC is appropriate discount rate 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 • We need to determine the appropriate discount rate for that project • Large companies with multiple divisions often require separate discount rates for each division

  40. Pure Play Approach • Find one or more companies that specialize in the product or service that being considered • Compute the average beta for these companies • Use that average beta in the CAPM to find the appropriate return for a project of that risk • But it is often difficult to find pure play companies

  41. Subjective Approach • Consider the project’s risk relative to the firm overall • If the project is riskier than the firm • Use a discount rate greater than the WACC • If the project is less risky than the firm • Use a discount rate less than the WACC • This may result in accepting projects that you should reject and rejecting projects you should accept • But the error rate should be lower than ignoring the difference in risk

  42. Compare D/V vs. D/E • If D/V = 20% then calculate D/E: • E/V = 1 - D/V = 80% • D/E = (D/V)/(E/V) = D/E = 0.20/0.80 = 0.25 • If D/V = 50% then calculate D/E: • E/V = 1 - D/V = 50% • D/E = (D/V)/(E/V) = D/E = 0.50/0.50 = 1.00 • If D/V = 60% then calculate D/E: • E/V = 1 - D/V = 40% • D/E = (D/V)/(E/V) = D/E = 0.60/0.40 = 1.50

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