This Document Contains Chapters 9 to 12 Chapter 9 Time Value of Money Author's Overview This is one of the most important chapters in the book as far as student comprehension is concerned. The instructor should first determine how much prior knowledge of time value of money the students have acquired from accounting or lower mathematics. While most students are generally familiar with the concepts of future value and present value, they often lack the ability to identify and categorize the nature of the problem before them. The material in this chapter will serve as a springboard to the remaining chapters in this section on valuation, cost of capital and capital budgeting related topics. A good background in time value of money will ease the transition. The authors suggest a liberal use of homework problems and a quiz to reinforce the importance of this material. This chapter has made use of time lines that should be particularly helpful to students in understanding concepts. These are very good at relating future value to present value, present value to the present value of annuities, and future value to future value of annuities. Chapter Objectives 1. Explain the concept of the time value of money. This is the idea that a dollar received today is worth more than a dollar received in the future. 2. Calculate present values, future values, and annuities based on the number of periods involved and the going interest rate. 3. Calculate yield based on the time relationships between cash flows. Annotated Outline and Strategy I. Money has a time value associated with it. A. The investor/ lender demands that financial rent be paid on his or her funds. B. To understand the effective rate on a business loan, the return on an investment, etc., is dependent on using the time value of money. C. Calculator 1. Study the time value keys on a business calculator. 2. Shown on the time line the calculator keys should be similar to those below: 3. The compute key assumes payments (PMT) are at the end of each period (n). The begin (BGN), or due, key assumes payments (PMT) are at the start of each period (n). 4. Input known values and solve for the unknown value. D. The interest rate is also referred to as a discount rate, rate of return, or yield. II. Future Value: Single Amount A. In determining future value, we measure the value of an amount that is allowed to grow at a given interest rate over a period of time. B. The relationship may be expressed by the following formula: (9-1; page 258) C. (Optional) The formula may be restated as: The FVIF term is found in appendix A. D. Calculator Compute FV = $1,262.48 E. To get the interest factor with the calculator input 1 for the present value. III. Effective or Nominal Interest Rate A. The effective interest rate includes any compounding effects over the relevant time period. By formula: (1 + i) n – 1 = effective interest rate (9-2; page 259) Where i = interest rate per compounding period Finance in Action: Starting Salaries 50 Years from Now - Will $284,267 Be Enough? The rate of inflation will determine the acceptable levels of salary in the future. Although inflation did increase to double digits in recent history, 3-4% is the historical average. This box demonstrates a real world example of how money compounds. www.bankofcanada.ca IV. Present Value: Single Amount (Discounted value) A. The present value of a future sum is the amount invested today, at a given interest rate that will equal the future sum at a specified point in time. Also referred to as a discounted value. B. The relationship may be expressed in the following formula: (9-3; page 262) Perspective 9-2: The instructor may wish to use Figure 9-1 to demonstrate the relationship between present and future value. PPT 7of 37 Relationship of present value and future value (Figure 9-1) C. (Optional) The formula may be restated as: PV = FV × PVIF The PVIF term is found in appendix B. D. Calculator Compute PV = $2,000. V. Future Value: Annuity (Cumulative future value) A. An annuity represents consecutive payments or receipts of equal amount. B. The annuity value is normally assumed to take place at the end of the period. C. The future value of an annuity represents the sum of the future value of the individual flows. Also referred to as a cumulative future value. PPT 16 of 37 Compounding process for annuity (Figure 9-2) D. The formula for the future value for an annuity is: (9-4a; page 263) E. (Optional) The formula may be restated as: FVA = A × FVIFA The FVIFA term is found in appendix C. F. Calculator Compute FV = $43,459.69 G. Future Value: Annuity in Advance (Annuity due) (9-4b; page 264) Also: FVA (BGN) = FVA (1 + i) Calculator Compute FV = $46,936.46 VI. Present Value: Annuity (Cumulative Present value) A. The present value of an annuity represents the sum of the present value of the individual flows. Also referred to as a cumulative present value. B. The formula for the present value of an annuity is: (9-5a; page 264) C. (Optional) The formula may be restated as: PVA = A PVIFA The PVIFA term is found in appendix D. D. Calculator Compute FV = $20,790.63 E. Present Value: Annuity in Advance (Annuity due) (9-5b; page 265) Calculator Compute PV = $22,038.07 Also: PVA (BGN) = PVA (1 + i) VII. Annuity Equalling a Future Value (Sinking fund value) A. The process can be reversed to find an annuity value that will grow to equal a future sum. Also referred to as a sinking fund value. B. The formula for the future value of an annuity is: (9-6a; page 266) C. The formula may be restated as: FVA = A × FVIFA The FVIFA term is found in Appendix C. D. Calculator Compute PMT = $2,219.21 E. The formula for an annuity (in advance) equalling a future value is as follows: (9-6b; page 267) VIII. Annuity Equalling a Present Value (Capital recovery value) A. The formula for the present value of an annuity, also referred to as a capital recovery value is: (9-7a; page 267) B. The formula may be restated as: PVA = A × PVIFA The PVIFA term is found in Appendix D. C. The annuity value equal to a present value is often associated with withdrawal of funds from an initial deposit or the repayment of a loan. D. The formula for an annuity in advance equalling a present value is as follows: (9-7b; page 268) Perspective 9-3: This can be a good point to demonstrate how annuities work in everyday situations. The withdrawal example and payoff table are shown in Tables 9-1 and 9-2, respectively. PPT 25 of 37 Relationship of present value to annuity (Table 9-1) PPT 26 of 37 Payoff table for loan (amortization table) (Table 9-2) Perspective 9-4: Ten different formulas have been presented so far. This is a good point in the discussion to review them. After this has been accomplished, the instructor can feel more comfortable in presenting additional material. PPT 28 & 29 of 37 Review of formulas (Page 269) IX. Determining the Yield on an Investment A. The formula for the yield on an investment is: (9-8; page 270) B. (Optional) The unknown value is now assumed to be the yield. 1. Yield: Present value of a single amount (page 270). a. The rate equating FV to PV must be found. b. The first step is to determine PVIF. c. The next step is to find this value in Appendix B to identify the yield. d. Interpolation may be used to find a more exacting answer. 2. Yield: Present value of an annuity (page 271) (no formula). a. The rate equating A to PV must be found. b. The first step is to determine PVIFA. c. The next step is to find this value in Appendix D to identify the yield. d. Interpolation may be used to find a more exacting answer. C. Calculator Compute %i = 11.99% X. Special Considerations in Time Value Analysis A. Semi-annual, quarterly, monthly, etc compounding. B. Present value of deferred annuity. 1. Two step solution process PPT 31 – 33 of 37 Present value of deferred annuity: twostep process 2. Single step solution PVIFA for total period – PVIFA for initial period PVIFA for deferred period × annuity C. Perpetuities PPT 9-34 1. Perpetual annuity (9-9, page 274) 2. Perpetual growing annuity (9-10, page 274) 3. Perpetual growing annuity (fixed period) (9-11, page 275) XI. Canadian Mortgages A. Monthly payments and semiannual interest compounding require a monthly effective interest rate by formula: r = nominal annual rate B. If $95,999 is borrowed over 20 years at 8%. Calculator Compute PMT = $786.94 Finance in Action: Is a Weekly Mortgage a Good Idea? Calculations examine whether or not a weekly mortgage is an advantage over a monthly mortgage. Perspective 9-5: Encourage the students to ‘Review of the Formulas’. The numerous end of chapter problems help the student to apply the correct formula and analysis. Summary Listing of Suggested PowerPoint Slides PPT 7 Relationship of present value and future value (Figure 9-1) PPT 16 Compounding process for annuity (Figure 9-2) PPT 25 Relationship of present value to annuity (Table 9-1) PPT 26 Payoff table for loan (amortization table) (Table 9-2) PPT 28 & 29 Review of formulas PPT 31 – 33 Present value of deferred annuity PPT 34 Perpetuities PowerPoint Presentation The Chapter 9 PowerPoint Presentation, which covers the same essential points as the annotated outline, consists of 37 frames. Chapter 10 Valuation and Rates of Return Author's Overview The student can clearly see that the material covered in the previous chapter on time value of money is now being applied. The recurring theme throughout the chapter is that valuation is based on the present value of benefits to be received in the future. The instructor should establish this point at the outset and then repeatedly demonstrate it in the evaluation of bonds, preferred stock, and common stock. The instructor should also emphasize the relationship of the discount rate in present value analysis to the required rate of return demanded by security holders. The authors suggest that the instructor go through the process of defining the investor's required return in terms of a real rate of return, an inflation premium, and a risk premium. The instructor can then vary one of these components and show the impact on overall required return and valuation. Learning Objectives 1. Describe valuation of a financial asset as based on the present value of future cash flows. 2. Propose that the required rate of return in valuing an asset is based on the risk involved. 3. Assess the current value (price) of bonds, preferred (perpetuals) and common shares based on the future benefits (cash flows). 4. Evaluate the yields on financial claims based on the relationship between current price and future expected cash flows. 5. Describe the use of a price-earnings ratio to determine value. Annotated Outline and Strategy PPT 8 of 34 The relationship between time value of money, required return, cost of financing, and investment decisions (Figure 10-1) I. Valuation Concepts A. The value of an asset is the present value of the expected cash flows associated with the asset. In order to compute the present value of an asset, an investor must know or estimate the amount of expected cash flows, the timing of expected cash flows and the risk characteristics of the expected flows (to assist in establishing the discount rate to be used as the required rate of return). B. Actually, the price (present value) of an asset will be based on the collective assessment of the asset's cash flow characteristics, by the many capital market participants. C. Yield 1. Three factors influence an investor's required rate of return. a. The required real rate of return-the rate of return demanded for giving up current use of funds on a non-inflation adjusted basis. b. An inflation premium-a premium to compensate the investor for the effect of inflation on the value of the dollar. c. Risk premium-all financial decisions are made within a risk-return framework. An astute investor will require compensation for risk exposure. There are two types of risk of primary interest in determining the required rate of return (yield): i. Business risk; the possibility of a firm not being able to sustain its competitive position and growth in earnings. Related to capital assets and operating leverage. ii. Financial risk: the possibility that a firm will be unable to meet its debt obligations as they come due. This relates to chapter 5 concept of financial leverage. iii. Note: default, liquidity and maturity risk Finance in Action: Market Yields and Market Values The discussion is tied into the market place with references to sources of market information. www.globeandmail.com www.tmx.com II. Valuation of Bonds A. The value of a bond is derived from cash flows composed of periodic interest payments and a principal payment at maturity. B. The present value (price) of a bond can be expressed as follows: (10-1; page 295) Where: Pb = the market price of the bond It = the periodic interest payments (Fixed by contract) Pn = the principal payment at maturity (Fixed by contract) t = the period from 1 to n N = the total number of periods Y = the yield to maturity (required rate of return) or graphical as: C. (Optional) The present value tables may be used to compute the price of a bond. The stream of periodic interest payments constitutes an annuity. The present value of the stream of interest payments may be computed by multiplying the periodic interest payment by the present value of an annuity interest factor. PVA = A × PVIFA (n, i) The present value of the principal payment may be computed by applying the present value of a $1 formula. PV = FV × PVIF (n, i) The present value (price) of the bond will be the sum of the present value of the interest payments plus the present value of the principal. D. An understanding of the relationship between the required rate of return (yield to maturity) and the coupon rate (the annual interest payment divided by the par value) will allow one to “anticipate” the value of a bond prior to calculation. If the market rate is the coupon rate, the bond will sell at a discount (below par value) If the market rate is = the coupon rate, the bond will sell at par value If the market rate is the coupon rate, the bond will sell at a premium (above par value) Finance in Action: The Ups and Downs of Bond Prices Uncertainty in the markets can have pronounced impacts on the pricing of bonds incurring capital gains or capital losses. Government of Canada bonds are examined. 1. Bond prices are inversely related to required rates of return. A change in the required rate of return will cause a change in the bond price in the opposite direction. The impact of the change in required rate of return on the bond price is dependent upon the remaining time to maturity. The impact will be greater the longer the time to maturity. Perspective 10-1: Table 10-1 illustrates the impact of differences between yield to maturity and coupon rates on bond prices. Bond prices go from a high of $2,308.11 to as low of $406.92. Table 10-2 shows the critical effect of time to maturity on bond price sensitivity, and is further supported by Figure 10-2 PPT 14 of 34 Bond price sensitivity to yield to maturity (Table 10-1) PPT 16 of 34 Bond price sensitivity to time to maturity changes (Table 10-2) Perspective 10-2: This table shows the critical effect of time to maturity on bond price sensitivity. PPT 17 of 34 Relationship between time to maturity and bond price (Figure 10-2) Perspective 10-3: The critical effect of time to maturity on bond price sensitivity is further supported by figure 10-2. E. Determining yield to maturity 1. If the bond price, coupon rate, and number of years to maturity are known, the yield to maturity (market determined required rate of return) can be computed. a. Trial and error process. This process requires one to "guess" various yields until the yield to maturity that will cause the present value of the stream of interest payments plus the present value of principal payment to equal the bond price is determined. The initial "guess" is not completely blind, however, since the relationship between the coupon rate, yield to maturity (market rate), and the bond price is known. Perspective 10-4: This process can be taken one step further by employing Appendix 10A: ‘The Bond Yield to Maturity Using Interpolation.’ This, of course, is optional. Many instructors may not wish to go into that degree of detail. PPT 18 of 34 Reading bond quotes b. (Optional) Often, a less exact calculation of the yield to maturity is sufficient. The text on page 305, as a footnote, presents an approximate formula. c. An exact calculation of the yield to maturity can be made using a good calculator or computer software. Perspective 10-5: Some instructors may choose to make specific references to Appendix E at the back of the text which covers the use of calculators to compute yield to maturity and other values. F. Often interest payments are made more frequently than once a year. Semiannual interest payments are common. To compute the price of such a bond, we divide the annual amount of interest and yield to maturity by two and multiply the number of years to maturity by two. Perspective 10-6: Although the initial presentation in the chapter is based on annual payments, the instructor should probably cover the section on semiannual payments as well. Students have the opportunity to use both approaches in working problems at the back of the chapter. III. Valuation of Preferred Stock A. Preferred stock is usually valued as a perpetual stream of fixed dividend payments. (10-2; page 301) Where: Pp = the price of preferred stock. Dp = the annual dividend for preferred stock. Kp = required ROR (discount rate) applied to preferred stock dividends. B. Since the dividend stream is a perpetuity, the preferred stock valuation formula can be reduced to a more usable form. (10-3; page 302) C. If Kp changes after preferred stock is issued, Pp will change in an inverse fashion. 1. Since preferred stock theoretically has a perpetual life, it is highly sensitive to changes in the required rate of return (Kp). D. If the market price of preferred stock and the annual dividend are known, the market determined required rate of return may be computed by using the valuation equation and solving for Kp. (10-4; page 303) IV. Valuation of Common Stock A. The value of a share of common stock is the present value of an expected stream of dividends. (10-5; page 303) Where: Po = price of the stock at time zero (today). D = dividend for each year. Ke = the required rate of return for common stock. B. Unlike dividends on most preferred stock, common stock dividends may vary. The valuation formula may be applied, with modification, to three different circumstances: no growth in dividends, constant growth in dividends, and variable growth in dividends. 1. No growth in dividends: Common stock with constant (no growth) dividends is valued in the same manner as preferred stock. (10-6; page 304) 2. Constant growth in dividends: The price of common stock with constant growth in dividends is the present value of an infinite stream of growing dividends. Fortunately, in this circumstance the basic valuation equation can be reduced to the more usable form below if the discount rate (Ke) is assumed to be greater than the growth rate. (10-8; page 305) Where: D1 = dividend expected at the end of the first year = Do (1+g) g = constant growth rate in dividends Perspective 10-7: The students get a much clearer picture of what is driving the model if the instructor highlights examples that illustrate the impact of the changes in Ke and g on the model. a. The above formula, which is labeled 10-8 in the text, can also be thought to represent the present value of dividends for a period of time (such as N = 3) plus the present value of the stock price after a period of time (such as P3). Since P3 represents the present value of dividends from D4 through D, Po will still represent the present value of all future dividends. Perspective 10-8: The authors use problem 32 at the back of the chapter to illustrate the equality described above. Of course, it is up to the instructor to decide if he or she wishes to go into this much detail. b. The value of Po is quite sensitive to any change in Ke (required rate of return) and g (the growth rate). Finance in Action: Estimating Value with the Dividend Capitalization Model Using several web sites the dividend model is used to estimate the price of Royal Bank shares. This is in the text on page 306. www.rbc.com RY c. Rearrangement of the constant growth equation allows the calculation of the required rate of return, Ke, when Po, D1, and g are given. The first term represents the dividend yield that the shareholder expects to receive and the second term represents the anticipated growth in dividends, earnings and stock price. (10-9; page 307) 3. Variable growth in dividends: The most likely variable growth case is one of supernormal growth followed by constant growth. a. Value can be found through taking the present value of the dividends during the supernormal growth period plus the price of the stock at end of the supernormal growth period. Since growth is then constant, Formula 10-8 can be used. b. Another type of variable growth is where the firm is assumed to pay no dividends for a period of time and then begins paying dividends. In this case, the present value of deferred dividends can be computed as a representation of value. c. If no dividends are ever intended, then valuation may rest solely on the present value of future earnings and the present value of a future stock price. 4. Stock valuation may also be linked to the concept of price-earnings ratios discussed in Chapter 2. Although this is a less theoretical, more pragmatic approach than the dividend valuation models, the end results may be similar because of the common emphasis on risk and growth under either approach. Perspective 10-9: Table 10-3 illustrates how P/E ratios are shown in the financial press. Royal Bank (RY.) and Research in Motion (RIM) can be highlighted in the table and dividend yield and price changes can also be mentioned to stimulate interest PPT 32 of 34 Reading stock quotations Finance in Action: Diamonds, Nickel, Gold or the Blackberry - for Value? This box highlights some of the excitement surrounding the search for diamonds in Canada, gold (or the hoax) in Borneo, the discovery of nickel in Labrador and the tapping of the Blackberry for riches. The large increases/ decreases in share price are of interest to students. Perspective 10-10: The use of the appendix is optional. PPT 26 & 27 of 34 Stock valuation under supernormal analysis Summary Listing of Suggested PowerPoint Slides PPT 8 Relationship between time value of money, required return, cost of financing and investment decisions (Figure 10-1) PPT 14 Bond price sensitivity to yield to maturity (Table 10-1) PPT 16 Bond price sensitivity to time to maturity changes (Table 10-2) PPT 17 Relationship between time to maturity and bond price (Figure 10-2) PPT 32 Reading a stock quotations PPT 26 & 27 Stock valuation under supernormal growth analysis PowerPoint Presentation The Chapter 10 PowerPoint Presentation, which covers the same essential points as the annotated outline, consists of 34 frames. Chapter 11 Cost of Capital Author’s Overview Chapter 11 on "Cost of Capital" naturally follows Chapter 10 on "Valuation and Rates of Return." The instructor should emphasize, at the outset that the investors' required rate of return translates into the cost of financing for the firm. There should be a dual emphasis on properly determining the after tax cost for each type of financing and on determining the appropriate weights to be assigned to the various sources of financing. Various costs are determined from current market yields. It is important to emphasize to the student that the cost of capital is used as an evaluation tool, to accept or reject capital investments. It is the cost of financing of the future. It is the acceptance criterion that adds to shareholder value. The cost of debt and the cost of preferred stock are reasonably straightforward, but additional guidance is required in determining the cost of common equity. The instructor should indicate the firm's ability to acquire equity capital through retained earnings or through new common stock and the associated cost of each. The cost of retained earnings should be explained as an opportunity cost for the use of the shareholders' funds. For that reason, it is assumed the shareholders can earn as much on these funds, if distributed, as they are currently earning in the firm. Thus, the cost of retained earnings is also equal to Ke (the firm's return on common equity). After the various costs are computed, the instructor can direct more attention to the weighing scheme given to the components in the capital structure. The instructor may wish to refer to the authors' example in which the increased use of debt initially decreases the cost of capital, but then ultimately increases it. The interdependent nature (of costs and weights) should be stressed in discussing the optimal capital structure. An extensive discussion of the historical and present nature of Capital Structure Theory and Modigliani and Miller is presented in Appendix 11B. Capital structure for COC calculations is based on market value weightings. Students sometimes have difficulty calculating the market values of the capital components from a balance sheet. The text converts a book value balance sheet to a market value balance sheet. The instructor has the option of introducing the student to the capital asset pricing model in the text and more fully in Appendix 11A. The concepts of regression analysis, the beta coefficient, and the security market line are introduced and related to previously discussed material on the cost of capital. This chapter as well as subsequent chapters is fully comprehensible without the use of this material. The appendix is available, however, for those instructors who wish to go over the capital asset pricing model in detail. Learning Objectives 1. Explain that the cost of capital represents the overall cost of financing to the firm. 2. Define the cost of capital as the discount rate normally used to analyze an investment. It is an evaluation tool. 3. Construct the cost of capital based on the various valuation techniques from Chapter 10 as applied to bonds, preferred stock and common shares. 4. Examine how a firm attempts to find a minimum cost of capital through varying the mix of its sources of financing. 5. Apply the marginal cost of capital concept. Annotated Outline and Strategy I. The Overall Concept A. A business firm must strive to earn at least as much as the cost of the funds if it is to increase shareholder value. The cost of capital (calculated) is employed to analyze investment decisions provided: 1. Capital structure will be maintained 2. Projects of the same risk are analyzed B. Usually a firm has several sources of funds and each source may have a different cost. C. The overall cost of the funds employed is a proportionate average of the various sources. D. The firm's required rate of return that will satisfy all suppliers of capital is called its cost of capital. E. There are several steps in measuring a firm's cost of capital. 1. Compute the cost of each source of capital. 2. Assign weights to each source. Conversion of historical cost capital structure to market values may be required. 3. Compute the weighted average of the component costs. PPT 7 of 41 Cost of capital-Baker Corporation (Table 11-1) Finance in Action: Double – Double with that Capital Tim Hortons raises capital through the equity markets, incurring flotation costs II. Interdependence of Valuation and Cost of Capital A. To achieve the firm’s goal, shareholder’s wealth maximization, the firm’s assets must be employed to earn at least the required rate of return (cost of capital). B. A firm’s required rate of return (cost of capital) is determined in the market by the suppliers of capital. C. The market-determined required rate of return for each source of capital depends upon the market’s perceived level of risk associated with the individual securities. The perceived risk is based on future expectations. D. The market allocates capital at varying rates of return based on perceptions of an individual firm’s riskiness, efficiency, and expected returns. E. A firm’s risk will be determined in part by its collection of assets. F. Market-determined yields on various financial instruments will equal the cost of those instruments to the firm with adjustment tax and flotation cost considerations. III. The Cost of Debt A. The basic cost of debt to the firm is the effective yield to maturity. The yield to maturity is a market determined rate and can be found by examining the relationships of security price, periodic interest payments, maturity value, and length of time to maturity. The yield to maturity for a corporate bond may be found by solving for Y in the following equation: (10-1; page 295) Where: Y = the yield to maturity Pn = the principal at maturity Pb = the market price of the bond t = the period from 1 to n I t = the periodic interest payments N = the total number of periods An accurate calculator computation is shown in the text on page 328. B. Yield should be adjusted for: 1. Tax considerations, as interest is tax deductible (lowers cost). 2. Flotation costs (increases cost). C. The after-tax cost of debt is: Kd = Y (1-T) (11-1a; page 329) Where: Kd = Cost of debt Y = Yield The after-tax cost to of bonds issued at par paying $100 annual interest would be 6 percent if the firm's marginal tax rate were 40 percent. This approximation works best if the bond maturity is greater than 10 years. D. Flotation costs of a debt issue may be included by use of the formula: (11-1b; page 330) Where: F = Flotation, or selling, cost (as a percent) Perspective 11-1: Table 11-2 with sample bond information is useful in relating risk to bond yields and for identifying the difference between yield and coupon rate. Finance in Action: Debt Costs around the Globe A comparison of debt financing costs in several countries Perspective 11-2: Explain that the cost of preferred stock and common stock is calculated on an after-tax basis as the return comes out of after-tax income, the cost of debt is adjusted for taxes so that all three sources of capital are on an after-tax cost basis. IV. The Cost of Preferred Stock A. Preferred stock is similar to debt in that the preferred dividend is fixed but dissimilar in that dividends are not tax deductible. B. The cost of preferred stock to a firm may be determined by examining the relationship of its annual (usually fixed) dividend and its market determined price. Preferred stock, unlike debt, has no maturity and therefore the dividends are expected to be perpetual. C. The cost of preferred stock Kp is computed by dividing the annual dividend payment by the net proceeds received by the firm in the sale of preferred stock. (11-2a & b; page 331 - 332) Where: Kp = cost of preferred stock Dp = preferred stock dividend F = flotation, or selling cost (percentage or dollar cost) Pp = market price of preferred stock V. The Cost of Common Equity A. The basis of computation of the price of common stock is the Dividend Valuation Model. B. Assuming constant growth, the Dividend Valuation Model can be reduced a required rate of return Ke, (11-3; page 333) Where: Ke = required rate of return D1 = expected dividend in first year P0 = price per share of stock g = constant growth rate in dividends With flotation costs: (11-4; page 335) Where: Pn = net proceeds received on a new share issue after flotation costs and any underpricing of the share price C. The equation for common stock cost is composed of two parts, the dividend yield, D1/P0 plus the anticipated growth rate, g, of dividends. D. Alternative Calculation of the Required Return on Common Stock: using the Capital Asset Pricing Model (CAPM). 1. Under the CAPM, the required return for common stock can be described by the following formula: Kj = Rf + βj (Rm – Rf) (11-5; page 336) Where: Kj = Required Return on Common Stock Rf = Risk-free rate of return; usually the current rate on Treasury bill securities βj = Beta coefficient. The beta measures the historical volatility of an individual stock's return relative to a stock market index. A beta greater than 1 indicates greater volatility (price movements) than the market, while the reverse would be true for a beta less than 1. Rm = Return in the market as measured by an appropriate index With flotation costs: (11-6; page 336) 2. Both Kj and Ke should be equal under the case of market equilibrium with efficient markets. 3. Appendix 11A presents the capital asset pricing model in more detail for those who wish to expand the textbook coverage on this concept. E. Common stock financing is available through the retention of earnings belonging to present shareholders or by issuing new common stock. 1. The cost of retained earnings is equivalent to the rate of return on the firm’s common stock. This is the opportunity cost. Thus the cost of common equity in the form of retained earnings is: (11-3: page 333) 2. The cost of new common stock is higher than the cost of retained earnings because the firm's proceeds from sale of the stock is less than the price paid by the shareholder due to flotation costs (F). The firm receives a price (Pn) less than the price to investors (P0). Perspective 11-3: The overview of common stock costs, the two models and external versus internal financing should be brought home to the student. Finance in Action: CU, Return on Common Equity and Cost of Capital Deregulation has changed the operation of the utilities industry, yet Canadian Utilities still calculates their cost of capital to determine service rates on which it earns its return to equity. VI. Optimal Capital Structure - Weighting Costs A. The firm should seek to minimize its cost of capital by employing the optimal mix of capital financing. B. The Baker Corporation example on page 338 demonstrates the concept of weighted average cost of capital numerically while Figure 11-1 does so graphically. C. Although debt is the cheapest source of capital, there are limits to the amount of debt capital that lenders will provide (recall the D/ E relationships discussed in Chapter 3). The cost of both debt and equity financing rise as debt becomes a larger portion of the capital structure. PPT 14 of 41 Cost of capital curve (Figure 11-1) D. Traditional financial theory maintains that the weighted average cost of capital declines as lower costing debt is added to the capital structure. The optimum mix of debt and equity corresponds to the minimum point on the average cost of capital curve. PPT 15 of 41 Debt (total) to total assets, early 2011 (Table 11-3) E. The optimal debt equity mix varies among industries. The more cyclical the business, the lower the D/E ratio is required to be. F. The weights applied in computing the weighted average cost should be market value weights on the presumption that this is the optimum financing mix that will be used to finance projects in the future. This will require the conversion of the historical based balance sheet to its market value equivalent before weightings are determined. (A text example is presented on pages 341-342). Finance in Action: EVA, the Music of Shareholder Value Economic value added is a financial decision-making concept that enjoys many adherents and is an extension of the cost of capital concept. VII. Capital Acquisition and Investment Decision Making A. The discount rate used in evaluating capital projects should be the weighted average cost of capital. PPT 16 of 41 Cost of capital over time (Figure 11-2) B. If the cost of capital is earned on all projects, the residual claimants of the earnings stream, the owners, will receive their required rate of return. If the overall return of the firm is less than the cost of capital, the owners will receive less than their desired rate of return because providers of debt capital must be paid. Perspective 11-2: This is a good time to discuss the impact of economic cycles on the cost of capital. Often when yields are low, the economy is sluggish and capital needs are not crucial. Recognizing that costs of capital shift from time to time over the business cycle is important in pointing out that companies raise capital in an uneven fashion, often raising capital before it is all needed in anticipation of rising costs. C. For most firms, the cost of capital is fairly constant within a reasonable range of debt equity mixes (flat portion of curve in Figure 11 2). Changes in money and capital market conditions (supply and demand for money), however, cause the cost of capital for all firms to vary upward and downward over time. D. Cost of Capital in the Capital Budgeting Decision 1. It is the current cost of each source of funds that is important. 2. The cost of each source of capital will vary with the amount of capital derived from that source. 3. The required rate of return or discount rate for capital budgeting decisions will be the weighted average cost of capital. PPT 18 of 41 Investment projects available to the Baker Corporation (Table 11-4) PPT 19 of 41 Cost of capital and investment projects for the Baker Corporation (Figure 11-3) VIII. Marginal Cost of Capital A. The marginal cost of debt (the cost of the last amount of debt financing) will rise as more debt financing is used. The marginal cost of equity also rises when the shift from retained earnings to external (common stock) equity financing is necessary. IX. Appendix 11A: Cost of Capital and the Capital Asset Pricing Model A. The Capital Asset Pricing Model (CAPM) relates the risk return tradeoffs of individual assets to market returns. B. The CAPM encompasses all types of assets but is most often applied to common stock. C. The basic form of the CAPM is a linear relationship between returns on individual stocks and the market over time. Using least squares regression analysis, the return on an individual stock Kj is: Kj = α + βj Rm + e (11A-1; page 360) Where: Kj = Return on individual common stock of company α = Alpha, the intercept on the y-axis βj = Beta, the coefficient of stock (j) Rm = Return on the stock market (an index of stock returns is used, usually the S&P/ TSX Composite Index) E = Error term of the regression equation D. Using historical data, the beta coefficient is computed. The beta coefficient is a measurement of the return performance of a given stock relative to the return performance of the market. PPT 26 of 41 Performance of PAI and the market (Table 11A-1) PPT 27 - 29 of 41 Linear regression of returns between PAI and the market (Figure 11A-1) E. The CAPM is an expectational model. There is no guarantee that historical data will be repeated. F. The CAPM evolved into a risk premium model. 1. Investors expect higher returns if higher risks are taken. 2. The minimum return expected by investors will never be less than can be obtained from a riskless asset (usually considered to be Treasury bills). The relationship is expressed as follows: Kj = Rf + βj (Rm – Rf) (11A-2; page 362) Where: Rf = Risk-free rate of return βj = Beta coefficient from Formula 11A-1 Rm = Return on the market index Rm – Rf = Premium or excess return of the market versus the risk-free rate (since the market is riskier than Rf, the assumption is that the expected Rm will be greater than Rf) βj (Rm – Rf) = Expected return above the risk-free rate for the stock of Company j, given the level of risk 3. Beta measures the sensitivity of an individual security's return relative to the market. a. By definition, the market beta = 1. b. A security with a beta = 1, is expected to have returns equal to and as volatile as the market. One with a beta of 2 is twice as volatile (up or down). 4. Beta measures the impact of an asset on an individual's portfolio of assets. G. A risk return graph can be derived from the risk premium model. The graphed relationship between risk (measured by beta) and required rates of return is called the Security Market Line (SML). Finance in Action: Risks and Return Three Canadian companies are discussed based on their betas, individually and as a portfolio. H. Cost of capital considerations 1. If required returns rise, prices of securities fall to adjust to the new equilibrium return level and as required returns fall, prices rise. 2. A change in required rates of return is represented by a shift in the SML. a. The new SML will be parallel to the previous one if investors attempt to maintain the same risk premium over the risk free rate. b. If investors attempt to maintain purchasing power in an inflationary economy, the slope of the new SML may be greater than before due to an inflation premium. c. An investor's required rate of return and thus a firm's cost of capital will also change if investors risk preferences change. The slope of the SML would change even if the risk free rate remained the same. X. Appendix 11B: Capital Structure Theory and Modigliani and Miller A. A capital structure that provides the lowest cost of capital and therefore the highest market value of owner's equity would be deemed to be the optimal capital structure for a firm. Whether such a capital structure exists is not clear and has been a focal question in the field of finance for many years. B. Professor David Durand provided three descriptive alternative theories of cost of capital and valuation in the early 1950s. 1. Net Income (NI) Approach: The costs of debt and equity were assumed to be constant regardless of capital amounts employed. PPT 34 of 41 Net income (NI) approach (Figure 11B-1) PPT 35 of 41 Net operating income (NOI) approach (Figure 11B-2) 2. Net Operating Income (NOI) Approach: Durand proposed an alternative theory that stated that although the cost of debt remained constant over varying levels of debt utilization, the cost of equity would rise in such a manner that the overall cost of capital remained constant. 3. Finally, Durand described an approach in between the NI and NOI alternative called the Traditional Approach. PPT 36 of 41 Traditional approach as described by Durand (Figure 11B-3) C. Professors Franco Modigliani and Merton Miller made major contributions to capital structure theory by providing behavioral and mathematical substance rather than relying on naive assumptions. 1. Initially, M & M maintained that a firm's cost of capital and the value of the firm were independent of its capital structure. Their posture was similar to the NOI approach of Durand, but M & M provided the behavioral process and mathematical proofs to support their arguments. M & M argued that owners demand an additional risk premium as debt is employed that will exactly offset the decline in the cost of capital because debt is cheaper. If their hypothesis held, the cost of capital and value of the firm would be independent of capital structure. (11B-1; page 370) 2. M & M "corrected" their hypothesis to include corporate taxes. Once the tax deductibility of interest payments was included in their analysis, the market value of the firm was directly tied to the amount of debt employed. The more debt a firm used, the higher its market value would be. (11B-4; page 371) PPT 37 of 41 Modigliani and Miller with corporate taxes (Figure 11B-4) 3. The next step in M & M's evolutionary consideration of capital structure was the inclusion of bankruptcy probabilities and costs. The threat of bankruptcy offsets some of the benefits from using debt and yields a U shaped cost of capital curve. In other words, initially, debt provides market value benefits but as more debt is used, the threat of bankruptcy begins to erase the benefits. An optimal capital structure would be possible. PPT 38 & 39 of 41 Combined impact of the corporate tax effect and bankruptcy effect on valuation and cost of capital (Figure 11B-5) 4. Finally, in 1976, Professor Miller (without Modigliani) reverted to their original position that cost of capital and market values were independent of capital structure. His premise was based on the effect of including personal taxes in the capital structure issue. Miller said that the lower tax rates on long term gains from stock ownership offset the tax benefits from tax deductibility of interest payments. D. The optimal capital structure issue has not been fully reconciled. Changes in tax laws and the dynamic changes in market risk perceptions continue to impact on this question. There is general acceptance, however, of the idea that the prudent use of debt does lower the cost of capital. E. Both professor’s Modigliani and Miller have been awarded the Nobel Prize in economics. Summary Listing of Suggested PowerPoint Slides PPT 7 Cost of capital - Baker Corporation (Table 11-1) PPT 14 Cost of Capital Curve (Figure 11-1) PPT 15 Debt (total) to total assets, mid 2004 (Table 11-3) PPT 16 Cost of capital over time (Figure 11-2) PPT 19 Investment projects available to the Baker Corporation (Table 11-4) PPT 18 Cost of capital and investment projects for the Baker Corporation (Figure 11-3) PPT 21 Cost of capital for different amounts of financing (Table 11-5) PPT 22 Cost of capital for increasing amounts of financing (Table 11-6) PPT 23 Marginal cost of capital and Baker Corporation investment alternatives (Figure 11-4) PPT 24 Cost of components in the capital structure (Table 11-7) PPT 26 Performance of PAI and the market (Table 11A-1) PPT 27 &28 Linear regression of returns between PAI and the market (Figure 11A-1) PPT 30 The security market line (SML) (Figure 11A-2) PPT 31 The security market line and changing interest rates (Figure 11A-3) PPT 32 The security market line and changing investor expectations (Figure 11A-4) PPT 34 Net income (NI) approach (Figure 11B-1) PPT 35 Net operating income (NOI) approach (Figure 11B-2) PPT 36 Traditional approach as described by Durand (Figure 11B-3) PPT 37 Modigliani and Miller with corporate taxes (Figure 11B-4) PPT 38 & 39 Combined impact of the corporate tax effect and bankruptcy effect on valuation and cost of capital (Figure 11B-5) PowerPoint Presentation The Chapter 11 PowerPoint Presentation, which covers the same essential points as the annotated outline, consists of 41 frames. Chapter 12 The Capital Budgeting Decision Author's Overview While early comments on administrative procedures and accounting considerations are helpful, the major thrust of Chapter 12 is on the various methods for ranking investment proposals. The basic selection methods are established, mutually exclusive versus non-mutually exclusive events are compared, capital rationing and the net present value profile are presented. Emphasis is placed on the net presented value (NPV) approach. Encouraging students to develop time lines for the relevant cash flows usually assists in helping solve the more complex problems. The Chapter continues with a comprehensive discussion of procedures for amortization (CCA) write-off and integrates the resultant cash flow determination with the capital budgeting decision. There is a wide array of problems at the back of Chapter 12. They are constructed on a building block basis, in which the student moves from the simple to the complex. Each problem tends to introduce a new variable, with the later problems dealing with fairly complex decisions. Having the student focus on the incremental cash flows that would result from a decision is quite important. Learning Objectives 1. Define capital budgeting decisions as long-term investment decisions. 2. Explain that cash flows rather than accounting earnings are evaluated in the capital budgeting decision. 3. Evaluate investments by the average accounting return, the payback period, the internal rate of return, the net present value and the profitability index. 4. Appraise the use of the cost of capital as the discount rate in capital budgeting analysis. 5. Integrate the resultant cash flows that result from an investment decision, including the after tax operating benefits and the tax shield benefits of capital cost allowance (amortization). 6. Perform NPV analysis to assist in the decision-making concerning long-run investments. Annotated Outline and Strategy I. Characteristics of Capital Budgeting Decisions A. Capital expenditures are outlays for projects with lives extending beyond one year and perhaps for many years. B. Intensive planning is required. Capital budgeting sets a strategic direction. C. Capital expenditures usually require initial cash flows, often large, with the expectation of future cash inflows. The differing time periods of inflows and outflows require present value analysis using the firms cost of capital as the basic discount rate. D. The longer the time horizon associated with a capital expenditure, the greater the uncer¬tainty. Areas of uncertainty are: 1. Annual costs and inflows 2. Product life 3. Interest rates 4. Economic conditions 5. Technological change Finance in Action: Research and Development: The Start of Capital Investment Various levels of R & D at two Canadian companies are highlighted. www.teck.com www.rim.com II. Administrative Considerations PPT 6 of 45 Capital budgeting procedures (Figure 12-1) A. Search and discovery of investment opportunities B. Collection of data C. Evaluation and decision making D. Reevaluation and adjustment III. Accounting Flows versus Resultant Cash Flows A. The capital budgeting process focuses on cash flows rather than income on an after tax basis. Income figures do not reflect the cash available to a firm due to the deduction of noncash expenditures such as amortization (CCA). PPT 7 & 8 of 45 Cash flow for Alston Corporation (Table 12-1) and Revised cash flow for Alston Corporation (Table 12-2) B. Evaluation involves the incorporation of all resultant cash flows (incremental and decremental) in the capital budgeting analysis. All costs and benefits that will occur as a result of the investment decision should be included in the analysis. Sunk costs are ignored. Opportunity costs included. Cash flows that would occur regardless of the capital expenditure are non-resultant and are irrelevant to the decision. C. Accounting flows are not totally disregarded in the capital budgeting process. 1. Investors' emphasis on earnings per share may, under certain conditions, require use of income rather than cash as the decision criterion. 2. Top management may elect to glean the short term personal benefits of an income effect rather than the long-run cash-flow effects, which are more beneficial from the shareholder's viewpoint. IV. Methods for Ranking Investment Proposals A. Average Accounting Return (AAR) 1. The AAR is given by the following formula: 2. Deficiencies of the method a. Book values not market values are used, including accruals not cash flows. b. The pattern of cash flows is ignored, therefore, time value of money is not considered. B. Payback Period 1. The payback period is the length of time necessary for the sum of the expected annual cash inflows to equal the cash investment. A cutoff period is established for comparison. Capital proposals with a payback in excess of the cutoff are rejected. 2. Deficiencies of the method a. Inflows after the cutoff period are ignored. b. The pattern of cash flows is ignored, therefore, time value of money is not considered. 3. Though not conceptually sound, the payback method is frequently used. a. Easy to use b. Emphasizes liquidity c. Quick return is important to firms in industries characterized by rapid technological development. PPT 16 of 45 Investment alternatives (Table 12-3) PPT 20 of 45 Capital budgeting results (Table 12-4) Perspective 12-1: We adequately point out in the text that the net present value method and internal rate of return methods are theoretically superior to the payback method for ranking proposals. Nevertheless, it is worth discussing why companies still use payback as a decision tool. During periods of high inflation, a low payback on a project indicates a rapid return of funds for reinvestment at perhaps even higher inflated returns and some companies preferred this method over the superior IRR and NPV methods. C. Net Present Value (NPV) 1. In this method, the cash inflows are discounted at the firm's cost of capital or some variation of that measure. 2. If the present value of the cash inflows equals or exceeds the present value of the cash investment, the capital proposal is acceptable. D. Internal Rate of Return (IRR) 1. The IRR method requires calculation of the rate that equates the cash investment with the cash inflows. 2. The calculation procedure is the same as the yield computation (Chapter 9). a. If the inflows constitute an annuity, the IRR may be computed directly. The IFA may then be found in the present value of an annuity table and its correspon¬dent interest rate (IRR). b. If the cash inflows do not constitute an annuity, determination of IRR is a trial and ¬error process. c. The calculator can be effective d. A project is acceptable if the IRR exceeds a minimum rate of return. E. Profitability Index 1. The profitability index (PI) is equal to the present value of inflows divided by the present value of outflows. 2. Projects with a ratio greater than 1 are acceptable and this method provides a means to compare relative profitability of projects. Finance in Action: Strategy: Right or Wrong Expansion strategies of Inco and Teck are examined in light of tremendous capital commitments. V. Selection Strategy A. All non-mutually exclusive projects having a NPV > = 0 (which also means IRR > or = cost of capital should be accepted under normal conditions). B. The NPV method and the IRR method always agree on the accept reject decision on a capital proposal. C. A disagreement may arise between the NPV and IRR methods when a choice must be made from mutually exclusive proposals or all acceptable proposals cannot be taken due to capital rationing. 1. The primary cause of disagreement is the differing discounting assumptions. The NPV method of discounts cash inflows at the cost of capital. The IRR method discounts cash inflows at the internal rate of return. 2. The more conservative net present value technique is usually the recommended approach when a conflict in ranking arises. The IRR may also produce more than one IRR (which may be confusing). 3. The modified internal rate of return (MIRR) utilizes the reinvestment assumption of the NPV method. PPT 25 of 45 PPT 23 & 26 of 45 The internal rate of return and net present value ($10,000 investment) (Table 12-5) and Multiple IRRs (Table 12-6) VI. Capital Rationing A. Management may implement capital rationing by artificially constraining the amount of investment expenditures. PPT 28 of 45 Capital rationing (Table 12-7) B. Under capital rationing, some acceptable projects may be declined due to management's fear of growth or hesitancy to use external financing. C. Under capital rationing, projects are ranked by NPV and accepted until the rationed amount of capital is exhausted. VII. Net Present Value Profile A. The characteristics of an investment may be summarized by the use of the net present value profile. Perspective 12-3: The net present value profile is an excellent way to examine the rate of return characteristics of projects with different lives under various rate of return assumptions. This is a good opportunity to reinforce the inverse nature of required rates of return and present value interest factors with their resultant impact on discounted cash flow streams. B. The NPV profile provides a graphical representation of an investment at various discount rates. C. Three characteristics of an investment are needed to apply the net present value profile: 1. The net present value at a zero discount rate 2. The net present value of the project at the normal discount rate (cost of capital) 3. The internal rate of return for the investment PPT 30 of 45 Net present value profile (Figure 12-2) D. The NPV profile is particularly useful in comparing projects when they are mutually exclusive or under conditions of capital rationing. PPT 31 of 45 Net present value profile with crossover (Figure 12-3) VIII. Capital Cost Allowance A. The income Tax Act of Canada allows an amortization expense from income under capital cost allowance system. A cash flow effect is created by reducing taxes payable and those tax saving must be considered in capital budgeting analysis. PPT 33 of 45 Capital cost allowance: tax savings (page 399) B. Several considerations determine the amount of (CCA) Capital Cost Allowance (amortization) allowable as the result of a particular capital acquisition. 1. Each capital acquisition is assigned to a particular asset class (asset pool) which determines the rate of CCA. PPT 34 of 45 Some declining-balance CCA classes (Table 12-8) 2. Only half the CCA rate is allowable in the year of acquisition. 3. Amortization for the most part is on the declining balance method and it is the asset pool, not the individual asset that is amortized for tax purposes. As a result, if an asset pool remains open an acquired asset is effectively amortized to infinity. 4. Therefore, tax savings result each year to infinity as a result of a capital acquisition. 5. The sale of an acquired asset reduces the amount remaining in an asset pool (its Undepreciated Capital Cost). PPT 35 of 45 Capital cost allowance for investment A or B (Table 12-9) Finance in Action: Tax Savings Disappear Into the Air! Because of large ongoing losses Air Canada cannot take advantage of tax savings. www.aircanada.ca C. The following formula gives the present value of all the tax savings resulting from CCA of an acquired capital asset, taking into account the half rate rule assuming the asset pool continues indefinitely: PV of CCA tax shield = (12-1; page 403) Where: Cpv = change in capital cost pool resulting from acquiring the asset Spv = change in capital cost pool resulting from the salvage value r = discount rate d = CCA rate for the asset class Tc = corporate tax rate n = number of years in the future we intend to sell off the asset D. If an asset pool ends certain tax consequences are triggered. The difference between the Undepreciated Capital Cost (UCC) and the last asset sold must be: 1. Added back to income if UCC is less than the sale price (Recaptured CCA). 2. Deducted from income if UCC exceeds the sale price (Terminal Loss). PPT 36 of 45 Liquidation of asset pool (Table 12-10) IX. Investment Tax Credit A. The Income Tax Act allows for tax credits on certain capital investments deemed appropriate for economic reasons by the Federal government. Cash flow consequences result. 1. A direct reduction in taxes payable by the amount of the investment tax credit. 2. A reduction in tax saving through CCA because the amount of investment tax credit is deducted from the asset pool (UCC) in the year following acquisition. The half rate rule will not apply. Finance in Action: Continual Capital Budgeting The success of Syncrude Canada in bringing its production costs down through capital expenditures and “debottlenecking” is examined. www.syncrude.ca X. Comprehensive Investment Analysis (NPV) PPT 42 of 45 Differential analysis of the new computer (Table 12-16) PPT 41 of 45 Net price of the new computer (Table 12-15) Summary Listing of Suggested PowerPoint Slides PPT 6 Capital budgeting procedures (Figure 12-1) PPT 7 & 8 Cash flow for Alston Corporation (Table 12-1) and Revised cash flow for Alston Corporation (Table 12-2) PPT 16 Investment alternatives (Table 12-3) PPT 20 Capital budgeting results (Table 12-4) PPT 23 & 26 The internal rate of returns and net present value ($10,000 Investment) (Table 12-5) and Multiple IRRs (Table 12-6) PPT 28 Capital rationing (Table 12-7) PPT 30 Net present value profile (Figure 12-2) PPT 31 Net present value profile with crossover (Figure 12-3) PPT 33 Capital cost allowance: tax savings (page 417) PPT 34 Some declining-balance CCA classes (Table 12-8) PPT 35 Capital cost allowance for investment A or B (Table 12-9) PPT 36 Liquidation of asset pool (Table 12-10) PPT 41 Net price of the new computer (Table 12-15) PPT 42 Differential analysis of the new computer (Table 12-16) PowerPoint Presentation The Chapter 12 PowerPoint Presentation, which covers the same essential points as the annotated outline, consists of 45 frames. Instructor Manual for Foundations of Financial Management Stanley B. Block, Geoffrey A. Hirt, Bartley Danielsen, Doug Short, Michael Perretta 9780071320566, 9781259268892, 9781259261015
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