INTRODUCTION TO CORPORATE FINANCE Laurence Booth W. Sean Cleary Prepared by Ken Hartviksen CHAPTER 20 Cost of Capital Lecture Agenda Learning Objectives Important Terms Financing Sources The Cost of Capital Estimating the Component Costs The Effect of Operating and Financial Leverage Growth Models and the Cost of Common Equity Risk-Based Models and the Cost of Common Equity The Cost of Capital and Investment Summary and Conclusions
Concept Review Questions Appendix 1 Steep Hill Mines # 1 CHAPTER 20 Cost of Capital 20 - 3 Learning Objectives 1. How ROE and the required return by common equity investors are related to a firms growth opportunities 2. How to apply the steps involved in estimating a firms weighted average cost of capital, including how to estimate the market values of the various components of capital, and how to estimate the various costs of these components 3. How operating and financial leverage affect firms 4. The advantages and limitations of using growth models and/or risk models to estimate the cost of common equity. CHAPTER 20 Cost of Capital 20 - 4 Important Chapter Terms
Asset turnover ratio Beta coefficient Capital asset pricing model Capital structure Cash cow Cost of capital Debt-to-equity ratio Dog Earnings yield Hurdle rate Investment opportunities schedule (IOS) Issuing (or floatation) costs Marginal cost of capital (MCC) Market-to-book (M/B) ratio Market risk premium Multi-stage growth DDM Operating leverage Present value of existing
opportunities (PVEO) Present value of growth opportunities (PVGO) Return on assets (ROA) Return on invested capital (ROIC) Return on equity (ROE) CHAPTER 20 Cost of Capital 20 - 5 Important Chapter Terms Risk-based model Risk-free rate of return Star Turnaround Weighted average cost of capital (WACC) CHAPTER 20 Cost of Capital 20 - 6 The Short Story of WACC Purposes/Use
The weighted average cost of capital (WACC) serves three primary purposes: 1. To evaluate capital project proposals before-the-fact. 2. To set performance targets in order for management to sustain or grow market values, and 3. to measure management performance after-the-fact. CHAPTER 20 Cost of Capital 20 - 7 The Short Story of WACC What Costs are Measured? Costs associated with financing the firms invested capital including: Debt Costs: Bank loans Long-term debt bonds/debentures Equity Costs: Preferred equity costs Common equity costs CHAPTER 20 Cost of Capital 20 - 8 The Short Story of WACC Why the Marginal Cost? What capital cost the firm 5 months, 5 years or 5 decades ago is irrelevant.
What is relevant is what the next dollar of capital will cost in todays economic environment for this particular firm. CHAPTER 20 Cost of Capital 20 - 9 The Short Story of WACC Steps in Solving for the WACC 1. Identify the relevant sources of capital (debt and equity). 2. Estimate the market values for the sources of capital and determine the market value weights. 3. Estimate the marginal, after-tax, and afterfloatation cost for each source of capital. 4. Calculate the weighted average. CHAPTER 20 Cost of Capital 20 - 10 The Short Story of WACC The Formula Once you have the specific marginal costs of capital (after accounting for taxes and floatation costs) and you have found the appropriate weights to use, the actual calculation of a WACC is a simple matter. S D WACC K a K e K d (1 T ) V
V The cost of equity times the market value weight of equity CHAPTER 20 Cost of Capital The cost of debt after tax times the market value weight of debt 20 - 11 The Short Story of WACC The Spreadsheet Approach (1) Type of Capital Long-Term Debt Preferred Stock Common Stock (2) (3) (4) = (2)*(3) Specific Marginal Cost Weighted
after tax and Market Specific floatation Value Marginal costs Weights Cost 5.5% 11.4% 12.9% 43.0% 11.0% 46.0% WACC = 0.02365 0.01254 0.05934 9.55% WACC is the sum of the weighted specific marginal costs of each source of capital. CHAPTER 20 Cost of Capital 20 - 12 The Short Story of WACC Frequently Asked Questions 1. Why dont we include the cost of accruals and accounts payable in the cost of capital?
These are spontaneous liabilities that rise and fall with the volume of business activity, and are not subject to formal lending arrangements. Accruals (wages and taxes), it can be argued, dont have an explicit cost. For major corporations, spontaneous liabilities are often a very small part of the overall capitalization of the firm (are immaterial for cost of capital purposes). CHAPTER 20 Cost of Capital 20 - 13 The Short Story of WACC Frequently Asked Questions 2. Why is the cost of capital an estimate and does this matter? WACC is calculated based on a current estimate of what it will cost for the next dollar of debt and equity. Since that next dollar hasnt yet been raised, we are attempting for forecast or estimate that cost. To estimate the cost of debt we often assume it is equal to the required rate of return on existing debt outstanding in the markets (Of course, when a firm actually goes to the market, conditions may have changed, underwriting costs may be greater, etc.) Forecasting WACC also requires estimating the cost of equity. There may different approaches to this task, and will result in a range of estimates. In the end, WACC will still be an estimate. The key thing to ensure is
that the NPV of the project be positive over the range of possible WACCs. (Graph an NPV profile and determine the range of WACCs that will still produce a positive NPV.) CHAPTER 20 Cost of Capital 20 - 14 The Short Story of WACC Frequently Asked Questions 3. Why is the component cost of capital greater than the investors required return ? Table 20-1 Main Balance Sheet Accounts Cash and marketable securities Accruals Accounts receivable Accounts payable Inventory Short-term debt Total current liabilities Prepaid expenses Total current assets Net fixed assets Total assets $18.00
Investment Dealer $20.00 Long-term debt Shareholders' equity Total liabilities and shareholders' equity Investment dealer gives the issuing Investor requires buys onea firm $18.00 for the The company must produce Issuing company new share returninona her share, pocketsthan10% Conclusion: The is and greater $2.00 income on an cost $18.00of external capital receives
$18.00. company and of $20. pays $2.00 forbecause providing of investment investment to meet thethe investors required return the investment This is a $2.00 underwriting investors expectations. This is floatation costs. dealer on return $20invested for it. services. an 11.1% return. capital. CHAPTER 20 Cost of Capital 20 - 15 The Short Story of WACC Summary
WACC measures the firms cost of financing future growth today, based on current capital market conditions, and assuming the firm use a long-term average of financing sources. WACC is an estimate. WACC is used to make capital investment decisions. WACC is used to set performance targets for sales, and ROE. WACC is used to assess managements performance, answering the question, has management added value? CHAPTER 20 Cost of Capital 20 - 16 Financing Sources Capital Structure Table 20 - 1 illustrates the basic structure of a firms balance sheet:
This is a snapshot of the firms financial position at one point in time. Left-hand side of the Balance Sheet Assets the things the firm owns Note the structure of assets (relative proportions of current assets and net fixed assets) Right-hand side of the Balance Sheet Liabilities the borrowed sources of financing Note the structure of liabilities (the relative proportions of current versus long-term debt) Shareholders equity owners investment in the business Note the amount of capital invested versus the amount of earnings that have been reinvested in the business CHAPTER 20 Cost of Capital 20 - 17 Financing Sources Capital Structure Table 20-1 Main Balance Sheet Accounts Cash and marketable securities Accruals Accounts receivable Accounts payable Inventory
Short-term debt Prepaid expenses Total current assets Net fixed assets Total assets Total current liabilities Long-term debt Shareholders' equity Total liabilities and shareholders' equity Capital The Financial Structure Structure CHAPTER 20 Cost of Capital 20 - 18 Important Terms Financial Structure The whole right-hand side of the balance sheet Includes both short-term and long-term sources of financing (debt and equity) Capital Structure How the firm finances its invested capital Excludes accruals and accounts payable short-term liabilities that are not strictly debt contracts, that spontaneously change in response to the operations of the business. Includes:
Bank Loans Long-term debt Common stock and retained earnings (See Table 20 2 for a typical example) CHAPTER 20 Cost of Capital 20 - 19 Financing Sources Capital Structure Table 20-2 A "Simplified" Balance Sheet Cash and marketable securities Accounts receivable Inventory Prepaid expenses Total current assets Net fixed assets Total assets $50 200 250 0 500 1,500 $2,000 Accruals Accounts payable Short-term debt Total current liabilities Long-term debt
Shareholders' equity Total liabilities and shareholders' equity $100 200 50 350 650 1,000 $2,000 Financial Capital Structure Structure==$1,700 $2,000 CHAPTER 20 Cost of Capital 20 - 20 Financing Sources Interpreting Balance Sheets Balance sheets are prepared in accordance with GAAP: Represent historical costs which may not be relevant for current decision-making purposes. Analysis of reported data should include ratios such as: Debt to Equity: Interest bearing debt to shareholders equity plus minority interest Convert book values to market values This is done by multiplying the market-to-book ratio times the book
value. Interpret the ratios again. (Table 20 2 will be used to illustrate the adjustment process from book values to market values) CHAPTER 20 Cost of Capital 20 - 21 Financing Sources Debt-to-Equity Ratio Table 20-2 A "Simplified" Balance Sheet Cash and marketable securities Accounts receivable Inventory Prepaid expenses Total current assets Net fixed assets Total assets $50 200 250 0 500 1,500 $2,000 Accruals Accounts payable Short-term debt Debt =
Total current liabilities Long-term debt Equity = Shareholders' equity Total liabilities and shareholders' equity Debt - to - Equity Ratio $100 200 50 350 650 1,000 $2,000 $50 $650 0.70 $1,000 CHAPTER 20 Cost of Capital 20 - 22 Financing Sources Converting Book Value to Market Values Table 20-2 A "Simplified" Balance Sheet Cash and marketable securities Accounts receivable Inventory Prepaid expenses
Total current assets Net fixed assets Total assets $50 200 250 0 500 1,500 $2,000 Book Values Accruals $100 Accounts payable 200 Short-term debt 50 Total current liabilities 350 Long-term debt 650 Equity = Shareholders' equity 1,000 Total liabilities and shareholders' equity $2,000 Market valuevalue of debt will
be very close not equal) to the book The market market value ofoflong-term equity isdebt greatly will(if depend affected on byinterest rate values stated balance sheet. to This is market-to-book because these are changes management. sinceon the Itthe isdebt not was
uncommon originally issued. see As the bonds contractual claims that are not negotiable (traded in secondary approach ratios of 2maturity, or more, their reflecting market the pricegrowth will move prospects progressively the to markets). The amounts stated amounts that are
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market-to-book ratio of 2.5. CHAPTER 20 Cost of Capital 20 - 23 Financing Sources Converting Book Value to Market Values Table 20-2 A "Simplified" Balance Sheet Cash and marketable securities Accounts receivable Inventory Prepaid expenses Total current assets Net fixed assets Total assets $50 200 250 0 500 1,500 $2,000 Accruals Accounts payable Short-term debt Total current liabilities Long-term debt Shareholders' equity Total liabilities and shareholders' equity
Book Values Market Values $100 $100 200 200 50 50 350 350 650 650 1,000 2,500 $2,000 $3,500 When adjusted for market value effects, the apparent $50 $650 high debtvaltoued" equity (.7)Ratio is a much lower " Market Debt -ratio to - Equity 0.0.28. 28 $2,500 This confirms the importance of using relevant data when
making decisions. CHAPTER 20 Cost of Capital 20 - 24 The Most Important Corporate Finance Decisions It is the managers job to maximize shareholders wealth. In this and the next chapter we will address two of the most important ways manager can add value to the firm: Changing the mix of financing used by the firm (changing the relative proportions of debt and equity), and Determining the minimum rate of return needed to maintain the current market value. CHAPTER 20 Cost of Capital 20 - 25 Valuation Equation for a Perpetuity Three Ways of Using the Valuation Equation In Chapter 5 you learned how to determine the present value of an infinite stream of equal, periodic cash flows (an infinite annuity). If the annual cash [ 20-1] $2.00S X S
$20.00 [ 20-1] 0.10 K e flow is $2.00 and the investors required return is 10%, the present value of the perpetuity is $20. Where: S = the present value of the perpetuity X = the forecast annual earnings Ke = the investors required return CHAPTER 20 Cost of Capital 20 - 26 Valuation Equation for a Perpetuity Three Ways of Using the Valuation Equation The equation can be rearranged to solve for the required return Ke also known as the earnings yield: [ 20-2] X X $2.00 K e Ke 10% S S $20.00 The earnings yield is not normally used as the
investors required return because it simply measures forecast earnings as a percentage of the market price, ignoring growth opportunities. CHAPTER 20 Cost of Capital 20 - 27 Valuation Equation for a Perpetuity Three Ways of Using the Valuation Equation The perpetuity valuation model can be further rearranged to solve for the forecast earnings given the current market price and investors required return. [ 20-3] X K Kee SS 0.10 $20.00 $2.00 This helps managers determine their earnings target that must be met to support the current market value. If the manager knows the investor requires a 10% rate of return and the market price is $20.00, she knows the firm must generate $2.00 in EPS to sustain the stock price. CHAPTER 20 Cost of Capital 20 - 28 Setting Performance Targets Using Required Returns and Market Values
Given market values and required rates of return, it is possible to establish performance targets for management to sustain market values: For a firm financed by bondholders and stockholders, the firm must plan to earn sufficient returns as follows: (1) Debt (D) Equity (S) V=D+S = Market Value $700 2500 $3,200 (2) Required Return 6.0% 12.0% (3) =(1)(2) Earnings Required $42 300 $342 Working back from these requirements we can forecast the level of sales the firm must earn in order to achieve these operating resultsthereby setting a sales performance target for management.
CHAPTER 20 Cost of Capital 20 - 29 Setting Performance Targets Deriving the Required Income Statement Sales Variable Costs Fixed Costs EBIT $300 $158 $542 $1,000 Table 20-3 A Forecasted Income Statement Sales Variable costs Fixed costs EBIT Interest Tax (40%) Net Income ? 300 158 ? 42 #VALUE! $300 $1,000 300 158 $542 42 200 $300
Given the to Net need Income EBIT Interest earn $42 to cover (1 T ) interest, and to $300 earn $42 $300after$42 $500 $542 (1 .4) tax for shareholders, and given a fixed corporate tax rate and other costs, we can determine the Sales required to achieve these goals. This is the very process that is used by regulators to approve regulated It is $1,000 utility rates based on market-determined required rates of return. So, the cost of capital drives utility rate increases. CHAPTER 20 Cost of Capital
20 - 30 Setting Performance Targets How Market Value is Related to Book Value and ROE Once you have the sales performance target you can establish other operating targets through the application of ratios. Since equity in this case is a perpetuity we can express the price per share as: [ 20-4] P EPS ROE BVPS Ke Ke Dividing both sides of Equation 20 4 by BVPS we get the basic relationship that drives the M/B ratio: CHAPTER 20 Cost of Capital 20 - 31 Setting Performance Targets The Relationship Between BVPS and MVPS How to Increase Shareholder Value Equation 20 5 tells us: If the ROE exceeds the investors required return ( Ke) then the price of the stock will rise above book value.
[ 20-5] P ROE BVPS Ke This is a crucial goal of the financial manager to add to shareholder value. CHAPTER 20 Cost of Capital 20 - 32 The Cost of Capital Determining the Weighted Average Cost of Capital (WACC) The overall market value of the firm is: V=D+S In our example V= $3,200 After-tax ROI = 19.13% = (EBIT)(1-T) = ($542 (1-.4)) = $325.20 This is the required net income if the firm is financed 100% with equity (no deduction for interest.) CHAPTER 20 Cost of Capital 20 - 33 The Cost of Capital Determining the Weighted Average Cost of Capital (WACC) Where the value of the firm is $3,200 and EBIT (1 T) is
$325.60, we can find the discount rate that sets them equal. First rewrite EBIT minus taxes as ROI IC and re-express the valuation equation as: [ 20-6] V ROI IC Ka Equation 20 6 can be rearranged to solve for Ka for an all equity firm: CHAPTER 20 Cost of Capital 20 - 34 The Cost of Capital Determining the Weighted Average Cost of Capital (WACC) Ka [ 20-7] ROI IC V Using the numbers from the continuing example the WACC is: Ka ROI IC $325.20
10.16% V $3,200 On the following slide will show how we can now substitute in component costs for both equity and debt to develop the general equation for WACC (Ka) CHAPTER 20 Cost of Capital 20 - 35 The Cost of Capital Determining the Weighted Average Cost of Capital (WACC) [ 20-8] Ka ROI IC K e S K d ( 1 T)D S D K e K d ( 1-T) V V V V The WACC is simply the weighted average of the component costs. CHAPTER 20 Cost of Capital
20 - 36 The Cost of Capital Determining the Weighted Average Cost of Capital (WACC) The equation for WACC including common equity, preferred share financing and debt is: [ 20-9] WACC K e S P D K p K d ( 1-T) V V V In this case the value of the firm equals the sum of the value of stock, preferred and debt: V=S+P+D CHAPTER 20 Cost of Capital 20 - 37 Estimating Market Values Market Value of Equity The total market value of equity (market capitalization) is the price per share times the
number of shares outstanding: [ 20-10] S P0 n CHAPTER 20 Cost of Capital 20 - 38 Estimating Market Values Market Value of Preferred Stock The market price for preferred is simply the annual preferred dividend divided by the preferred shareholders required return. [ 20-11] P0 Dp kp The market value of all preferred stock is simply the price per share times the number of shares outstanding. [ 20-10] S P0 n CHAPTER 20 Cost of Capital 20 - 39
Estimating Market Values Market Value of Bonds As previously mentioned, the market value of bonds will differ from their book value only if required rates of return in the market have changed since the bonds original issue. Knowing the term to maturity, the coupon rate and the bondholders required return we can determine the market value of bonds with equation 20 - 12: [ 20-12] 1 1 ( 1 k )n b B I kb 1 F ( 1 k b )n CHAPTER 20 Cost of Capital
20 - 40 Estimating Market Values Market Value of Bonds Once you know the market value of the bonds, you multiply their price by the number of bonds outstanding to determine total market value. [ 20-10] B Pb n CHAPTER 20 Cost of Capital 20 - 41 Market Value Weights An Example Given: Market price for common stock = $21.50 Bonds are trading for 95% of face value In order to calculate market value (MV) weights, you will need to know the total market value of debt, and common stock (and preferred stock if the company uses it.) To calculate total MV you need to know the current price of the security in each class, as well as the total number of securities outstanding: Total Market Capitalization = Price Quantity The following balance sheet date, when combined with market price data, will allow you to calculate MV weights. CHAPTER 20 Cost of Capital
20 - 42 Market Value Weights An Example XYZ Company Limited XYZ Company Limited Balance Sheet Balance Sheet as at January 30, 2xxx as at January 30, 2xxx ASSETS ASSETS Current Assets Current Assets Net Fixed Assets Net Fixed Assets Common stock (1,000,000 outstanding) Common stock (1,000,000 outstanding) Retained earnings Retained earnings TOTAL ASSETS TOTAL ASSETS LIABILITIES: LIABILITIES: $147,000Current $147,000Current Liabilities $147,000Current $147,000Current Liabilities 15,000,2508.5% 15,000,2508.5% 2020 Mortgage Bonds 15,000,2508.5%
15,000,2508.5% 2020 Mortgage Bonds $75,250 $75,250 4,000,000 4,000,000 7,155,000 7,155,000 3,917,000 3,917,000 $15,147,250TOTAL $15,147,250TOTAL LIABILITIES AND O. EQUITY $15,147,250TOTAL $15,147,250TOTAL LIABILITIES AND O. EQUITY $15,147,250 $15,147,250 Number Face value of common of bonds shares are $1,000, outstanding therefore is read there frommust the be 4,000
balance bondssheet. outstanding. CHAPTER 20 Cost of Capital 20 - 43 Market Value Weights An Example Continued Total MV of Equity = Price per share times number of shares = 1M $21.50 = $21.5M Total MV of Bonds = Price per bond times number of bonds = $950 4,000 = $3,800,000 Type of Capital Bonds Stock Market Total Market price Number Value $950.00 4,000 $3,800,000 $21.50 1,000,000 $21,500,000 TOTAL= $25,300,000 Market Value
Weight 15.02% 84.98% 100.00% These weights could now be used to calculate WACC. CHAPTER 20 Cost of Capital 20 - 44 Bond Value General Formula In the example, you didnt have to calculate the bond value because you were given the fact that it was trading at 95% of par. In the event that you do, however, simply use equation 20 -12. [ 20-12] 1 1 ( 1 k )n b B I kb 1 F
( 1 k b )n Where: I = interest (or coupon ) payments kb = the bond discount rate (or market rate) n = the term to maturity F = Face (or par) value of the bond CHAPTER 20 Cost of Capital 20 - 45 Estimating the Component Costs Floatation Costs Issuing or floatation costs are incurred by a firm when it raises new capital through the sale of securities in the primary market. These costs include: Underwriting discounts paid to the investment dealer Direct costs associated with the issue including legal and accounting costs The result: Net proceeds on the sale of each security is less than what the investor invests, and The component cost of capital > investors required return. Table 20 4 illustrates average issuing costs for different forms of capital. CHAPTER 20 Cost of Capital 20 - 46
Estimating the Component Costs Floatation Costs and the Marginal Cost of Capital (MCC) Table 20-4 Average Issuing Costs Commercial paper Medium-term notes Long-term debt Equity (large) Equity (small) Equity (private) 0.125% 1.0% 2.0% 5.0% 5.0% - 10.0% 10.0% and up Floatation costs for debt securities is lowest because debt is normally privately placed with large institutional investors not requiring underwriting costs and because debt is either issued by high quality issuers or sits at the top of the priority of claims list in the case of default.
What issue costs mean is that there is a financing wedge between what the investor pays and what the firm receives, the difference being the money that is lost to these costs. Issue costs are responsible for the component cost of capital being greater than the investors required return. CHAPTER 20 Cost of Capital 20 - 47 WACC versus MCC Floatation Costs and the Marginal Cost of Capital (MCC) The Marginal Cost of Capital (MCC) is the weighted average cost of the next dollar of financing to be raised. At low levels of financing the WACC = MCC As a firm raises more and more capital in a given year, it will exhaust the supply of lower cost sources, and then have to access marginally higher cost sources. Therefore MCC increases with the amount of capital to be raised. The following figure illustrates the MCC concept. CHAPTER 20 Cost of Capital 20 - 48 The Marginal Cost of Capital MCC S D K d (1 t ) V V There is only one break in the MCC curve. It
60 40 12% 8%(1 .3)occurs at $5,500,000. At this point the firm has 100 100 exhausted its internal equity and to raise more 12%(.6) 5.6%(.4) equity capital will mean accessing external 7.2% 2.24% 9.44equity % using the services of an underwriter. MCC1 K e (%) 15 MCC2= 10.64% MCC1=WACC= 9.44% 10 Each dollar of capital invested up to $5.5 million is financed 60% by internal equity (R/E). (60% cost 5 S D K d (1 t )
V V 60 40 14% 8%(1 .3) 100 100 14%(.6) 5.6%(.4) 8.4% 2.24% 10.64% MCC2 K e of retained earnings = 7.2%) Each dollar of capital invested beyond $5.5 million is financed 60% by new equity. (60% cost of new equity = 8.4%) 2.24% Each dollar of capital invested is financed 40% by debt. (40% after-tax cost = 2.24%) 0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000
Dollars of Capital to be Raised CHAPTER 20 Cost of Capital 20 - 49 The Component Cost of Debt The cost of debt is a function of: The investors required rate of return The tax-deductibility of interest expense The floatation costs incurred to issue new debt CHAPTER 20 Cost of Capital 20 - 50 The Component Cost of Debt If you know the debt investors required rate of return Kd , the corporate tax rate and the floatation cost percentage for debt, you can estimate the cost of debt in the following manner: Assume: Kd = 10% (debt investors required return) T = 40% (corporate tax rate) fd = 3% (floatation cost percentage) Cost of Debt
The after tax cost of debt is lower than the investors required return because of the tax shield on interest expense. Investor's Required Return (1 - T) 1- fd 10% (1.0 - 0.4) 6% 6.19% 1 - .03 0.97 CHAPTER 20 Cost of Capital 20 - 51 Estimating the Component Costs Debt Alternatively you can adjust the bond valuation formula for the tax-deductibility of interest expense and the net proceeds the firm would receive on the sale of one bond (after floatation costs) and solve for the rate (Ki ) that causes the formula to become and equality: Coupon interest times 1 minus corporate tax rate = after tax cost of interest [ 20-13]
1 1 ( 1 K )n i NP I (1 T ) Ki 1 F ( 1 K i )n Net proceeds on the sale of the bond = Selling price floatation cost per bond. Ki = the after-tax and after-floatation cost of debt. CHAPTER 20 Cost of Capital 20 - 52 Estimating the Component Costs Preferred Shares If you know the preferred share investors required rate of return Kp , and the floatation cost percentage for
preferred share financing, you can estimate the cost of preferred shares in the following manner: Floatation costs cause the component cost to be greater than the investors required return. Cost of Preferred Assume: Kp = 14% (preferred investors required return) F = 5% (floatation cost percentage) Investor's Required Return 1- fp 14% 14% 14.74% 1 - .05 0.95 NOTE: Preferred dividends are paid out of after-tax earnings, therefore there are no taxation effects on the preferred share component cost of capital.
CHAPTER 20 Cost of Capital 20 - 53 Estimating the Component Costs Preferred Shares Alternatively, the component cost of preferred shares can be found using equation 20 -14, where NP is the selling price per preferred share less the floatation costs per share. [ 20-14] Kp Dp NP CHAPTER 20 Cost of Capital 20 - 54 Estimating the Component Costs Common Shares Estimating the component cost of common stock is the most difficult because: Promised cash flows are uncertain Growth opportunities, their timing and magnitude will influence the cost The riskiness of the stock is influenced by corporate decisions such as the use of leverage
There are numerous alternative approaches that we will present to estimate the component cost of equity. Before doing so, we will first address the effect of leverage on shareholders. CHAPTER 20 Cost of Capital 20 - 55 Leverage The increased volatility in operating income over time, created by the use of fixed costs in lieu of variable costs. Leverage magnifies profits and losses. There are two types: Operating leverage Financial leverage Both types of leverage have the same effect on shareholders but are accomplished in very different ways, for very different purposes strategically. CHAPTER 20 Cost of Capital 20 - 56 Leverage Effects on Operating Income When a firm
increases Normal volatility of the use of fixed costs it operating income increases the volatility of operating income. Operating Income + 0 Years CHAPTER 20 Cost of Capital 20 - 57 Operating Leverage What is it? How is it Increased? Your textbook defines operating leverage as: The increased volatility in operating income caused by fixed operating costs. You should understand that managers do make decisions affecting the cost structure of the firm. Managers can, and do, decide to invest in assets that give rise to additional fixed costs and the intent is to
reduce variable costs. This is commonly accomplished by a firm choosing to become more capital intensive and less labour intensive, thereby increasing operating leverage. CHAPTER 20 Cost of Capital 20 - 58 Operating Leverage Advantages and Disadvantages Advantages: Magnification of profits to the shareholders if the firm is profitable. Operating efficiencies (faster production, fewer errors, higher quality) usually result increasing productivity, reducing downtime etc. Disadvantages: Magnification of losses to the shareholders if the firm does not earn enough revenue to cover its costs. Higher break even point High capital cost of equipment and the illiquidity of such an investment make it: Expensive (more difficult to finance) Potentially exposed to technological obsolescence, etc. CHAPTER 20 Cost of Capital 20 - 59
Financial Leverage What is it? How is it Increased? Your textbook defines financial leverage as: The increased volatility in operating income caused by fixed financial costs. Financial leverage can be increased in the firm by: Selling bonds or preferred stock (taking on financial obligations with fixed annual claims on cash flow) Using the proceeds from the debt to retire equity (if the lenders dont prohibit this through the bond indenture or loan agreement) CHAPTER 20 Cost of Capital 20 - 60 Financial Leverage Advantages and Disadvantages Advantages: Magnification of profits to the shareholders if the firm is profitable. Lower cost of capital at low to moderate levels of financial leverage because interest expense is tax-deductible. Disadvantages: Magnification of losses to the shareholders if the firm does not earn enough revenue to cover its costs. Higher break even point. At higher levels of financial leverage, the low after-tax cost of debt is offset by other effects such as:
Present value of the rising probability of bankruptcy costs Agency costs Lower operating income (EBIT), etc. CHAPTER 20 Cost of Capital 20 - 61 Effects of Operating and Financial Leverage Summary Equity holders bear the added risks associated with the use of leverage. The higher the use of leverage (either operating or financial) the higher the risk to the shareholder. Leverage therefore can and does affect shareholders required rate of return, and in turn this influences the cost of capital. HIGHER LEVERAGE = HIGHER COST OF CAPITAL CHAPTER 20 Cost of Capital 20 - 62 The Importance of Growth To this point we have been valuing stock as a perpetuity: This means that we are assuming the current dividend will be paid each year in the future into infinity. Table 20 8 illustrates the importance of growth opportunities to the price of dividend paying stocks on the TSX. On average, 62.22% of the market value of this
sample of firms could be attributed to growth opportunities and the remaining 37.78% to the present value of the current dividend (perpetuity value) CHAPTER 20 Cost of Capital 20 - 63 Growth Models and the Cost of Common Equity The Importance of Adjusting for Growth Current stock price Table 20-8 Stock Prices and Growth Prospects Stock Market Time Horizon Company Price ($) DPS ($) AGF BC Gas CAE Dennings EL Financial GSW (A) Hammersen Intrawest Jannock Average
25.75 30.60 11.50 3.50 285 26.75 14.05 6.95 29.60 0.283 1.13 0.161 0.102 0.570 0.428 0.197 0.292 0.148 Dividend Perpetuity Growth Yield (%) ($) Value (%) 1.10 3.70 1.40 2.90 0.20 1.60 1.40 4.20 0.50
1.89 5.66 22.60 3.22 2.04 11.40 8.56 3.94 5.84 2.96 78.0 26.0 72.0 42.0 96.0 68.0 72.0 16.0 90.0 Perpetuity value of current dividend % of Current Market Value explained by growth opportunities.
62.22 Source: Booth, Laurence, Table 1 from "What Drives Shareholder Value." Financial Intelligence IV-6, Spring 1999. CHAPTER 20 Cost of Capital 20 - 64 Growth Models and the Cost of Common Equity The Constant Growth Model The Gordon model assumes constant growth in the stream of dividends from t =1 through : [ 20-15] P0 D1 K g The price of a share (P0 ) today equals the expected dividend at t =1 dividend b the required shareholder return (K e ) minus the long-run growth rate (g) . This formula can be rearranged to solve for the investors required rate of return (K e ): CHAPTER 20 Cost of Capital 20 - 65 Constant Growth Model The Cost of Common Equity Using Internal Funds
Investors required rate of return consists of two components: 1. Expected dividend yield 2. Expected long-run growth rate (g) [ 20-16] Ke D1 g P0 This is the cost of internal equity (the cost of retained earnings where the firm does not need to incur floatation costs) CHAPTER 20 Cost of Capital 20 - 66 Constant Growth Model The Cost of New Equity The model can be modified to solve for the cost of new equity by using NP (net proceeds the firm receives for each new share sold after floatation costs)
[ 20-17] K ne D1 g NP CHAPTER 20 Cost of Capital 20 - 67 Constant Growth Model Caution The constant growth model can only be used in cases where it is reasonable to assume that the growth rate can be sustained in the very long term. This usually means, using it only for large, mature blue-chip companies that already pay a significant dividend. The Gordon model SHOULD NOT be used on smaller, more rapidly growing firms where high current growth rates are experienced, but cannot be sustained in the long term. CHAPTER 20 Cost of Capital 20 - 68 Growth Models and the Cost of Common Equity
Growth and ROE One way to estimate growth is the sustainable growth method: Growth rate is the product of the firms retention rate (b), times the forecast ROE: [ 20-18] g b ROE This definition of g can be used in the Gordon model: CHAPTER 20 Cost of Capital 20 - 69 Growth Models and the Cost of Common Equity Growth and ROE Substituting the sustainable growth rate into the Gordon model: [ 20-19] P0 D1 K e b ROE Now we can recognize that the expected dividend D1 is the expected earnings per share (X1) times the dividend payout ratio (one minus the retention rate):
CHAPTER 20 Cost of Capital 20 - 70 Growth Models and the Cost of Common Equity Growth and ROE This equation shows that the price per share is determined by: The firms forecast EPS Dividend payout (1 b) ROE Required return by common shareholders (Ke) [ 20-20] P0 X 1 (1 b) K e b ROE This equation shows the higher the growth rate, the higher the share price because larger future dividends and earnings are forecast. CHAPTER 20 Cost of Capital 20 - 71
Growth Models and the Cost of Common Equity Growth and ROE Rearranging Equation 20 20 by substituting alternative expressions for D1 and g : [ 20-21] Ke D1 X ( 1 b) g 1 b ROE P0 P0 When this equation is used to estimate the cost of equity capital (internal) for three different growth scenarios (10%, 12% and 14%) we get some unusual results summarized in Table 20 9: CHAPTER 20 Cost of Capital 20 - 72 Growth Models and the Cost of Common Equity Growth and ROE Table 20-9 Growth and K e ROE
P0 Expected Dividend Yield Sustainable Growth Rate Ke 10% 12% 14% $14.29 $16.67 $20.00 7% 6% 5% 5% 6% 7% 12% 12% 12% Three
different sustainable Stock Aprice lower rises dividend as As The firms retention rate, and thus its dividend payout ratio,yield. is reflected in the growth expectedprices growthrise, ratedividends rises. as a constant growth DDM as b. rates. percentage of share price, Table 20 10 on the next slide gives the share pricefall. if the retention rate changes under the three scenarios where ROE is 10, 12 and 14%. CHAPTER 20 Cost of Capital 20 - 73
Growth Models and the Cost of Common Equity Growth and ROE Table 20-10 Retention Rates, ROE, and Share Prices ROE Retention rate increases as you go south. b 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58
0.59 0.60 14.0% $18.75 18.85 18.95 19.06 19.18 19.30 19.42 19.56 19.70 19.84 20.00 20.16 20.34 20.52 20.72 20.93 21.15 21.39 21.65 21.93 22.22 12.0% $16.67 16.67 16.67 16.67 16.67 16.67
16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 CHAPTER 20 Cost of Capital 10.0% $15.00 14.94 14.87 14.81 14.74 14.67 14.59 14.52 14.44 14.37 14.29 14.20 14.12 14.03
13.94 13.85 13.75 13.65 13.55 13.44 13.33 The shareholders required return is 12%. When When ROE ROE = = When ROE = 14%, share 10%, 12%, share share price price When a firm retains more price remains increases as decreases as earnings and
thereinvests same as the firm retains the the firm retains them at a lower rate than firm more money. more money. what shareholders increases the require, theretention value ofrate. the firm falls. Clearly, the key to share price growth is to reinvest earnings at rates greater than the cost of capital. 20 - 74 Hurdle Rate The Cost of Capital
Table 20 -10 tells us that the cost of capital is a hurdle rate. The HURDLE RATE is the return on an investment required to create value; below this rate, an investment will destroy value. CHAPTER 20 Cost of Capital 20 - 75 Growing Firms Versus Growth Firms Growing Firms Reinvests in projects that offer rates equal to its cost of capital: ROE = Ke Growth Firms Does something that shareholders cannot do reinvest earnings at rates higher than the cost of capital. ROE > Ke CHAPTER 20 Cost of Capital 20 - 76 Growth Firms Importance of the Reinvestment Rate of Return Growth Firms Does something that shareholders cannot do reinvest earnings at rates higher than the cost of capital. ROE > Ke
This is the reason earnings yield is not an appropriate estimate of the firms cost of capital. What is relevant is NOT whether dividends or earnings are growing, but rather WHETHER THE FIRM IS INVESTING AT RATES OF RETURN GREATER THAN THE COST OF CAPITAL. Of course, this means, the firm should be investing in projects with positive NPVs (IRRs > cost of capital) CHAPTER 20 Cost of Capital 20 - 77 Growth Models and the Cost of Common Equity Multi-Stage Growth Models Multi-stage DDM is a version of the DDM that accounts for different levels of growth in earnings and dividends. There is no limit to the number of growth stages one can forecast for a given company, so this is a very flexible model. See Chapter 7 for detailed pricing model description. CHAPTER 20 Cost of Capital 20 - 78 Simple Two-stage Growth Model Multi-Stage Growth Models
Equation 20 22 is a simple, two-stage growth model. It breaks the stock price into two components: 1. 2. PVEO present value of existing opportunities (the value of the firms current operations assuming no new investment) and PVGO present value of growth opportunities the net present value today of the firms future investments. [ 20-22] ROE1 BVPS Inv ROE2 K e P0 ( ) Ke (1 K e ) Ke PVEO CHAPTER 20 Cost of Capital PVGO 20 - 79 Simple Two-stage Growth Model PVEO and PVGO
[ 20-22] P0 ROE1 BVPS Inv ROE2 K e ( ) Ke (1 K e ) Ke PVEO PVGO PVGO is discounted back to the present by one year because it represents an incremental investment decision today that wont result in the first cash flow until one year from now. PVGO does add a perpetual amount represented by the difference between ROE2 earned on this added investment and Ke CHAPTER 20 Cost of Capital 20 - 80 Simple Two-stage Growth Model PVGO and ROE2
[ 20-22] P0 ROE1 BVPS Inv ROE2 K e ( ) Ke (1 K e ) Ke PVGO If If ROE2 = Ke then the future investment adds nothing to the value of the firm ROE2 > Ke then the future investment adds value to the firm CHAPTER 20 Cost of Capital 20 - 81 Simple Two-stage Growth Model Scenarios PVEO and PVGO
P0 [ 20-22] ROE1 BVPS Inv ROE2 K e ( ) Ke (1 K e ) Ke PVGO Four Scenarios: High PVEO and High PVGO High PVEO and Low PVGO Low PVEO and High PVGO Low PVEO and Low PVGO - Star - Cash Cow - Turnaround - Dog (These four scenarios are found in matrix form in Figure 20 -1 ) CHAPTER 20 Cost of Capital 20 - 82 Simple Two-stage Growth Model Growth Opportunities and Firm Type
20 - 1 FIGURE CHAPTER 20 Cost of Capital 20 - 83 Simple Two-stage Growth Model Growth Opportunities and Firm Type Star Growth Company High PVEO and high PVGO DCF methods of valuation are unreliable due to high growth Turnaround Growth Company Low PVEO and high PVGO Poor PVEO drags down stock price today DCF methods of valuation are unreliable due to high growth Cash Cow High PVEO and low PVGO DCF methods of valuation are reliable due to lack of growth we are valuing a perpetuity Dog Low PVEO and low PVGO High earnings yield forecast to lose value from future investments depressing the current share price.
(See Table 20 -11 for earnings yield and Market-to-book ratios for each type.) CHAPTER 20 Cost of Capital 20 - 84 Simple Two-stage Growth Model Growth Opportunities and Firm Type Table 20-11 The Impact of Growth Opportunities on Share Prices Earnings Yield (%) Market-to-Book Star 8.84 2.26 Cash cow 12.00 1.67 Turnaround 2.63 0.76 114.29 0.02
Dog CHAPTER 20 Cost of Capital 20 - 85 Growth Models and the Cost of Common Equity The Fed Model Used by the U.S. central bank to estimate whether the stock market was over- or undervalued Used to decide whether the Central Reserve Bank should send signals to the market to encourage reason in the market place (to avoid speculative bubbles and the inevitable price collapse that follows) Attempting to avoid irrational exuberance! The Fed Model equation is found on the next slide. CHAPTER 20 Cost of Capital 20 - 86 Growth Models and the Cost of Common Equity The Fed Model [ 20-23] Vactual Vactual
) VFed Exp( EPS ) /( K TBond 1.0%) Actual value Expected of the EPS U.S. on stock S&P 500 index Estimate of the U.S. stock Aggregate valuation across the entire market is easier because a market. divided (Total by market yield on
long U.S. market value from the Fed unsystematic risk attached to individual securities is eliminated as a capitalization). model. Treasury bonds. factor for the market as a whole. CHAPTER 20 Cost of Capital 20 - 87 Growth Models and the Cost of Common Equity The Fed Model The Feds estimate of market value = Expected EPS on S&P 500 divided by Yield on Long U.S. Treasury Bonds minus 1.0%. All of this data is continuously, readily available so this estimate of value is easy to produce and to track over time as illustrated in Figure 20 2 on the following slide: [ 20-24] VFed Exp( EPS ) ) ( K TBond 1.0%) Aggregate valuation across the entire market is easier because unsystematic risk attached to individual securities is eliminated as a factor for the market as a whole.
CHAPTER 20 Cost of Capital 20 - 88 The Fed Model Feds Stock Valuation Model 20 - 2 FIGURE CHAPTER 20 Cost of Capital 20 - 89 Growth Models and the Cost of Common Equity The Fed Model If the Fed Model is rearranged it can show when the market is fairly valued: [ 20-25] X PS&P 500 K TBond -1.0% CHAPTER 20 Cost of Capital 20 - 90 Growth Models and the Cost of Common Equity The Fed Model
When the earnings yield on the S&P 500 (market) is equal to the long-term Treasury Bond yield minus 1.0 percent, the market is fairly valued. The earnings yield is the appropriate discount rate for the nogrowth case. (perpetuities), whereas we would expect the market as a whole to grow at the nominal GDP growth rate. [ 20-25] X PS&P 500 K TBond -1.0% Required return on the market as a whole = Long Treasury Yield + 4.0% risk premium. (5% nominal GDP 1%). CHAPTER 20 Cost of Capital 20 - 91 Growth Models and the Cost of Common Equity The Fed Model Required return on the market as a whole = Long Treasury Yield + 4.0% risk premium. (5% nominal GDP 1%). [ 20-25] X PS&P 500 K TBond -1.0% The required rate of return on the market as a whole can
serve as a useful benchmark for financial managers as they attempt to estimate their own firms cost of capital. CHAPTER 20 Cost of Capital 20 - 92 Risk-Based Models and the Cost of Common Equity Using the CAPM to Estimate the Cost of Common Equity CAPM can be used to estimate the required return by common shareholders. It can be used in situations where DCF methods will perform poorly (growth firms) CAPM estimate is a market determined estimate because: The RF (risk-free) rate is the benchmark return and is measured directly, today as the yield on 91-day T-bills The market premium for risk (MRP) is taken from current market estimates of the overall return in the market place less RF (ER M RF) CHAPTER 20 Cost of Capital 20 - 93 Risk-Based Models and the Cost of Common Equity Using the CAPM to Estimate the Cost of Common Equity As a single-factor model, we estimate the common shareholders required return based on an estimate of the systematic risk of the firm (measured by the firms beta coefficient)
[ 20-26] K e RF MRP e Where: Ke = investors required rate of return e = the stocks beta coefficient Rf = the risk-free rate of return MRP = the market risk premium (ERM - Rf ) CHAPTER 20 Cost of Capital 20 - 94 Risk-Based Models and the Cost of Common Equity Estimating the Market Risk Premium [ 20-26] K e RF MRP e Rf is observable (yield on 91-day T-bills) Getting an estimate of the market risk premium is one of the more difficult challenges in using this model. We really need a forward looking of MRP or a forward looking estimate of the ERM One approach is to use an estimate of the current, expected MRP by examining a long-run average that prevailed in the past. Table 20 -12 illustrates the % returns on S&P/TSX Composite annually for the first five years of this century. CHAPTER 20 Cost of Capital
20 - 95 Risk-Based Models and the Cost of Common Equity Using the CAPM to Estimate the Cost of Common Equity Table 20-12 Returns on the S&P/TSX Composite Index Returns 2000 7.5072% 2001 -12.572% 2002 -12.438% 2003 26.725% 2004 14.480% 2005 24.127% Investors are
It would be unlikely to expect better use negativetoreturns on the stock average market. If they realized did, no one would returns over hold shares! an entire Who would have business/mar guessed before ket there cycle. hand, would be two consecutive years of aggregate market losses? Such is the reality of investing since none of us are clairvoyant.
CHAPTER 20 Cost of Capital 20 - 96 Risk-Based Models and the Cost of Common Equity Using the CAPM to Estimate the Cost of Common Equity Long-run average rates of return are more reliable. Table 20-13 Average Investment Returns and Standard Deviations (1938 to 2005) Annual Annual Arithmetic Geometric Average (%) Mean (%) Government of Canada Treasury Bills Government of Canada Bonds Canadian Stocks U.S. Stocks 5.20 6.62 11.79 13.15 5.11 6.24 10.60 11.76 Standard Deviation of Annual Returns (%)
4.32 9.32 16.22 17.54 Source: Data f rom Canadian Institute of Actuaries Average premium ofisCanadian The risk consensus that the stocks bonds 5.17% bondover yield (anwas observable Canadian MRP over the long-term yield) is between 4.0 and 5.5%. CHAPTER 20 Cost of Capital 20 - 97 Risk-Based Models and the Cost of Common Equity Using the CAPM to Estimate the Cost of Common Equity Table 20-14 Long-Run Financial Projections Financial Forecasts
Average Annual Percent Return Bank of Canada Overnight Rate 4.50 Cash: 3-Month T-bills 4.40 Income: Scotia Universe Bond Index 5.60 Canadian Equities: S&P/TSX Composite Index 7.30 U.S. Equities: S&P 500 Index 7.80 International Non-U.S. Equities: MSCI EAFE Index 7.50 Source: TD Economics The Scotia Universe is a long-term bond index that An estimate of ERM isBond
very Index important. contains Canadas and corporate bonds with default risk. TD Economicson recently generated the above Nevertheless, a risk-adjusted basis, the TDestimates forecast of forforward MRP is looking rates. consistent with an arithmetic risk premium of 4.3% CHAPTER 20 Cost of Capital 20 - 98 Risk-Based Models and the Cost of Common Equity Estimating Betas After obtaining estimates of the two important market rates (Rf and MRP), an estimate for the company beta is required. Figure 20 -3 illustrates that estimated betas for major sub-indexes of the S&P/TSX have varied widely over time:
CHAPTER 20 Cost of Capital 20 - 99 Risk-Based Models and the Cost of Common Equity Estimated Betas for Sub Indexes of the S&P/TSX Composite Index 20 - 3 FIGURE CHAPTER 20 Cost of Capital 20 - 100 Risk-Based Models and the Cost of Common Equity Estimated Betas for Sub Indexes of the S&P/TSX Composite Index Actual data for Figure 20 -3 is presented in Table 20 15 on the following slide: You should note: IT sub index shows rapidly increasing betas Other sub index betas show constand or decreasing trends. Reasons: The weighted average of all betas = 1.0 (by definition they are the market) If one sub index is changingthat change alone affects all others in the opposite direction. What Happened in the 1995 2005 decade? The internet bubble of the late 1990s resulted in rapid growth in the IT sector till it burst in the early 2000s. CHAPTER 20 Cost of Capital
20 - 101 Risk-Based Models and the Cost of Common Equity Estimating Betas IT Bubble Table 20-15 S&P/TSX Sub Index Beta Estimates Energy Materials Industrials ConsDisc ConsStap Health Fin IT Telco Utilities 1995 0.93 1.41 1.19
0.82 0.68 0.36 0.92 1.25 0.53 0.67 1996 0.93 1.28 1.10 0.83 0.66 0.39 1.02 1.36 0.61
0.65 1997 0.98 1.33 0.97 0.82 0.62 0.60 0.93 1.56 0.62 0.53 1998 0.85 1.12 0.94
0.80 0.60 1.02 1.11 1.40 0.92 0.55 1999 0.91 1.04 0.78 0.73 0.43 1.00 1.00 1.55 1.11
0.30 2000 0.67 0.74 0.73 0.69 0.23 1.10 0.79 1.78 0.92 0.14 2001 0.50 0.60 0.82
0.68 0.10 0.98 0.67 2.12 0.94 -0.03 2002 0.43 0.57 0.86 0.73 0.11 0.99 0.67 2.27 0.92
-0.06 2003 0.27 0.42 0.91 0.74 -0.04 0.85 0.39 2.75 0.82 -0.26 2004 0.17 0.42 1.04
0.81 -0.02 0.84 0.41 2.89 0.55 -0.14 2005 0.48 0.78 1.12 0.84 0.14 0.74 0.58 2.71 0.71
-0.01 Source: Data from Financial Post Corporate Analyzer Database CHAPTER 20 Cost of Capital 20 - 102 Risk-Based Models and the Cost of Common Equity Nortel Stock Price Nortels stock price reflects the IT bubble and crash. (See Figure 20 -4 on the following slide for Nortel Stock Price history) CHAPTER 20 Cost of Capital 20 - 103 Risk-Based Models and the Cost of Common Equity Nortel Stock Price 20 - 4 FIGURE CHAPTER 20 Cost of Capital 20 - 104 Risk-Based Models and the Cost of Common Equity
IT Bubble effect on Betas of Other Companies Outside the Sector The bubble in IT stocks has driven down the betas in other sectors. This is demonstrated in Rothmans beta over the 1966 2004 period. Remember, Rothmans is a stable company and its beta should be expected to remain constant. (See Figure 20 -5 on the following slide for Rothmans beta history) CHAPTER 20 Cost of Capital 20 - 105 Risk-Based Models and the Cost of Common Equity Rothmans Beta Estimates 20 - 5 FIGURE CHAPTER 20 Cost of Capital 20 - 106 Risk-Based Models and the Cost of Common Equity Adjusting Beta Estimates and Establishing a Range When betas are measured over the period of a sector bubble or crash, it is necessary to adjust the beta estimates of firms in other sectors. Take the industry grouping as a major input, plus the individual company beta estimate.
Using current MRP and Rf Develop estimates of Ke using the range of Company betas prior to the bubble or crash CHAPTER 20 Cost of Capital 20 - 107 Risk-Based Models and the Cost of Common Equity Using CAPM to Estimate Kne We can scale our estimate of the equity holders required return when accessing new equity and incurring floatation costs. [ 20-27] K ne K e P0 / NP CHAPTER 20 Cost of Capital 20 - 108 The Investment Opportunity Schedule The IOS is the ranking of a firms investment opportunities from highest to lowest profitability according to expected IRR. When superimposed on the MCC curve, the firm is able to identify projects that will increase the value of the firm. A stylized version of this for Rothmans is found in Figure 20 6.
CHAPTER 20 Cost of Capital 20 - 109 Cost of Capital and Investment Rothmans Inc.s IOS Schedule, 2006 20 - 6 FIGURE OPTIMAL INVESTMENT Rate of Return Projects expected to increase the value of the firm. IOS Projects rejected. The break in the MCC at $177,607 million indicates that the firm has a surplus of internally-generated fundsmore than enough to fund the $11,976 of capital investments. WACC
Internal Funds Available $11,976 Million $177,607 Million CHAPTER 20 Cost of Capital 20 - 110 Investment Opportunity Schedule A Detailed Example In practice, the IOS is a detailed list, rank ordered from highest IRR to lowest of the investment project proposals for one year. As you can see on the following slides: The width of the columns indicate the capital investment each project requires, and The height of the columns indicates the forecast IRR for the project CHAPTER 20 Cost of Capital 20 - 111 Investment Opportunity Schedule A Detailed Example In any one year, a firm may consider a number of capital projects. The greater the number of projects undertaken, the more
money that the firm will have to raise in order to finance them. There is a limit to the amount of money that can be raised in any one year (ie. the capital markets are finite ie. there is a limit to the number of investors and their investment dollars that will consider investing in any prospect in any given year.) hence it is important that the capital budgeting analysis be extended to take this fact into account. CHAPTER 20 Cost of Capital 20 - 112 Investment Opportunity Schedule A Detailed Example This Investment opportunity schedule is the prioritized list of capital projects, listed by IRR (internal rate of return) from highest to lowest. At the same time, the cumulative investment required is listed. Example: Consider a firm that has six different capital investment proposals this year. Each project has its own IRR and capital cost. (see the next slide) CHAPTER 20 Cost of Capital 20 - 113 Investment Opportunity Schedule A Detailed Example
Example: Consider a firm that has six different capital investment proposals this year. Each project has its own IRR and capital cost. Each project has the same risk as the firm as a whole. Capital Project A B C D E F Project A can be eliminated at this point because it has a negative NPV. Initial Cost $1,500,000 $2,300,000 $3,750,000 $180,000 $985,000 $2,154,000 Annual ATCF Useful Benefits Life NPV IRR $290,000
7 -$88,159 8.19% $529,000 6 $3,933 10.06% $940,000 6 $343,945 13.07% $40,000 7 $14,737 12.45% $318,540 5 $222,517 18.50% $421,500 8 $94,671 11.20% CHAPTER 20 Cost of Capital 20 - 114 Investment Opportunity Schedule A Detailed Example Example: The first step in developing an IOS is to order the projects from highest IRR to lowest, and then to calculate the cumulative capital cost of the projects. Capital Cumulative Cost Project Initial Cost of the Projects E
C D F B A $985,000 $3,750,000 $180,000 $2,154,000 $2,300,000 $1,500,000 $985,000 $4,735,000 $4,915,000 $7,069,000 $9,369,000 $10,869,000 CHAPTER 20 Cost of Capital IRR 18.50% 13.07% 12.45% 11.20% 10.06% 8.19% 20 - 115 Investment Opportunity Schedule
A Detailed Example Continued Example: It was clear at the start that project A was unacceptableit had a negative NPV. The remaining projects certainly meet the first investment screen (they have positive NPVs that is, they offer rates of return in excess of the firms WACC). Now we can prepare a graphical representation of the IOS by plotting the projects IRR against the cumulative dollars of capital to be raised. CHAPTER 20 Cost of Capital 20 - 116 Investment Opportunity Schedule (IOS) A Detailed Example Continued IRR E (%) The height of each cylinder is equal to the projects IRR; the width is equal to the initial investment for the project. D IRR = 18.5% 15
The upper surface of the columns is the IOS IRR = 12.45% C IRR = 13.07% 10 F B IRR = 11.2% IRR = 10.06% 5 0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000
Dollars of Capital to be Raised CHAPTER 20 Cost of Capital 20 - 117 Investment Opportunity Schedule (IOS) A Detailed Example Continued IRR E (%) D IRR = 18.5% 15 IOS IRR = 12.45% C IRR = 13.07% 10 F
B IRR = 11.2% IRR = 10.06% 5 0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000 Dollars of Capital to be Raised CHAPTER 20 Cost of Capital 20 - 118 MCC Superimposed on the IOS A Detailed Example Continued IRR E
(%) D IRR = 18.5% 15 The break in the MCC IRRis caused MCC2 B < by the exhaustionso ofthis low project cost retained earnings and the need Itto is rejected. finance project F through willexternal not offering of equity,increase incurringthe floatation costs. value of the firm. IRR = 12.45%
C IRR = 13.07% MCC2= 10.64% 10 MCC1=WACC= 9.44% F B IRR = 11.2% IRR = 10.06% 5 0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000 Dollars of Capital to be Raised
CHAPTER 20 Cost of Capital 20 - 119 The Break In the IOS A Detailed Example Continued The break in the IOS curve (the amount of capital investment that exhausts retained earnings) can be estimated as: Break in MCC $ of Retained Earnings Available for Investment Percentage that Equity Makes Up in the Capital Structure Assuming the firm has $3.3 million in internal capital to invest and equity represents 60% of the firms capital structure the break point occurs at: Break in MCC $3,300,000 $5,500,000 60% CHAPTER 20 Cost of Capital 20 - 120 MCC and IOS The foregoing is consistent with economic theory that states a firm will operate where marginal cost equals marginal revenue. Now the rationale for this must be clear. The
value of the firm will fall if it undertakes projects that offer a rate of return that is less than the marginal cost of capital used to finance them. CHAPTER 20 Cost of Capital 20 - 121 Divisional Costs of Capital An overall cost of capital developed for a highly diversified conglomerate may not be appropriate for decisions made within specific divisions of the company. High-risk divisions (with high return possibilities) would have a disproportionate share of their investment proposals accepted if they use an overall WACC. The solution to this is to develop risk-adjusted discount rates that reflect the unique risk characteristics of each division. Developing these estimates can sometimes be accomplished by looking at other firms in that industry that are not highly diversified in their operations this is called the pure play approach. CHAPTER 20 Cost of Capital 20 - 122 Summary and Conclusions In this chapter you have learned: How types of equity differ in their degree of equityness and therefore have different costs of capital WACC is the market value weighted average of the after-tax costs of all securities used to finance the firm. If a firm earns more than its WACC, the value of the firm will
rise. Common shareholders are residual claimants hence they hold the riskiest securities issued by the firm. The most difficult estimate in WACC is the cost of common equity. DCF approaches to estimating the cost of equity is particularly prone to errors for high growth firms. CAPM can be used to minimize estimation errors, however, estimation of beta can be affected by recent stock market performance. CHAPTER 20 Cost of Capital 20 - 123 Appendix 1 Steep Hill Mines 1 An Exercise in Cost of Capital Steep Hill Mines # 1 The Question Steep Hill Mines Ltd. shares are publicly traded on the Toronto Stock Exchange. The shares currently trade at a price of $30.00 per share. Security analysts that follow the stock have estimated it's beta coefficient to be 0.9. Steep Hill paid a dividend on its common stock last year that totaled $1.50 per share. Dividends have been growing at a 4% compound rate for the past six years and the expectation is that this growth can continue into the foreseeable future. Steep Hill also has it's long-term bonds trading on public markets. The bonds are currently trading at a discount from their par value of 96.54%. These 5.75% bonds have ten years left until they mature. Steep Hill Mines Ltd. has an important capital project to consider. Project A is expected to produce annual cash flows after tax of $100,000 for the next eight years. It is considered to be of similar risk to
the risk of the firm itself. It will cost Steep Hill $400,000 this year to get this project up and running. CHAPTER 20 Cost of Capital 20 - 125 Steep Hill Mines # 1 The Question Cathy Jones, Steep Hill's manager of finance has collected current data from the firm's underwriters. Government of Canada 91-day Treasury bills are currently yielding 4.25%. The expected return on the TSE 300 composite index is forecast to be 10% in the next year New equity capital could be raised by the firm at the current market price, but floatation costs would amount of 4% of the value of the issue. New bonds could be sold into the market, but the floatation cost percentage would be 6%. The firm faces a corporate tax rate of 40%. The company will seek to sustain the current capital structure based on existing market value weights. If the firm goes ahead with the capital project, it will have to seek external financing since there is no internal cash flow available for reinvestment. The firm's most recent financial statements are found below: CHAPTER 20 Cost of Capital 20 - 126 Steep Hill Mines # 1 The Question Assets: Cash 100
Accounts Receivable Inventories Total Current Assets Gross Fixed Assets Accumulated Depreciation Net Fixed Assets TOTAL ASSETS Steep Hill Mines Ltd. Balance Sheet As at December 31, 20XX In $ '000s Liabilities: Accruals 30 220 Accounts Payable 312 450 ____ 770 Total Current Liabilities 342 4,000 5.75% bonds 1,000 1,500 Common stock (100,000 outstanding) 1,000 2,500 Retained earnings 928 3,270 TOTAL CLAIMS
3,270 Required: Find the WACC using book value weights, market value weights and target capital structure weights. Using the target capital structure weights, is the proposed project viable? CHAPTER 20 Cost of Capital 20 - 127 Steep Hill Mines # 1 The Solution The Equity Investors Required Return Investor's Required Return on Equity Capital: DDM Approach: KS D0 (1 g ) $1.50(1.04) $1.56 g .04 .04 0.052 .04 9.2% P0 $30 $30 CAPM Approach: K S RF Bs [ ERM RF ] 4.25% 0.9[10% 4.25%] K S 4.25% 5.175% 9.425% CHAPTER 20 Cost of Capital 20 - 128
Steep Hill Mines # 1 The Solution The Cost of Equity Investor's Required Return on Equity Capital The average of our two estimates for the cost of retained earnings is: (9.2 + 9.425)/2 = 9.3% This is the returns our current shareholders are demanding on our stock. If we raise external capital, we will incur floatation costs (underwriter's fees, legal costs, etc.) This represents 4%. Investors Required Return 1- f 9.3% 9.3% 9.7% .96 1 - .4 Cost of New Equity CHAPTER 20 Cost of Capital 20 - 129 Steep Hill Mines # 1 The Solution Investor's Required Return on Debt [ 20-12]
1 1 n ( 1 kb ) 1 F B I kb ( 1 k b )n 1 1 20 ( 1 kb ) 1 F $965.40 $28.75 kb ( 1 kb )20
k b 3.11% semiannually k b 3.11% 2 6.22% CHAPTER 20 Cost of Capital 20 - 130 Steep Hill Mines # 1 The Solution The Cost of Debt Since interest on debt is tax deductible to the firm, the after-tax and after floatation cost of debt is: 6.22%(1 T ) 6.22%(1 .4) Kd 3.97% 1 f 1 .06 Where: T= f= 40% 6% CHAPTER 20 Cost of Capital 20 - 131 Steep Hill Mines # 1 The Solution Determining Market Value Weights
Market Value Weights: Market values are always found by multiplying the number of outstanding securities times their price per unit. Market Value of LT Debt = 1,000 bonds outstanding times $965.40 = Market Value of Equity = 100,000 times $30.00 = TOTAL MARKET VALUE OF THE FIRM = $965,400 3,000,000 3,965,400 Market Value Weight of LT Debt = $965,400/$3,965,400 = 24.35% Market Value Weight of Equity = (1 - .2435) = 75.65% CHAPTER 20 Cost of Capital 20 - 132 Steep Hill Mines # 1 The Solution Market Value WACC The Cost of Capital Using Market Value Weights: Source of Capital L. T. Debt Preferred Common Market Value
Weight 24.4% 0.0% 75.7% Specific Marginal Cost 3.97% 0.00% 9.70% WACC = CHAPTER 20 Cost of Capital Weighted Cost 0.97% 0.00% 7.34% 8.30% 20 - 133 Steep Hill Mines # 1 The Solution Viability of the Capital Project Since the project has similar risk characteristics to the firm as a whole, we do not have to calculate a risk-adjust discount rateinstead, we can just use the firm's WACC. Since the market value capital structure weights will be used by the firm in the long run, let's use that as the WACC, and discount the prospective after-tax cash flows on this project
back to the present and compare that with the cost of the project to see if there is a positive NPV. CHAPTER 20 Cost of Capital 20 - 134 Steep Hill Mines # 1 The Solution Project NPV [ 13-1] NPV CF1 CF2 CF3 ... CF0 1 2 3 (1 k ) (1 k ) (1 k ) n CF t i 1
t CF0 (1 k ) $100,000(PVIFA n 8,k WACC ) $400,000 $100,000(PVIFA n 8,k 8.3% ) $400,000 1 (1.083)8 $100,000 $400,000 .083 $100,000(5.681788) $400,000 $568,178 $400,000 1- NPV $168,178 CHAPTER 20 Cost of Capital Using Equation 13 -1 for NPV, and substituting in the annual cash flow benefits of $100,000 aftertax, initial cost, useful life of 8 years, and WACC of 8.3% we find the project offers a positive NPV. 20 - 135
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