MBA Finance
jaikrishna
Ch09ToolKit.xlsxChapter
| Tool Kit | Chapter 9 | 11/20/18 | ||||||||||||||||||
| The Cost of Capital | ||||||||||||||||||||
| 9-1 The Weighted Average Cost of Capital | ||||||||||||||||||||
| The cost of capital is the weighted average cost of the debt, preferred stock, and common equity that the firm uses to finance its assets, or its WACC. | ||||||||||||||||||||
| Definitions | ||||||||||||||||||||
| WACC = | Weighted average cost of capital | |||||||||||||||||||
| = | wd rd(1 – T) + wps rps + ws rs | |||||||||||||||||||
| rd = | Cost of debt | |||||||||||||||||||
| rps = | Cost of preferred stock | |||||||||||||||||||
| rs = | Cost of stock (common equity) | |||||||||||||||||||
| wd = | Percent of target capital structure financed with debt | |||||||||||||||||||
| wps = | Percent of target capital structure financed with preferred stock | |||||||||||||||||||
| ws = | Percent of target capital structure financed with stock (common equity) | |||||||||||||||||||
| T = | Tax rate | |||||||||||||||||||
| 9-2 Choosing Weights for the Weighted Average Cost of Capital | ||||||||||||||||||||
| Figure 9-1 | ||||||||||||||||||||
| MicroDrive, Inc.: Selected Capital Structure Data (Millions of Dollars, December 31, 2019) | ||||||||||||||||||||
| Investor-Supplied Capital | Target Capital Structure | |||||||||||||||||||
| Book | Market | |||||||||||||||||||
| Percent of Total | Book Value | Percent of Total | Market Value | Percent of Total | ||||||||||||||||
| Liabilities and Equity | ||||||||||||||||||||
| Accounts payable | $?2,0,0?? | 5.5% | ||||||||||||||||||
| Notes payable | ?1,5,0?? | 4.2% | $?1,5,0?? | 5.0% | $?1,5,0?? | 5.7% | wstd = | 4% | ||||||||||||
| Accruals | ?4,0,0?? | ??11.1% | ||||||||||||||||||
| Total C.L. | $?7,5,0?? | 20.8% | ||||||||||||||||||
| Long-term debt | ?5,2,0?? | ??14.4% | ?5,2,0?? | 17.3% | ?5,2,0?? | 19.8% | wd = | 20% | ||||||||||||
| Total liabilities | $?1,2,7,0?? | 35.2% | ||||||||||||||||||
| Preferred stock | ?1,0,0?? | 2.8% | ?1,0,0?? | 3.3% | ?1,0,0?? | 3.8% | wps = | 2% | ||||||||||||
| Common stock | ?5,0,0?? | 13.9% | ||||||||||||||||||
| Retained earnings | ?1,7,4,0?? | ??48.2% | ||||||||||||||||||
| Total common equity | $?2,2,4,0?? | ??62.0% | $?2,2,4,0?? | ??74.4% | $1,860 | ??70.7% | ws = | 74% | ||||||||||||
| Total | $3,610 | 100.0% | $3,010 | 100.0% | $2,630 | 100.0% | 100% | |||||||||||||
| Other Data (Millions, except per share data): | ||||||||||||||||||||
| Number of common shares outstanding = | 60 | Coupon rate on long-term debt = | 10.00% | |||||||||||||||||
| Price per share of common stock = | $31.00 | Interest rate on short-term debt = | 8.00% | |||||||||||||||||
| Number of preferred shares outstanding = | 1 | Risk-free rate = | 5.02% | |||||||||||||||||
| Price per share of preferred stock = | $100.00 | Beta = | 1.33 | |||||||||||||||||
| Coupon rate on preferred stock = | 7.00% | Market risk premium = | 6.00% | |||||||||||||||||
| Flotation cost for issuing preferred stock = | 2.10% | Tax rate = | 25% | |||||||||||||||||
| Notes: | ||||||||||||||||||||
| 1. The market value of the notes payable is equal to the book value. Some of the long-term bonds sell at a discount and some sell at a premium, but their aggregate market value is approximately equal to their aggregate book value. | ||||||||||||||||||||
| 2. The common stock price is $31 per share. There are 60 million shares outstanding, for a total market value of equity of $31(60) = $1,860 million. | ||||||||||||||||||||
| 3. The preferred stock price is $100 per share. There are 1 million shares outstanding, for a total market value of preferred of $100(1) = $100 million. | ||||||||||||||||||||
| 9-3 The Cost of Debt | ||||||||||||||||||||
| The relevant cost of debt is the after-tax cost of new debt, taking account of the tax deductibility of interest. The after-tax cost is calculated by multiplying the interest rate (or the before-tax cost of debt) times one minus the tax rate. | ||||||||||||||||||||
| 9-3a After-Tax Cost of Short-Term Debt: rstd (1 − T) | ||||||||||||||||||||
| MicroDrive has a 25% tax rate and notes payable with an 8% interest rate: | ||||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| rstd = | 8% | |||||||||||||||||||
| After-tax cost of short-term debt: rstd (1 - T) = | 6.0% | |||||||||||||||||||
| 9-3b After-Tax Cost of Long-Term Debt: rd (1 − T) | ||||||||||||||||||||
| MicroDrive can issue new bonds at 10%, so this is the pre-tax cost of debt. | ||||||||||||||||||||
| Return required by investors in long-term debt = | 10% | |||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| After-tax cost of long-term debt: rd (1 - T) = | 7.5% | |||||||||||||||||||
| After-tax Cost of Debt for an Outstanding Bond Trading at Par | ||||||||||||||||||||
| The yield should be equal to the coupon rate on a par bond. Verify this by calculating the yield. | ||||||||||||||||||||
| Number of years to maturity | 15 | |||||||||||||||||||
| Number of payments per year | 2 | |||||||||||||||||||
| Annual coupon rate | 10% | |||||||||||||||||||
| Par value | $1,000 | |||||||||||||||||||
| Issue price = Par = PV = | $1,000 | |||||||||||||||||||
| N = | 30 | |||||||||||||||||||
| PMT = | $50 | |||||||||||||||||||
| FV = | $1,000 | |||||||||||||||||||
| I/YR = rd = | 5.0% | |||||||||||||||||||
| Annualized rd = | 10.0% | |||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| After-tax cost of long-term debt: rd (1 - T) = | 7.5% | |||||||||||||||||||
| Cost of Debt for an Outstanding Bond not Trading at Par: Hypothetical Example | ||||||||||||||||||||
| Use the RATE function to find the yield on the bonds with the following information: | ||||||||||||||||||||
| Number of years to maturity | 15 | |||||||||||||||||||
| Number of payments per year | 2 | |||||||||||||||||||
| Annual coupon rate | 9% | |||||||||||||||||||
| Par value | $1,000 | |||||||||||||||||||
| Current price = PV = | $923.14 | |||||||||||||||||||
| N = | 30 | |||||||||||||||||||
| PMT = | $45 | |||||||||||||||||||
| FV = | $1,000 | |||||||||||||||||||
| I/YR = rd = | 5.0% | |||||||||||||||||||
| Annualized rd = | 10.0% | |||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| After-tax cost of long-term debt: rd (1 - T) = | 7.5% | |||||||||||||||||||
| 9-3c Yield to Maturity versus Expected Rate of Return | ||||||||||||||||||||
| Use the RATE function to find the yield on the bonds with the following information: | ||||||||||||||||||||
| Number of years to default | 14 | |||||||||||||||||||
| Recovery percentage at default | 70% | |||||||||||||||||||
| Number of payments per year | 2 | |||||||||||||||||||
| Annual coupon rate | 10% | |||||||||||||||||||
| Par value | $1,000 | |||||||||||||||||||
| Current price = PV = | $1,000 | |||||||||||||||||||
| N = | 28 | |||||||||||||||||||
| PMT = | $50 | |||||||||||||||||||
| FV = | $700 | |||||||||||||||||||
| I/YR = rd = | 4.44% | |||||||||||||||||||
| Annualized rd = | 8.88% | |||||||||||||||||||
| 9-3d Flotation Costs and the Cost of Debt | ||||||||||||||||||||
| For illustrative purposes, suppose a bond is issued with 10-years until maturity, a $1,000 par value, an 8% annual coupon rate, and will make semiannual payments. The issue price is equal to par and the bond will initially sell at its par value. The tax rate is 25% and the flotation percentage cost is 2.8%. | ||||||||||||||||||||
| Input Data: | ||||||||||||||||||||
| Years to maturity = | 10 | |||||||||||||||||||
| Number of payments per year = | 2 | |||||||||||||||||||
| Maturity payment= M = Par = | $1,000 | |||||||||||||||||||
| Issue price = | $1,000 | |||||||||||||||||||
| Annual coupon rate = | 8.0% | |||||||||||||||||||
| Flotation percentage cost (F) = | 2.8% | |||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| The Constant Yield Method | ||||||||||||||||||||
| The net issue price per bond to the issuer is the issue price minus the flotation cost. The first step in the constant yield method is to calculate the issuer's pre-tax yield to maturity based upon the net issue price. Then multiply the pre-tax yield by 1 – T. The result is the after-tax cost of debt. | ||||||||||||||||||||
| Net issue price per bond = | $972.00 | |||||||||||||||||||
| N = | 20 | |||||||||||||||||||
| PMT = | $40.00 | |||||||||||||||||||
| PV = | -$972.00 | |||||||||||||||||||
| FV = | $1,000.00 | |||||||||||||||||||
| Issuer's pre-tax YTM = | 8.420% | |||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| After-tax cost of long-term debt: rd (1 - T) = | 6.315% | |||||||||||||||||||
| After-Tax Cost of Debt for a Par Bond: Flotation Costs ≥ De Minimis | ||||||||||||||||||||
| The after-tax cost of debt depends upon flotation costs, but it also depends upon whether or not the flotation cost per bond is greater than de minimis, which is defined as: | ||||||||||||||||||||
| de minimis = 0.0025(M)(Par) = | $25.00 | |||||||||||||||||||
| If the flotation cost per bond is greater than de minimis, then the constant yield method should be used. That is true for this example, as shown below. | ||||||||||||||||||||
| Flotation costs per bond = | $28.00 | ≥ | $25.00 | = de minimis | ||||||||||||||||
| After-Tax Cost of Debt for a Par Bond: Flotation Costs < De Minimis | ||||||||||||||||||||
| Now consider a bond exactly like the bond in the previous example except that it has a 28 year maturity instead of a 10 year maturity. | ||||||||||||||||||||
| Input Data: | ||||||||||||||||||||
| Years to maturity = | 28 | |||||||||||||||||||
| Number of payments per year = | 2 | |||||||||||||||||||
| Maturity payment= M = Par = | $1,000 | |||||||||||||||||||
| Issue price = | $1,000 | |||||||||||||||||||
| Annual coupon rate = | 8.0% | |||||||||||||||||||
| Flotation percentage cost (F) = | 2.8% | |||||||||||||||||||
| Tax rate = | 25% | |||||||||||||||||||
| If the flotation cost per bond is greater than than de minimis, then the flotation cost must be allocated equally over each payment period as a noncash expense that reduces the issuer's taxes in each payment period. The after-tax cost of debt is equal to the yield to maturity, base upon after-tax cash interest payments. Otherwise, the constant yield method should be used. | ||||||||||||||||||||
| de minimis = 0.0025(M)(Par) = | $70.00 | |||||||||||||||||||
| Flotation costs per bond = | $28.00 | |||||||||||||||||||
| The net discount is < de minimis, so use the allocation method. | ||||||||||||||||||||
| The first step is to allocate flotation costs in equal portions to each payment period. The allocated flotation costs are a noncash expense but they may be deducted for tax purposes. This creates a tax shield each period in the amount of T(allocated flotation cost). The second step is to calculate the after-tax coupon payments. Use these after-tax values to calculate the yield to maturity, which is the after-tax cost of debt. | ||||||||||||||||||||
| Number of coupon payments = N = | 56 | |||||||||||||||||||
| Allocated flotation cost/period = Allocated cost/N = | $0.50 | |||||||||||||||||||
| Tax savings from allocated cost = T(allocated cost) = | $0.125 | |||||||||||||||||||
| After-tax coupon payment = Pre-tax coupon (1 − T) = | $30.00 | |||||||||||||||||||
| Net after-tax payment including tax savings = PMT= | $29.875 | |||||||||||||||||||
| Net issue price per bond = Issue price − flotation costs = PV = | -$972.00 | |||||||||||||||||||
| Payment of face value at maturity = FV= | $1,000.0 | |||||||||||||||||||
| Semiannual yield to maturity = Rate = | 3.0933% | |||||||||||||||||||
| Annual yield to maturity = After-tax cost of debt = | 6.1867% | |||||||||||||||||||
| Suppose the analyst incorrectly ignored the allocation of flotation expenses and instead used the constant yield method. How much difference is there between this incorrect approach and the correct approach? | ||||||||||||||||||||
| After-tax cost of long-term debt: constant yield method = | ||||||||||||||||||||
| N = | 56 | |||||||||||||||||||
| PMT = | $40.00 | |||||||||||||||||||
| PV = | -$972.00 | |||||||||||||||||||
| FV = | $1,000.00 | |||||||||||||||||||
| Semiannual yield to maturity = Rate = | 4.128995% | |||||||||||||||||||
| Annual yield to maturity = | 8.25799% | |||||||||||||||||||
| After-tax cost of debt = annual YTM(1-T) = | 6.1935% | Keep in mind that this is the incorrect approach. | ||||||||||||||||||
| After-tax cost of long-term debt: allocation method = | 6.1867% | |||||||||||||||||||
| −After-tax cost of long-term debt: constant yield method = | 6.1935% | |||||||||||||||||||
| Error = | -0.0068% | |||||||||||||||||||
| Most analysts would consider this to be too small a difference and would therefore use the easier constant yield method. | ||||||||||||||||||||
| 9-3e The After-Tax Cost of Debt: Flotation Costs, Premium Bonds, and Discount Bonds | ||||||||||||||||||||
| The appropriate tax treatment depends upon whether the bond has a total net premium or total net discount. | ||||||||||||||||||||
| Total net premium if: | Issue price – flotation costs > Par | |||||||||||||||||||
| Total net discount if: | Issue price – flotation costs < Par | |||||||||||||||||||
| If the bond has a total net premium, use the constant yield method. If the bond has a total net discount, use the same approach as applied above for a bond with flotations costs. | ||||||||||||||||||||
| 9-4 Cost of Preferred Stock, rps | ||||||||||||||||||||
| The cost of preferred stock is simply the preferred dividend divided by the price the company will receive if it issues new preferred stock. No tax adjustment is necessary, as preferred dividends are not tax deductible. | ||||||||||||||||||||
| What is the cost of preferred stock for a company that pays a preferred dividend of $7 per share if the company could sell new preferred with a par value of $100 and a flotation cost of 2.1%? | ||||||||||||||||||||
| Pref. coupon | 7.0% | |||||||||||||||||||
| Par value | $100.00 | |||||||||||||||||||
| Pref. Dividend | $7.00 | |||||||||||||||||||
| Flotation % | 2.1% | |||||||||||||||||||
| Net preferred issue price | $97.90 | |||||||||||||||||||
| rps = | DivPref | ÷ | Net Pref. Price | |||||||||||||||||
| rps = | $7.00 | ÷ | $97.90 | = | 7.150% | |||||||||||||||
| 9-5 Cost of Common Stock: The Market Risk Premium, RPM | ||||||||||||||||||||
| Before addressing the required return of an individual stock, what is the required return for the stock market? What is the Market Risk Premium (RPM), which is excess return investor require to induce them to invest in the stock market rather than a long-term T-bond? | ||||||||||||||||||||
| There are 3 methods to estimate the market risk premium. (1) Use historical market data as an estimate for the current risk premium. (2) Ask experts. (3) Estimate a forward looking risk premium, found as the differential between expected returns on the S&P 500 over some forecasted future period and the current long-term bond rate. | ||||||||||||||||||||
| 9-5a Historical Risk Premiums | ||||||||||||||||||||
| Many analysts use data provided by Ibbotson Associates, which has collected data from 1926. Ibbotson publishes information annually that enables use of different periods and thus different historical risk premiums. Ibbotson recommends using the longest set of data, but others disagree, arguing that events that occurred back in the period of say 1926 to 1966 are less relevant than events that occurred during the last 50 or so years. | ||||||||||||||||||||
| Ibbotson Historical Risk Premium: 1926-Current Date | ||||||||||||||||||||
| Average | ||||||||||||||||||||
| Arithmetic | Geometric | |||||||||||||||||||
| Stock market return (return on large stocks) | 12.00% | 10.00% | ||||||||||||||||||
| Risk-free rate: | ||||||||||||||||||||
| 20-year T-bond yield at beginning of year | 6.00% | 5.60% | Note: Ibbotson actually uses the bond's return due to income as a proxy for the yield. | |||||||||||||||||
| Historical risk premium: | ||||||||||||||||||||
| RM minus T-bond yield = | 6.00% | 4.40% | ||||||||||||||||||
| Our Historical Risk Premium: 1968-Current Date | ||||||||||||||||||||
| Data | ||||||||||||||||||||
| S&P 500 | 10-Year T-bond (Treasury 10-year constant maturity) | Premium | For calculation of geometric mean: wealth relative | |||||||||||||||||
| Index Level Mike Ehrhardt: Level from www.finance.yahoo.com, symbol, ^GSPC, level on last trading day of year. | Total Return, rM Mike Ehrhardt: The easiest source is https://ycharts.com/indicators/sandp_500_total_return_annual. It used to come from WSJ annual year-end review; usually reported on first business day after Dec. 30. but not reported this year Could construct from http://us.spindices.com/documents/additional-material/sp-500-eps-est.xlsx since it gives per share quarterly dividends | Capital Gains | Return on Dividends | Reported yield on last day of year Mike Ehrhardt: FRED: Title: 10-Year Treasury Constant Maturity Rate Series ID: DGS10 Source: Board of Governors of the Federal Reserve System Release: H.15 Selected Interest Rates Seasonal Adjustment: Not Applicable Frequency: Annual Aggregation Method: End of Period | Yield on First Day of Year, Required rRF Mike Ehrhardt: Estimated as yield on last day of previous year. | Actual Return During Year, Actual rRF | rM − Required rRF | rM − Actual return of 10-year bond | Total Return, rM | Capital Gains | Return on Dividends | Reported yield on last day of year | Yield on First Day of Year, Required rRF | Actual Return During Year, Actual rRF | rM − Required rRF | rM − Actual return of 10-year bond | ||||
| Year | ||||||||||||||||||||
| 2017 | 2,673.61 | 21.83% | 19.41% | 1.85% | 2.33% | 2.45% | 3.536% | 19.38% | 18.29% | 1.22 | 1.19 | 1.02 | 1.02 | 1.02 | 1.04 | 1.19 | 1.18 | |||
| 2016 | 2238.93 | 11.96% | 9.54% | 2.42% | 2.45% | 2.27% | 0.664% | 9.69% | 11.30% | 1.12 | 1.10 | 1.02 | 1.02 | 1.02 | 1.01 | 1.10 | 1.11 | |||
| 2015 | 2043.94 | 1.38% | -0.73% | 2.11% | 2.27% | 2.17% | 1.274% | -0.79% | 0.11% | 1.01 | 0.99 | 1.02 | 1.02 | 1.02 | 1.01 | 0.99 | 1.00 | |||
| 2014 | 2058.90 | 13.69% | 11.39% | 2.30% | 2.17% | 3.04% | 11.211% | 10.65% | 2.48% | 1.14 | 1.11 | 1.02 | 1.02 | 1.03 | 1.11 | 1.11 | 1.02 | |||
| 2013 | 1848.36 | 32.39% | 29.60% | 2.79% | 3.04% | 1.78% | -8.9% | 30.61% | 41.28% | 1.32 | 1.30 | 1.03 | 1.03 | 1.02 | 0.91 | 1.31 | 1.41 | |||
| 2012 | 1426.19 | 16.00% | 13.41% | 2.59% | 1.78% | 1.89% | 2.885% | 14.11% | 13.11% | 1.16 | 1.13 | 1.03 | 1.02 | 1.02 | 1.03 | 1.14 | 1.13 | |||
| 2011 | 1257.60 | 2.11% | -0.00% | 2.11% | 1.89% | 3.30% | 16.901% | -1.19% | -14.79% | 1.02 | 1.00 | 1.02 | 1.02 | 1.03 | 1.17 | 0.99 | 0.85 | |||
| 2010 | 1257.64 | 15.06% | 12.78% | 2.28% | 3.30% | 3.85% | 8.934% | 11.21% | 6.13% | 1.15 | 1.13 | 1.02 | 1.03 | 1.04 | 1.09 | 1.11 | 1.06 | |||
| 2009 | 1115.1 | 26.46% | 23.45% | 3.01% | 3.85% | 2.25% | -11.085% | 24.21% | 37.55% | 1.26 | 1.23 | 1.03 | 1.04 | 1.02 | 0.89 | 1.24 | 1.38 | |||
| 2008 | 903.25 | -37.00% | -38.49% | 1.49% | 2.25% | 4.04% | 21.628% | -41.04% | -58.63% | 0.63 | 0.62 | 1.01 | 1.02 | 1.04 | 1.22 | 0.59 | 0.41 | |||
| 2007 | 1468.36 | 5.49% | 3.53% | 1.96% | 4.04% | 4.71% | 10.938% | 0.78% | -5.45% | 1.05 | 1.04 | 1.02 | 1.04 | 1.05 | 1.11 | 1.01 | 0.95 | |||
| 2006 | 1418.3 | 15.79% | 13.62% | 2.17% | 4.71% | 4.39% | 1.554% | 11.40% | 14.24% | 1.16 | 1.14 | 1.02 | 1.05 | 1.04 | 1.02 | 1.11 | 1.14 | |||
| 2005 | 1248.29 | 4.91% | 3.00% | 1.91% | 4.39% | 4.24% | 2.900% | 0.67% | 2.01% | 1.05 | 1.03 | 1.02 | 1.04 | 1.04 | 1.03 | 1.01 | 1.02 | |||
| 2004 | 1211.92 | 10.88% | 8.99% | 1.89% | 4.24% | 4.27% | 4.540% | 6.61% | 6.34% | 1.11 | 1.09 | 1.02 | 1.04 | 1.04 | 1.05 | 1.07 | 1.06 | |||
| 2003 | 1111.92 | 28.70% | 26.38% | 2.32% | 4.27% | 3.83% | -0.047% | 24.87% | 28.75% | 1.29 | 1.26 | 1.02 | 1.04 | 1.04 | 1.00 | 1.25 | 1.29 | |||
| 2002 | 879.82 | -22.10% | -23.37% | 1.27% | 3.83% | 5.07% | 16.918% | -27.17% | -39.02% | 0.78 | 0.77 | 1.01 | 1.04 | 1.05 | 1.17 | 0.73 | 0.61 | |||
| 2001 | 1148.08 | -11.88% | -13.04% | 1.16% | 5.07% | 5.12% | 5.571% | -17.00% | -17.45% | 0.88 | 0.87 | 1.01 | 1.05 | 1.05 | 1.06 | 0.83 | 0.83 | |||
| 2000 | 1320.28 | -9.11% | -10.14% | 1.03% | 5.12% | 6.45% | 19.203% | -15.56% | -28.31% | 0.91 | 0.90 | 1.01 | 1.05 | 1.06 | 1.19 | 0.84 | 0.72 | |||
| 1999 | 1469.25 | 21.04% | 19.53% | 1.51% | 6.45% | 4.65% | -10.240% | 16.39% | 31.28% | 1.21 | 1.20 | 1.02 | 1.06 | 1.05 | 0.90 | 1.16 | 1.31 | |||
| 1998 | 1229.23 | 28.58% | 26.67% | 1.91% | 4.65% | 5.75% | 16.185% | 22.83% | 12.39% | 1.29 | 1.27 | 1.02 | 1.05 | 1.06 | 1.16 | 1.23 | 1.12 | |||
| 1997 | 970.43 | 33.36% | 31.01% | 2.35% | 5.75% | 6.43% | 12.750% | 26.93% | 20.61% | 1.33 | 1.31 | 1.02 | 1.06 | 1.06 | 1.13 | 1.27 | 1.21 | |||
| 1996 | 740.74 | 23.07% | 20.26% | 2.81% | 6.43% | 5.58% | -1.771% | 17.49% | 24.84% | 1.23 | 1.20 | 1.03 | 1.06 | 1.06 | 0.98 | 1.17 | 1.25 | |||
| 1995 | 615.93 | 37.43% | 34.11% | 3.32% | 5.58% | 7.84% | 30.486% | 29.59% | 6.94% | 1.37 | 1.34 | 1.03 | 1.06 | 1.08 | 1.30 | 1.30 | 1.07 | |||
| 1994 | 459.27 | 1.31% | -1.54% | 2.85% | 7.84% | 5.83% | -10.655% | -4.52% | 11.97% | 1.01 | 0.98 | 1.03 | 1.08 | 1.06 | 0.89 | 0.95 | 1.12 | |||
| 1993 | 466.45 | 9.99% | 7.06% | 2.93% | 5.83% | 6.70% | 14.859% | 3.29% | -4.87% | 1.10 | 1.07 | 1.03 | 1.06 | 1.07 | 1.15 | 1.03 | 0.95 | |||
| 1992 | 435.71 | 7.67% | 4.46% | 3.21% | 6.70% | 6.71% | 6.800% | 0.96% | 0.87% | 1.08 | 1.04 | 1.03 | 1.07 | 1.07 | 1.07 | 1.01 | 1.01 | |||
| 1991 | 417.09 | 30.55% | 26.31% | 4.24% | 6.71% | 8.08% | 21.229% | 22.47% | 9.32% | 1.31 | 1.26 | 1.04 | 1.07 | 1.08 | 1.21 | 1.22 | 1.09 | |||
| 1990 | 330.22 | -3.17% | -6.56% | 3.39% | 8.08% | 7.93% | 6.589% | -11.10% | -9.76% | 0.97 | 0.93 | 1.03 | 1.08 | 1.08 | 1.07 | 0.89 | 0.90 | |||
| 1989 | 353.4 | 31.49% | 27.25% | 4.24% | 7.93% | 9.14% | 20.659% | 22.35% | 10.83% | 1.31 | 1.27 | 1.04 | 1.08 | 1.09 | 1.21 | 1.22 | 1.11 | |||
| 1988 | 277.72 | 16.81% | 12.40% | 4.41% | 9.14% | 8.83% | 6.079% | 7.98% | 10.73% | 1.17 | 1.12 | 1.04 | 1.09 | 1.09 | 1.06 | 1.08 | 1.11 | |||
| 1987 | 247.08 | 5.23% | 2.03% | 3.20% | 8.83% | 7.23% | -6.152% | -2.00% | 11.38% | 1.05 | 1.02 | 1.03 | 1.09 | 1.07 | 0.94 | 0.98 | 1.11 | |||
| 1986 | 242.17 | 18.47% | 14.62% | 3.85% | 7.23% | 9.00% | 26.304% | 9.47% | -7.83% | 1.18 | 1.15 | 1.04 | 1.07 | 1.09 | 1.26 | 1.09 | 0.92 | |||
| 1985 | 211.28 | 32.16% | 26.33% | 5.83% | 9.00% | 11.55% | 37.359% | 20.61% | -5.20% | 1.32 | 1.26 | 1.06 | 1.09 | 1.12 | 1.37 | 1.21 | 0.95 | |||
| 1984 | 167.24 | 6.27% | 1.40% | 4.87% | 11.55% | 11.82% | 14.280% | -5.55% | -8.01% | 1.06 | 1.01 | 1.05 | 1.12 | 1.12 | 1.14 | 0.94 | 0.92 | |||
| 1983 | 164.93 | 22.51% | 17.27% | 5.24% | 11.82% | 10.36% | -1.951% | 12.15% | 24.46% | 1.23 | 1.17 | 1.05 | 1.12 | 1.10 | 0.98 | 1.12 | 1.24 | |||
| 1982 | 140.64 | 21.41% | 14.76% | 6.65% | 10.36% | 13.98% | 52.399% | 7.43% | -30.99% | 1.21 | 1.15 | 1.07 | 1.10 | 1.14 | 1.52 | 1.07 | 0.69 | |||
| 1981 | 122.55 | -4.91% | -9.73% | 4.82% | 13.98% | 12.43% | -0.605% | -17.34% | -4.30% | 0.95 | 0.90 | 1.05 | 1.14 | 1.12 | 0.99 | 0.83 | 0.96 | |||
| 1980 | 135.76 | 32.42% | 25.77% | 6.65% | 12.43% | 10.33% | -6.890% | 22.09% | 39.31% | 1.32 | 1.26 | 1.07 | 1.12 | 1.10 | 0.93 | 1.22 | 1.39 | |||
| 1979 | 107.94 | 18.44% | 12.31% | 6.13% | 10.33% | 9.15% | -0.918% | 9.29% | 19.36% | 1.18 | 1.12 | 1.06 | 1.10 | 1.09 | 0.99 | 1.09 | 1.19 | |||
| 1978 | 96.11 | 6.56% | 1.06% | 5.50% | 9.15% | 7.78% | -3.802% | -1.22% | 10.36% | 1.07 | 1.01 | 1.05 | 1.09 | 1.08 | 0.96 | 0.99 | 1.10 | |||
| 1977 | 95.1 | -7.18% | -11.50% | 4.32% | 7.78% | 6.81% | -1.536% | -13.99% | -5.64% | 0.93 | 0.88 | 1.04 | 1.08 | 1.07 | 0.98 | 0.86 | 0.94 | |||
| 1976 | 107.46 | 23.84% | 19.15% | 4.69% | 6.81% | 7.76% | 16.699% | 16.08% | 7.14% | 1.24 | 1.19 | 1.05 | 1.07 | 1.08 | 1.17 | 1.16 | 1.07 | |||
| 1975 | 90.19 | 37.20% | 31.55% | 5.65% | 7.76% | 7.40% | 4.214% | 29.80% | 32.99% | 1.37 | 1.32 | 1.06 | 1.08 | 1.07 | 1.04 | 1.30 | 1.33 | |||
| 1974 | 68.56 | -26.47% | -29.72% | 3.25% | 7.40% | 6.90% | 2.503% | -33.37% | -28.97% | 0.74 | 0.70 | 1.03 | 1.07 | 1.07 | 1.03 | 0.67 | 0.71 | |||
| 1973 | 97.55 | -14.66% | -17.37% | 2.71% | 6.90% | 6.41% | 2.100% | -21.07% | -16.76% | 0.85 | 0.83 | 1.03 | 1.07 | 1.06 | 1.02 | 0.79 | 0.83 | |||
| 1972 | 118.05 | 18.98% | 15.63% | 3.35% | 6.41% | 5.89% | 1.323% | 13.09% | 17.66% | 1.19 | 1.16 | 1.03 | 1.06 | 1.06 | 1.01 | 1.13 | 1.18 | |||
| 1971 | 102.09 | 14.31% | 10.79% | 3.52% | 5.89% | 6.50% | 12.151% | 7.81% | 2.16% | 1.14 | 1.11 | 1.04 | 1.06 | 1.07 | 1.12 | 1.08 | 1.02 | |||
| 1970 | 92.15 | 3.10% | 0.10% | 3.00% | 6.50% | 7.88% | 21.133% | -4.78% | -18.04% | 1.03 | 1.00 | 1.03 | 1.07 | 1.08 | 1.21 | 0.95 | 0.82 | |||
| 1969 | 92.06 | -8.36% | -11.36% | 3.00% | 7.88% | 6.16% | -8.137% | -14.52% | -0.22% | 0.92 | 0.89 | 1.03 | 1.08 | 1.06 | 0.92 | 0.85 | 1.00 | |||
| 1968 | 103.86 | 10.66% | 7.66% | 3.00% | 6.16% | 5.70% | 1.649% | 4.96% | 9.01% | 1.11 | 1.08 | 1.03 | 1.06 | 1.06 | 1.02 | 1.05 | 1.09 | |||
| 1967 | 96.47 | 5.70% | 1.057 | |||||||||||||||||
| Arithmetic average | 11.49% | 8.22% | 3.26% | 6.33% | 6.39% | 7.67% | 5.10% | 3.82% | ||||||||||||
| Geometric average | 10.10% | 6.87% | 3.25% | 6.29% | 6.36% | 6.98% | 3.64% | 1.54% | ||||||||||||
| Our Historical Risk Premium Based on Data | ||||||||||||||||||||
| Average | ||||||||||||||||||||
| Arithmetic | Geometric | |||||||||||||||||||
| Stock market return (S&P 500) | 11.49% | 10.10% | ||||||||||||||||||
| Risk-free rate: | ||||||||||||||||||||
| 10-year Treasury contestant maturity yield at beginning of year | 6.39% | 6.36% | ||||||||||||||||||
| Historical risk premium: | ||||||||||||||||||||
| RM minus T-bond yield = | 5.10% | 3.64% | ||||||||||||||||||
| Expert Opinions for Estimates of the Risk Premium | ||||||||||||||||||||
| Surveys of experts (CFO's, analysts, professors) are another way to estimate the risk premium. | ||||||||||||||||||||
| Forward-Looking Risk Premiums | ||||||||||||||||||||
| Historical risk premiums look at past data and assume that investors think the best estimate of the current risk premium is the historical differential between earned returns on stocks and bonds. Forward-looking risk premiums assume that investors expect equities to earn a rate that is equal to the expected dividend yield plus the expected capital gains (growth) rate and the current yield on Treasury securities. | ||||||||||||||||||||
| If we make these two assumptions, we can use the constant dividend growth model to estimate the expected return on the market: (1) growth is expected to be constant, (2) the firm pays out all available funds as dividends (i.e., there are no stock repurchases or purchases of short-term securities). | ||||||||||||||||||||
| rM = (D1/P0) + g | ||||||||||||||||||||
| To use this model, we need estimates of the expected dividend yield and the expected growth rate in the stock price (recall that in a constant growth model, the expected growth in stock price is also the expected growth in dividends). | ||||||||||||||||||||
| Simplified Illustration of Estimating a Forward-Looking Risk Premium | This data comes from the S&P estimates Excel file referenced in the Web chapter tab. | |||||||||||||||||||
| Estimating the Year-1 Dividend Yield (See source at right) | For current estimates from Standard & Poor’s, go to www.standardandpoors.com and select S&P Dow Jones Indices. Then select SP 500 under Indices. Then under Additional Info, select Index Earnings and download the spreadsheet. The forward-looking dividend yield is the one labeled Dividend yield (current indicated rate) around 90 lines down. Note that S&P reorganizes their site frequently and this spreadsheet may not be in the same location when you look! If you can't find it, search on Earnings Estimates, or EPSEST while in the S&P 500 Index section. | |||||||||||||||||||
| D1/P0 = | 2.00% | Get from S&P see source at right | Date | Date as a year | Annual DPS | LN(Dividends) | ||||||||||||||
| 12/31/88 | 89.06 | $9.75 | 2.2773 | |||||||||||||||||
| Estimating the Long-Term Growth Rate | 12/31/89 | 90.06 | $11.06 | 2.4029 | ||||||||||||||||
| 12/31/90 | 91.06 | $12.09 | 2.4920 | |||||||||||||||||
| Since 1988, the average dividend growth for the S&P 500 has been about: | 12/31/91 | 92.06 | $12.20 | 2.5017 | ||||||||||||||||
| 12/31/92 | 93.07 | $12.39 | 2.5165 | |||||||||||||||||
| g = | 4.99% | See estimate at right | Growth rate in dividends using the Excel function =LOGEST. | 12/31/93 | 94.07 | $12.58 | 2.5319 | |||||||||||||
| 4.99% | 12/31/94 | 95.07 | $13.17 | 2.5779 | ||||||||||||||||
| Estimated Forward-Looking Expected Market Return | 12/31/95 | 96.07 | $13.79 | 2.6238 | ||||||||||||||||
| 12/31/96 | 97.07 | $14.90 | 2.7013 | |||||||||||||||||
| rM = | (D1/P0) + g | We would like estimates of the function: dividend = a*e^(r*year). r will be the estimated growth rate of dividends, which is what we want. The Excel function =logest almost does this. It estimates a regression of the form: y = b*m^x, or in our case, dividends = b*m^year. A little algebra shows that r = ln(m), which is the growth estimate. r can be estimated directly, see below, with the linear regression ln(y) = c + r*year. The easiest way to do this directly is to use the =slope function. | 12/31/97 | 98.07 | $15.50 | 2.7406 | ||||||||||||||
| rM = | 6.99% | 12/31/98 | 99.07 | $16.20 | 2.7847 | |||||||||||||||
| 12/31/99 | 100.07 | $16.69 | 2.8149 | |||||||||||||||||
| 12/31/00 | 101.07 | $16.27 | 2.7894 | |||||||||||||||||
| Estimated Forward-Looking Premium | 12/31/01 | 102.07 | $15.74 | 2.7562 | ||||||||||||||||
| Yield on 10-year T-bond on Michael Ehrhardt: See https://fred.stlouisfed.org/series/DGS10 | 12/31/02 | 103.07 | $16.07 | 2.7772 | ||||||||||||||||
| rRF = | 2.97% | 5/4/18 | 12/31/03 | 104.07 | $17.39 | 2.8556 | ||||||||||||||
| Growth rate in dividends using the Excel function =SLOPE and ln(dividends) as y. | 12/31/04 | 105.07 | $19.44 | 2.9674 | ||||||||||||||||
| RPM = rM – rRF = | 4.02% | Assumes constant growth and no stock repurchases. | 4.86% | 12/31/05 | 106.07 | $22.22 | 3.1008 | |||||||||||||
| 12/31/06 | 107.07 | $24.88 | 3.2142 | |||||||||||||||||
| 12/31/07 | 108.07 | $27.73 | 3.3226 | |||||||||||||||||
| 9-6 Using the CAPM to Estimate the Cost of Common Stock, rs | 12/31/08 | 109.08 | $28.39 | 3.3459 | ||||||||||||||||
| 12/31/09 | 110.08 | $22.41 | 3.1093 | |||||||||||||||||
| rs = risk-free rate + (Market risk premium) (Beta) | 12/31/10 | 111.08 | $22.73 | 3.1236 | ||||||||||||||||
| = rRF + (RPM) bi (Recall that: RPM is the expected return on the market minus the risk-free rate.) | 12/31/11 | 112.08 | $26.43 | 3.2743 | ||||||||||||||||
| 12/31/12 | 113.08 | $31.25 | 3.4420 | |||||||||||||||||
| The Risk-Free Rate | 12/31/13 | 114.08 | $34.99 | 3.5551 | ||||||||||||||||
| 12/31/14 | 115.08 | $39.44 | 3.6749 | |||||||||||||||||
| The risk-free rate is often proxied by the yield on a long-term Treasury bond. When we wrote this, the rate on a 10-year T-bond was: | 12/31/15 | 116.08 | $43.39 | 3.7702 | ||||||||||||||||
| 12/30/16 | 117.08 | $45.70 | 3.8221 | |||||||||||||||||
| 12/29/17 | 118.08 | $48.93 | 3.8904 | |||||||||||||||||
| Date of data: | 5/4/18 | |||||||||||||||||||
| Yield on 10-year T-bond = rRF = | 2.97% | |||||||||||||||||||
| The Market Risk Premium | ||||||||||||||||||||
| The market risk premium is the return in excess of the risk-free rate that is required to induce investors to invest in the stock market. | ||||||||||||||||||||
| Assumed market risk premium = RPM = | 6.00% | |||||||||||||||||||
| Estimating Beta | ||||||||||||||||||||
| Beta can be estimated from historical stock returns using the following formula, where ρim is the correlation between Stock i and the market, σi is the standard deviation of Stock i, and σM is the standard deviation of the market. | ||||||||||||||||||||
| Beta for Stock i = bi = | riM(si/sM) | |||||||||||||||||||
| The same estimate for beta can be obtained as the estimated slope coefficient in a regression, with the company’s stock returns on the y-axis and market returns on the x-axis. Beta can also be obtained from many Web sources. | ||||||||||||||||||||
| MicroDrive's beta: | ||||||||||||||||||||
| bi = | 1.33 | |||||||||||||||||||
| An Illustration of the CAPM Approach: MicroDrive’s Cost of Equity, rs | ||||||||||||||||||||
| Risk-free rate | 5.02% | |||||||||||||||||||
| Market risk premium | 6.0% | |||||||||||||||||||
| Beta | 1.33 | |||||||||||||||||||
| rs = | rRF | + | (RPM) | (bi) | ||||||||||||||||
| rs = | 5.02% | + | 6.0% | 1.33 | ||||||||||||||||
| rs = | 5.02% | + | 8.0% | |||||||||||||||||
| rs = | 13.00% | |||||||||||||||||||
| 9-7 Dividend-Yield-Plus-Growth-Rate, or Discounted Cash Flow (DCF), Approach | ||||||||||||||||||||
| The simplest DCF model assumes that growth is expected to remain constant, and in this case: | rs = D1/P0 + g. | |||||||||||||||||||
| Estimating Inputs for the DCF Approach | ||||||||||||||||||||
| The next expected dividend is easy to estimate, and the stock price can be determined readily. However, it is not easy to determine the marginal investor's expected future growth rate. Three approaches are commonly used: (1) historical growth rates, (2) retention growth model, and (3) analysts' forecasts. | ||||||||||||||||||||
| 1. Historical Growth Rates | ||||||||||||||||||||
| Historical growth estimates are usually not good estimates of expected future growth except for a few very stable and mature companies. | ||||||||||||||||||||
| 2. Retention Growth Model | ||||||||||||||||||||
| Another method for finding the growth is utilizing the sustainable growth rate, found by multiplying the expected future return on equity (ROE) times the expected future retention ratio (i.e., the percentage of net income that is not paid out as dividends). This is: | ||||||||||||||||||||
| g = (Retention rate) (ROE) = (1 – Payout rate) (ROE) | ||||||||||||||||||||
| Suppose a firm's expected ROE is 14.5% and it pays out 63% of its earnings. What is the firm's sustainable growth rate? | ||||||||||||||||||||
| Payout rate = | 63% | |||||||||||||||||||
| ROE = | 14.50% | |||||||||||||||||||
| g = | (1 – Payout rate) x (ROE) | |||||||||||||||||||
| g = | 37% | x | 14.50% | |||||||||||||||||
| g = | 5.4% | |||||||||||||||||||
| 3. Analysts' Forecasts | ||||||||||||||||||||
| A third method for estimating the growth rate is to use analysts' forecasts. Value Line provides estimated dividends. IBES, Zack's, and many brokerage firms provide estimates of growth rates, which can be used as proxies for dividend growth. These often have a forecast for the next five years and then a long-term forecast for the period after five years, which requires the use of a nonconstant multi-stage growth model, as described in the Web Extension. | ||||||||||||||||||||
| An Illustration of the DCF Approach | ||||||||||||||||||||
| Suppose a firm's stock trades at $32 and its next dividend is expected to be $1.82. If the expected growth rate is 5.5%, what is the firm's cost of equity? | ||||||||||||||||||||
| P0 = | $32.00 | |||||||||||||||||||
| D1 = | $1.82 | |||||||||||||||||||
| g = | 5.4% | |||||||||||||||||||
| rs = | D1 | ÷ | P0 | + | g | |||||||||||||||
| rs = | $1.82 | ÷ | $32.00 | + | 5.4% | |||||||||||||||
| rs = | 11.1% | |||||||||||||||||||
| 9-8 The Weighted Average Cost of Capital (WACC) | ||||||||||||||||||||
| The weighted average cost of capital (WACC) is calculated using the firm's target capital structure together with its after-tax cost of long-term debt, after-tax cost of short-term debt, cost of preferred stock, and cost of common equity. | ||||||||||||||||||||
| WACC = | Weighted average cost of capital | |||||||||||||||||||
| = | wd rd(1 – T) + wstd(1 – T)rstd + wps rps + ws rs | |||||||||||||||||||
| A firm's target capital structure consists of the following capital structure. Using the relevant costs calculated previously, what is the firm's weighted average cost of capital? | ||||||||||||||||||||
| T = | 25% | |||||||||||||||||||
| wd = | 20% | rd = | 10.0% | |||||||||||||||||
| wstd = | 4% | rstd = | 8.0% | |||||||||||||||||
| wps = | 2% | rps = | 7.15% | |||||||||||||||||
| ws = | 74% | rs = | 13.0% | |||||||||||||||||
| Sources of Capital | ||||||||||||||||||||
| Long-term Debt | Short-term Debt | Preferred Stock | Common Stock | |||||||||||||||||
| Pre-tax cost of capital source, ri: | 10.00% | 8.00% | 7.15% | 13.00% | ||||||||||||||||
| After-tax cost of debt, (1-T)(ri): | 7.50% | 6.00% | ||||||||||||||||||
| Cost of capital component for WACC: | 7.50% | 6.00% | 7.15% | 13.00% | ||||||||||||||||
| Target capital structure weight, wi: | 20.00% | 4.00% | 2.00% | 74.00% | 100% | = Sum | ||||||||||||||
| Weighted component cost: | 1.5000% | 0.2400% | 0.1430% | 9.6200% | 11.50% | = Sum | ||||||||||||||
| WACC = | 11.50% | |||||||||||||||||||
| 9-9 Adjusting the Cost of Equity for Flotation Costs | ||||||||||||||||||||
| A company's stock sells for $32 and its next dividend is expected to be $1.82, with constant growth of 5.5%. What is the cost of equity using the DCF model? | ||||||||||||||||||||
| P0 = | $32.00 | |||||||||||||||||||
| D1 = | $1.82 | |||||||||||||||||||
| g = | 5.4% | |||||||||||||||||||
| rs = | D1 | ÷ | P0 | + | g | |||||||||||||||
| rs = | $1.82 | ÷ | $32.00 | + | 5.4% | |||||||||||||||
| rs = | 11.1% | |||||||||||||||||||
| If the firm in the preceding question incurred a flotation cost of 12.5% for issuing new stock, how much higher is its cost of equity from having to issue new common stock? | ||||||||||||||||||||
| Flotation percentage cost (F) = | 12.5% | |||||||||||||||||||
| Stock price = | $32.00 | |||||||||||||||||||
| Net proceeds after flotation costs = | (Stock Price) | (1 – F) | ||||||||||||||||||
| Net proceeds after flotation costs = | $32.00 | 88% | ||||||||||||||||||
| Net proceeds after flotation costs = | $28.00 | |||||||||||||||||||
| Net proceeds after flotation costs = | $28.00 | |||||||||||||||||||
| D1 = | $1.82 | |||||||||||||||||||
| g = | 5.40% | |||||||||||||||||||
| rs = | D1 | ÷ | Net Proceeds | + | g | |||||||||||||||
| rs = | $1.82 | ÷ | $28.00 | + | 5.4% | |||||||||||||||
| rs = | 6.5% | + | 5.4% | |||||||||||||||||
| rs = | 11.9% | |||||||||||||||||||
| Notice that this cost of stock is quite different than the cost of stock without flotation costs. | ||||||||||||||||||||
| To find the cost of perpetual preferred stock, simply use the procedure above with g = 0. If the preferred stock has a fixed maturity, then use the same procedure as for debt, except that the preferred dividend is not tax deductible. | ||||||||||||||||||||
| 9-10 Privately Owned Firms and Small Businesses | ||||||||||||||||||||
| A privately held firm often estimates its own beta as the average beta of publicly traded companies in the same industry. | ||||||||||||||||||||
| Own-Bond-Yield-Plus-Judgmental-Risk-Premium Approach | ||||||||||||||||||||
| This approach consists of adding a judgmental risk premium to the yield on the firm's own long-term debt. It is logical that a firm with risky, low-rated debt would also have risky, high-cost equity. Historically, we have observed that the risk premium for equity is in the range of 3 to 5 percentage points. In addition to applications to privately held firms, this method is used primarily in utility rate case hearings. | ||||||||||||||||||||
| Example: | ||||||||||||||||||||
| Judgmental over-own-bond-yield risk premium = | 4.0% | |||||||||||||||||||
| Bond yield or rd = | 10.0% | |||||||||||||||||||
| rs = | Extra Premium | + | rd | |||||||||||||||||
| rs = | 4.0% | + | 10.0% | |||||||||||||||||
| rs = | 14.0% | |||||||||||||||||||
| 9-11 Managerial Issues and the Cost of Capital | ||||||||||||||||||||
| There is a relationship between the cost of capital and risk--the higher a project's risk, the higher its cost of capital. When adjusting for risk, firms usually begin by estimating a divisional cost of capital, and then adjusting this estimate for the risk of individual projects. | ||||||||||||||||||||
| Consider a company with a single division, steel production. The risk-free rate of interest is 5%, and the market risk premium is 6%. If the firm has a beta of 1.1, what is the firm's cost of equity? | ||||||||||||||||||||
| Risk-free rate | 5% | |||||||||||||||||||
| Market risk premium | 6.0% | |||||||||||||||||||
| Steel Beta | 1.1 | rSteel = | 11.6% | |||||||||||||||||
| Suppose the firm undertakes a new operation (a barge project). The average beta of companies that only have barge operations (I.e., pure-play companies) is 1.5. What is the cost of equity for the new division? | ||||||||||||||||||||
| Risk-free rate | 5% | |||||||||||||||||||
| Market risk premium | 6.0% | |||||||||||||||||||
| Barge Beta | 1.5 | rBarge = | 14.0% | |||||||||||||||||
| Now suppose the firm undertakes a new low-risk operation (a distribution center). The average beta of companies that only have distribution centers (I.e., pure-play companies) is 0.5. What is the cost of equity for the new division? | ||||||||||||||||||||
| Risk-free rate | 5% | |||||||||||||||||||
| Market risk premium | 6.0% | rCenter = | 8.0% | |||||||||||||||||
| Distribution Beta | 0.5 | |||||||||||||||||||
| After adding the two new divisions, the Steel division will make up 70% of the company's value, the Barge division will make up 20%, and the Distribution division will make up 10%. What is the new beta for the entire company? (Hint: the beta of the firm is a weighted average of the divisional betas.) What rate of return will equity holders require the firm as a whole to provide? | ||||||||||||||||||||
| Beta of Steel Division | 1.1 | |||||||||||||||||||
| % of the firm | 70% | |||||||||||||||||||
| Beta of Barge Division | 1.5 | |||||||||||||||||||
| % of the firm | 20% | |||||||||||||||||||
| Beta of Distribution Division | 0.5 | |||||||||||||||||||
| % of the firm | 10% | New corp. beta = | 1.12 | |||||||||||||||||
| Risk-free rate | 5% | |||||||||||||||||||
| Market risk premium | 6.0% | |||||||||||||||||||
| Beta | 1.12 | New rs = | 11.72% |
9-3
| SECTION 9-3 | ||
| SOLUTIONS TO SELF-TEST | ||
| A company has outstanding long-term bonds with a face value of $1,000, a 10% coupon rate, 25 years remaining until maturity, and a current market value of $1,214.82. If it pays interest semiannually, what is the nominal annual required rate of return on debt? If the company’s tax rate is 25%, what is the after-tax cost of debt? | ||
| Number of years to maturity | 25 | |
| Number of payments per year | 2 | |
| Annual coupon rate | 10% | |
| Face value | $1,000 | |
| Tax rate | 25% | |
| N = | 50 | |
| PV = | ($1,214.82) | |
| PMT = | $50 | |
| FV = | $1,000 | |
| I/YR = rd = | 4.000% | |
| Annualized rd = | 8.000% | |
| A-T rd = | 6.000% |
9-4
| SECTION 9-4 | ||
| SOLUTIONS TO SELF-TEST | ||
| A company’s preferred stock currently trades at $50 per share and it pays a $3 annual dividend. Flotation costs are equal to 3% of the gross proceeds. If the company issues preferred stock, what is the cost of that stock? | ||
| Preferred stock price | $50 | |
| Dividend per share | $3 | |
| Flotation percentage | 3% | |
| rps | 6.19% |
9-6
| SECTION 9-6 | ||
| SOLUTIONS TO SELF-TEST | ||
| A company’s beta is 1.4, the yield on a 10-year T-bond is 5%, and the market risk premium is 5.5%. What is rs? | ||
| Beta | 1.40 | |
| 10-year T-bond yield | 4.0% | |
| Market risk premium | 4.5% | |
| rs | 10.30% |
9-7
| SECTION 9-7 | ||
| SOLUTIONS TO SELF-TEST | ||
| A company’s estimated growth rate in dividends is 6%. Its current stock price is $40, and its expected annual dividend is $2. Using the DCF approach, what is rs? | ||
| Growth | 6.0% | |
| Stock price | $40.00 | |
| Expected dividend | $2.00 | |
| rs | 11.00% |
9-8
| SECTION 9-8 | |
| SOLUTIONS TO SELF-TEST | |
| A firm has the following data: Target capital structure of 25% debt, 10% preferred stock, and 65% common equity; tax rate = 25%; rd = 7%; rps = 7.5%; and rs = 11.5%. Assume the firm will not isssue new stock. What is this firm’s WACC? | |
| wd | 25% |
| wps | 10% |
| ws | 65% |
| Tax rate | 25% |
| rd | 7.0% |
| rps | 7.5% |
| rs | 11.5% |
| WACC | 9.54% |
9-9
| SECTION 9-9 | ||
| SOLUTIONS TO SELF-TEST | ||
| A firm has common stock with D1 = $3.00; P0 = $30; g = 5%; and F = 4%. If the firm must issue new stock, what is its cost of external equity, re? | ||
| D1 | $3.00 | |
| P0 | $30.00 | |
| g | 5.0% | |
| F | 4.0% | |
| re | 15.42% |
9-10
| SECTION 9-10 | ||
| SOLUTIONS TO SELF-TEST | ||
| A company’s bond yield is 7%. If the appropriate over-own-bond-yield risk premium is 3.5%, what is rs, based upon the bond--yield-plus-judgmental-risk-premium approach? | ||
| Bond yield | 7.0% | |
| Bond risk premium | 3.5% | |
| rs | 10.50% |
Web 9A
| 11/20/18 | ||||||||||||
| Web Extension 9A: The Required Return Assuming Nonconstant Dividends and Stock Repurchases | ||||||||||||
| As we explained in the chapter, two assumptions underlie the constant dividend growth model: (1) firms do not repurchase any stock, and (2) growth in dividends will be constant. We now explain how to estimate the required return when those assumptions are violated. | ||||||||||||
| Estimating the Long-Term Growth Rate | ||||||||||||
| The long-term constant growth rate should be approximately equal to the long-term growth rate in sales revenue, which depends on prices and units sold. Prices will be determined by inflation in the long-term, and units sold will depend on sustainable population growth. | ||||||||||||
| The forward estimated inflation rate is the difference between yields on a regular 10-year Treasury bond and an inflation protected 10-year Treasury bond, called a TIPS. | ||||||||||||
| Yield on 10-year Treasury bond: | 2.87% | 2/28/18 | ||||||||||
| Yield on 10-year TIPS: | 0.75% | |||||||||||
| Forward estimate of inflation: | 2.12% | |||||||||||
| The Fed provides inflation data going back to 1947. The web site is: | https://fred.stlouisfed.org/series/CPIAUCSL | |||||||||||
| Historical inflation rate: | 3.47% | |||||||||||
| Range in expected long-term inflation: | ||||||||||||
| Forward estimate of inflation | to | Historical inflation rate | ||||||||||
| 2.12% | to | 3.47% | ||||||||||
| We estimate expected inflation as the average of the inflation premium from the TIPS and the historical average: | ||||||||||||
| Our estimate of expected inflation: | 2.79% | |||||||||||
| Estimates of long-term population growth range from: | ||||||||||||
| Low estimate of population growth | High estimate of population growth | |||||||||||
| 1.00% | 2.50% | |||||||||||
| Average of estimated population growth: | 1.75% | |||||||||||
| Estimates of long-term sales growth rate (inflation plus population growth rate): | ||||||||||||
| Low range | High range | |||||||||||
| 3.12% | 5.97% | |||||||||||
| Average of range as an estimate of long-term sales growth, g: | 4.54% | |||||||||||
| The Impact of Stock Repurchases on the Estimated Price | ||||||||||||
| When there are repurchases, the growth rate in dividends per share changes. | ||||||||||||
| The constant growth model is: | ||||||||||||
| This can be rearranged to give this formula: | ||||||||||||
| The two formulas are equivalent, as shown in the following example. | ||||||||||||
| g = | 5.0% | |||||||||||
| α = | 80.0% | |||||||||||
| rs = | 12.0% | |||||||||||
| D0 = | $2.00 | |||||||||||
| = | 6.329% | |||||||||||
| = | $37.50 | |||||||||||
| Alternatively: | ||||||||||||
| = | $37.50 | |||||||||||
| Estimating the Required Return | ||||||||||||
| In the textbook, we assumed constant growth and no repurchases. We now consider cases with repurchases and a period of nonconstant growth, beginning with the case of repurchases but constant growth. | ||||||||||||
| Repurchases and Constant Growth | ||||||||||||
| If there are repurchase but still constant growth, then we can invert the constant growth formula to solve for r. | ||||||||||||
| Repurchases and a Period of Nonconstant Growth | ||||||||||||
| It is often the case that a period of nonconstant growth is expected before growth becomes constant. The valuation model for this situation is: | ||||||||||||
| Estimating the Required Market Return when there are Repurchases and a Period of Nonconstant Growth | ||||||||||||
| In recent years, companies in the S&P 500 aggregately have distributed even more cash to shareholders in the form of stock repurchases than in the form of dividends. Recently, only about 40% of distributions are in the form of dividends. | ||||||||||||
| Percent of total distribution in the form of cash dividends = α = | 41.0% Daves, Phillip R: Daves, Phillip R: http://us.spindices.com/documents/additional-material/sp-500-buyback.xlsx?force_download=true |
|||||||||||
| The next step is to estimate the total S&P dividend payouts for the next 2 years. S&P provides historical data for earnings per share, and dividends per share. They also provide data for estimated earnings per share for the next 2 years. We can use the historical data to estimate a relationship between EPS and DPS, and then use that model and the estiamted EPS to estimate DPS. | ||||||||||||
| We obtained data from the Standard and Poor's Web site: | ||||||||||||
| http://www.standardandpoors.com/home/en/us | ||||||||||||
| For current estimates from Standard & Poor’s, go to www.standardandpoors.com and select S&P Dow Jones Indices. Then select SP 500 under Indices. Then under Additional Info, select Index Earnings and download the spreadsheet. This downloaded an Excel file with quarterly data for the S&P 500. We summed up the quarterly data to get annual data. We also summed up the quarterly forecasted EPS to get the next 2 years annual forecast of EPS. The data is shown below. Note that S&P reorganizes their site frequently and this spreadsheet may not be in the same location when you look! If you can't find it, search on Earnings Estimates, or EPSEST while in the S&P 500 Index section. | ||||||||||||
| Annualized Data | ||||||||||||
| Date | Year | Month | S&P Price | Annual EPS Daves, Phillip R: Daves, Phillip R: These are as reported earnings per share. | Annual DPS | Data for Regression Model | ||||||
| 12/31/88 | 1988 | 12 | 277.72 | $23.75 | $9.75 | Annual DPS | Lagged DPS | Annual EPS | Change in EPS | -0 | ||
| 12/31/89 | 1989 | 12 | 353.40 | $22.87 | $11.06 | $11.06 | $9.75 | $22.87 | -$0.88 | |||
| 12/31/90 | 1990 | 12 | 330.22 | $21.34 | $12.09 | $12.09 | $11.06 | $21.34 | -$1.53 | |||
| 12/31/91 | 1991 | 12 | 417.09 | $15.97 | $12.20 | $12.20 | $12.09 | $15.97 | -$5.37 | |||
| 12/31/92 | 1992 | 12 | 435.71 | $19.09 | $12.39 | $12.39 | $12.20 | $19.09 | $3.12 | |||
| 12/31/93 | 1993 | 12 | 466.45 | $21.89 | $12.58 | $12.58 | $12.39 | $21.89 | $2.80 | |||
| 12/31/94 | 1994 | 12 | 459.27 | $30.60 | $13.17 | $13.17 | $12.58 | $30.60 | $8.71 | |||
| 12/31/95 | 1995 | 12 | 615.93 | $33.96 | $13.79 | $13.79 | $13.17 | $33.96 | $3.36 | |||
| 12/31/96 | 1996 | 12 | 740.74 | $38.73 | $14.90 | $14.90 | $13.79 | $38.73 | $4.77 | |||
| 12/31/97 | 1997 | 12 | 970.43 | $39.72 | $15.50 | $15.50 | $14.90 | $39.72 | $0.99 | |||
| 12/31/98 | 1998 | 12 | 1229.23 | $37.71 | $16.20 | $16.20 | $15.50 | $37.71 | -$2.01 | |||
| 12/31/99 | 1999 | 12 | 1469.25 | $48.17 | $16.69 | $16.69 | $16.20 | $48.17 | $10.46 | |||
| 12/31/00 | 2000 | 12 | 1320.28 | $50.00 | $16.27 | $16.27 | $16.69 | $50.00 | $1.83 | |||
| 12/31/01 | 2001 | 12 | 1148.08 | $24.69 | $15.74 | $15.74 | $16.27 | $24.69 | -$25.31 | |||
| 12/31/02 | 2002 | 12 | 879.82 | $27.59 | $16.07 | $16.07 | $15.74 | $27.59 | $2.90 | |||
| 12/31/03 | 2003 | 12 | 1111.92 | $48.74 | $17.39 | $17.39 | $16.07 | $48.74 | $21.15 | |||
| 12/31/04 | 2004 | 12 | 1211.92 | $58.55 | $19.44 | $19.44 | $17.39 | $58.55 | $9.81 | |||
| 12/31/05 | 2005 | 12 | 1248.29 | $69.83 | $22.22 | $22.22 | $19.44 | $69.83 | $11.28 | |||
| 12/31/06 | 2006 | 12 | 1418.30 | $81.51 | $24.88 | $24.88 | $22.22 | $81.51 | $11.68 | |||
| 12/31/07 | 2007 | 12 | 1468.36 | $66.18 | $27.73 | $27.73 | $24.88 | $66.18 | -$15.33 | |||
| 12/31/08 | 2008 | 12 | 903.25 | $14.88 | $28.39 | $28.39 | $27.73 | $14.88 | -$51.30 | |||
| 12/31/09 | 2009 | 12 | 1115.10 | $50.97 | $22.41 | $22.41 | $28.39 | $50.97 | $36.09 | |||
| 12/31/10 | 2010 | 12 | 1257.64 | $77.35 | $22.73 | $22.73 | $22.41 | $77.35 | $26.38 | |||
| 12/31/11 | 2011 | 12 | 1257.60 | $86.95 | $26.43 | $26.43 | $22.73 | $86.95 | $9.60 | |||
| 12/31/12 | 2012 | 12 | 1426.19 | $86.51 | $31.25 | $31.25 | $26.43 | $86.51 | -$0.44 | |||
| 12/31/13 | 2013 | 12 | 1848.36 | $100.20 | $34.99 | $34.99 | $31.25 | $100.20 | $13.69 | |||
| 12/31/14 | 2014 | 12 | 2058.90 | $102.31 | $39.44 | $39.44 | $31.25 | $102.31 | $2.11 | |||
| 12/31/15 | 2015 | 12 | 2043.94 | $86.53 | $43.39 | $43.39 | $34.99 | $86.53 | -$15.78 | |||
| 12/30/16 | 2016 | 12 | 2238.83 | $99.26 | $45.70 | $45.70 | $39.44 | $99.26 | $12.73 | |||
| 12/30/17 | 2017 | 12 | 2,673.61 | $124.87 | $48.93 | $48.93 | $43.39 | $124.87 | $25.61 | |||
| Forecast | 2018 | 12 | $156.19 Daves, Phillip R: Daves, Phillip R: These are forecasts from S&P | see estimate below | ||||||||
| 2019 | 12 | $173.11 | see estimate below | |||||||||
| We estimated the following model: | Coefficients using the LINEST function Michael Ehrhardt: Michael Ehrhardt: To use LINEST, put your cursor in a cell and then highlight a 1 by k range, where 1 is the number of rows and k is the number of columns, which is equal to the number of coefficients to be estimated. In this example, k = 4. Then enter the formula for LINEST (start typing "=LINEST" and then select "LINEST"). Select the range for the y values and the range for the x values. You must enter this as an array by pressing CTRL-SHIFT-Enter. |
|||||||||||
| d | c | b | a | |||||||||
| Dt = a + b Dt-1 + c EPSt + d (Change in EPS) | -0.1035743 | 0.1187706 | 0.8719454 | -1.6381897 | ||||||||
| For more detailed regression results, go to the Data tab and select "Data Analysis". Scroll down and choose "Regression". A dialog box will open. Choose your Y variable range and your X variables range. Choose a cel for the "Output Range". The results from such a regression follow. Notice that the Adjusted R Square is very high, showing that themodel does a good job of predicting the dividend. | ||||||||||||
| SUMMARY OUTPUT | ||||||||||||
| Regression Statistics | ||||||||||||
| Multiple R | 0.9906493668 | |||||||||||
| R Square | 0.981386168 | |||||||||||
| Adjusted R Square | 0.9791525082 | |||||||||||
| Standard Error | 1.5738684709 | |||||||||||
| Observations | 29 | |||||||||||
| ANOVA | ||||||||||||
| df | SS | MS | F | Significance F | ||||||||
| Regression | 3 | 3264.9837379878 | 1088.3279126626 | 439.3624093975 | 9.61111393260662E-22 | |||||||
| Residual | 25 | 61.9265490962 | 2.4770619638 | |||||||||
| Total | 28 | 3326.910287084 | ||||||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||||
| Intercept | -1.6381897209 | 0.7546274762 | -2.170858831 | 0.0396410794 | -3.1923741012 | -0.0840053406 | -3.1923741012 | -0.0840053406 | ||||
| X Variable 1 | 0.8719453647 | 0.0670558492 | 13.0032707861 | 0 | 0.7338412581 | 1.0100494712 | 0.7338412581 | 1.0100494712 | ||||
| X Variable 2 | 0.1187705888 | 0.0210638636 | 5.6385946572 | 0.0000072145 | 0.0753887496 | 0.1621524279 | 0.0753887496 | 0.1621524279 | ||||
| X Variable 3 | -0.10357429 | 0.0222264369 | -4.6599592404 | 0.0000899547 | -0.1493504937 | -0.0577980863 | -0.1493504937 | -0.0577980863 | ||||
| Year | Predicted dividend, D | Estimated intercept, a | Estimated coefficient for lagged dividend, b | Lagged D | Estimated coefficient for EPS, c | Forecast EPS | Estimated coefficient for change in EPS, d | Forecast change in EPS | ||||
| 2018 | $53.52 | -1.638 | 0.872 | $45.70 Daves, Phillip R: Daves, Phillip R: This formula needs to be updated manually when data is added in row 192 | 0.119 | $156.19 | -0.104 | $31.32 Daves, Phillip R: Daves, Phillip R: this formula needs to be updated manually after adding data in Row 192 |
||||
| 2019 | $63.83 | -1.638 | 0.872 | $53.52 | 0.119 | $173.11 | -0.104 | $16.92 | ||||
| Create a time line showing the predicted dividends for each year until growth in payouts becomes constant. To do this, obtain estimates of the next 2 year's projected dividends for the market and the long-term growth rate in CASH FLOWS after year 2. | ||||||||||||
| Find the horizon value on the time line assuming constant growth and an initial assumption for the required return on the market. Find the present value of the annual payouts and the present value of the horizon value; this is the estimate of the value of the market index. If the difference between the actual current value of the market index and the estimated value is not zero, adjust the input for the required market return until the difference is zero. | ||||||||||||
| Figure 9A-1: | ||||||||||||
| Estimating the Forward-Looking Market Risk Premium | ||||||||||||
| INPUTS: | ||||||||||||
| Projected Year 1 dividend for S&P 500 = | $53.52 | |||||||||||
| Projected Year 2 dividend for S&P 500 = | $63.83 | |||||||||||
| Projected portion of distributions as dividends, α = | 41.0% | |||||||||||
| Projected long-term constant growth rate in cash flow, gL = | 4.54% | |||||||||||
| Actual price level of S&P 500 = | $2,673.61 | |||||||||||
| Key Input/Output: Estimate of rM | ||||||||||||
| Key Input and Output: Estimate of rM = | 9.79% | Use Goal Seek to set the blue cell to zero by changing the orange cell. | ||||||||||
| Price level of S&P 500: Actual - Estimated = | -$0.00 | |||||||||||
| Time Line: | ||||||||||||
| Year | 0 | 1 | 2 | |||||||||
| Estimated dividend = | $53.52 | $63.83 | ||||||||||
| Estimated P at Year 2 = [(D2/ α) (1+gL) ] / (rM − gL) = | $3,100.32 | |||||||||||
| Estimated price level of S&P 500 = (PV of dividends and P2) = | $2,673.61 | |||||||||||
| Estimate of the market risk premium based on this estimate of rM. | ||||||||||||
| Estimate of rM. | Risk free rate | |||||||||||
| 9.79% | 2.87% | |||||||||||
| Estimate of the market risk premium | 6.92% |
(
)
(
)
g
1
)
g
-
(r
g
1
r
)
g
-
(r
-
g
L
L
L
L
DPS
+
+
a
+
+
a
=
g1)g-(r
g1r)g-(r-
g
LL
LL
DPS
(
)
(
)
g
-
r
g
1
D
P
ˆ
DPS
DPS
0
0
+
=
(
)
(
)
g
-
r
g
1
D
1
P
ˆ
L
L
0
0
+
÷
ø
ö
ç
è
æ
a
=
g-r
g1D1
P
ˆ
L
L0
0
(
)
L
0
L
0
g
P
g
1
D
r
+
a
+
=
L
0
L0
g
P
g1D
r
(
)
(
)
(
)
ú
ú
û
ù
ê
ê
ë
é
+
+
+
+
+
+
t
t
2
2
1
1
r
1
D
r
1
D
r
1
D
L
(
)
(
)
t
L
L
t
r
1
g
r
)
g
(1
D
+
ú
û
ù
ê
ë
é
-
a
+
+
t
L
Lt
r1
gr
)g(1D
(
)
(
)
g
1
)
g
-
(r
g
1
r
)
g
-
(r
-
g
L
L
L
L
DPS
+
+
a
+
+
a
=
g1)g-(r
g1r)g-(r-
g
LL
LL
DPS
(
)
(
)
g
-
r
g
1
D
1
P
ˆ
L
L
0
0
+
÷
ø
ö
ç
è
æ
a
=
g-r
g1D1
P
ˆ
L
L0
0
(
)
(
)
g
-
r
g
1
D
P
ˆ
DPS
s
DPS
0
0
+
=
