Corporate Finance Online Exam Due Tomorrow SEE ATTACHED
Main Model
| Worksheet for Chapter 11 BOC Questions | 1/25/15 | ||||||||||
| We use this model to illustrate some points about the cost of capital, and also to provide practice with Excel modeling. The model is useful to give students a sense of some of the issues involved in cost of capital estimation. Each little piece is fairly easy and straightforward, but when the whole thing is put together, students perceive it as quite involved. Still, if someone actually has the task of estimating the cost of capital for a company, the model does provide a reasonably good framework. | |||||||||||
| Question 2. We illustrate the WACC calculation at the bottom of this worksheet, after we calculate the cost of equity. | |||||||||||
| Question 4-a. Assume the following data for a company: | |||||||||||
| CAPM r: rs = rRF + b(rM - rRF) | |||||||||||
| rRF: | 6% | ||||||||||
| rM: | 11% | ||||||||||
| Company's bi: | 1.20 | ||||||||||
| Company's rs = | 12.0% | ||||||||||
| Here is a data table that shows the effects of different expected market returns and betas. Given the normal | |||||||||||
| standard errors for beta and uncertainties about the market return, the true values of these variables could | |||||||||||
| easily be anywhere in the shaded, inner box, so the true cost of equity could easily be from 11% to 13%. | |||||||||||
| The CAPM may appear to yield precise results, but in actuality the CAPM cost of equity could vary | |||||||||||
| rather widely. | |||||||||||
| Cost of Equity from Retained Earnings | |||||||||||
| Beta | Expected Return on the Market | ||||||||||
| 12.0% | 10.0% | 10.5% | 11.0% | 11.5% | 12.0% | ||||||
| 1.00 | 10.0% | 10.5% | 11.0% | 11.5% | 12.0% | ||||||
| 1.10 | 10.4% | 11.0% | 11.5% | 12.1% | 12.6% | ||||||
| 1.20 | 10.8% | 11.4% | 12.0% | 12.6% | 13.2% | ||||||
| 1.30 | 11.2% | 11.9% | 12.5% | 13.2% | 13.8% | ||||||
| 1.40 | 11.6% | 12.3% | 13.0% | 13.7% | 14.4% | ||||||
| Question 4-b. | D1 | D2 | |||||||||
| DCF r: | Solve for rs in the equation Po = | + | + | ….. | |||||||
| (1+rs) | (1+rs) | ||||||||||
| Assume the following data: | |||||||||||
| P0 | $ 40.00 | Growth years 1-3: | 25.0% | Based on | |||||||
| D0 | $ 1.00 | Growth years 4-6: | 15.0% | Analysts' | |||||||
| Assumed ks | 12.0000% | Growth after year 6: | 8.000% | Forecasts | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Data for Graph | |||
| Growth | 25% | 25% | 25% | 15% | 15% | 15% | 8% | r | $48.8 | ||
| Dividend | $ 1.00 | $ 1.25 | $ 1.56 | $ 1.95 | $ 2.25 | $ 2.58 | $ 2.97 | $ 3.21 | 10.0% | $99.3 | |
| P6 | $ 80.20 | 11.0% | $65.6 | ||||||||
| $ 1.25 | $ 1.56 | $ 1.95 | $ 2.25 | $ 2.58 | $ 83.17 | 12.0% | $48.8 | ||||
| 12.8446% | $40.0 | ||||||||||
| Calc P0 = NPV = | $ 48.78 | Use the NPV function to find the stock's calculated price. | 14.0% | $32.0 | |||||||
| Actual Price | $ 40.00 | ||||||||||
| The calculated price is not equal to the market price. We need to find the k value that is reflected | |||||||||||
| in the market price. Do this as follows: | |||||||||||
| Put the pointer on cell C45, the calculated price (the NPV). | |||||||||||
| Then click Tools > Goal Seek. Enter 40 in the "To value" cell and C37 in the "by changing" cell. | |||||||||||
| Then click OK, and cell C37 will adjust to the discount rate that causes the calculated price to | |||||||||||
| equal the $40 market price. The cost of equity is seen to be 12.8%. The dilog box is shown below. | |||||||||||
| Different growth rates and stock prices would lead to different estimates of r, and stock prices | |||||||||||
| do change significantly and rapidly, and the growth expectations of the marginal investor are | |||||||||||
| uncertain. We didn't try to estimate r under different conditions with a data table, but here are | |||||||||||
| some "manually" calculated results (change the stock price and then use Goal Seek): | |||||||||||
| Effects of stock price changes on r. Growth assumptions unchanged, but stock prices changed as shown: | |||||||||||
| Price: | r | ||||||||||
| $ 30.00 | 14.400% | ||||||||||
| $ 40.00 | 12.845% | ||||||||||
| $ 50.00 | 11.900% | ||||||||||
| Stock price unchanged ($40), but the terminal growth rate was changed as shown: | |||||||||||
| Terminal Growth | $48.78 | We used Goal seek to find the terminal g (Cell C37) | |||||||||
| 6.947% | $40.00 | that would force the calculated stock price to the | |||||||||
| 8.00% | $48.78 | indicated $40 market price. That was 6.947%. We | |||||||||
| 10.00% | $90.92 | then set up and created the indicated data table. | |||||||||
| r would also change if we changed the short-term growth rates, or the duration of these rates. | |||||||||||
| Illustration of the problems associated with historical growth as predictor of future growth. | |||||||||||
| Historical Growth Rates for A-B enterprises (which is an extraordinarily stable company) | |||||||||||
| EPS | DPS | Cash Flow Per Share | |||||||||
| EPS | 1- year g | Avg from | DPS | 1- year g | Avg from | CFPS | 1- year g | Avg from | |||
| 2001 | $0.74 | 2001 | $0.24 | 2001 | $1.19 | 2001 | |||||
| 2002 | 0.81 | 9.5% | 9.5% | 0.27 | 12.5% | 12.5% | 1.29 | 8.4% | 8.4% | ||
| 2003 | 0.87 | 7.4% | 8.4% | 0.30 | 11.1% | 11.8% | 1.40 | 8.5% | 8.5% | ||
| 2004 | 0.89 | 2.3% | 6.4% | 0.34 | 13.3% | 12.3% | 1.49 | 6.4% | 7.8% | ||
| 2005 | 0.97 | 9.0% | 7.0% | 0.38 | 11.8% | 12.2% | 1.61 | 8.1% | 7.9% | ||
| 2006 | 0.95 | -2.1% | 5.2% | 0.42 | 10.5% | 11.8% | 1.53 | -5.0% | 5.3% | ||
| 2007 | 1.11 | 16.8% | 7.2% | 0.46 | 9.5% | 11.5% | 1.73 | 13.1% | 6.6% | ||
| 2008 | 1.18 | 6.3% | 7.0% | 0.50 | 8.7% | 11.1% | 1.92 | 11.0% | 7.2% | ||
| 2009 | 1.27 | 7.6% | 7.1% | 0.54 | 8.0% | 10.7% | 2.07 | 7.8% | 7.3% | ||
| 2010 | 1.47 | 15.7% | 8.1% | 0.58 | 7.4% | 10.3% | 2.41 | 16.4% | 8.3% | ||
| 2011 | 1.69 | 15.0% | 8.8% | 0.64 | 10.3% | 10.3% | 2.62 | 8.7% | 8.3% | ||
| 10-year regression average: | 7.9% Gene Brigham: Regression estimate. See below for calculating procedures. | 10.2% | 7.7% | ||||||||
| 5-year regression average: | 11.5% | 8.6% | 11.3% | ||||||||
| The 5 and 10 year average growth rates were obtained using Excel's LOGEST function (log estimation). This is a regression procedure that regresses the log of the variable (EPS or DPS) against years. The function returns (1+growth rate), so we must subtract 1.0 from the indicated value to get the compound growth rate. Regression takes account of all data points, it is the method least subject to the influence of "outliers," and it is generally considered to be the best procedure for determining historical growth rates. To use the function, click fx >Statistical>LOGEST and then enter the range A79:A89 for "known y's" and B79:B89 for "known x's, and leave the other menu items blank. | |||||||||||
| Observations about historical growth rates: | |||||||||||
| 1. Growth rates of earnings and dividends vary quite a bit from year to year, even for A-B, which | |||||||||||
| is one of the most stable firms in the world. If there is a company for which historical growth | |||||||||||
| could be used to predict future growth, it's A-B, yet even here it is hard to identify a good rate | |||||||||||
| for DCF purposes. If one had picked a growth rate based on data through 1995, it would not have | |||||||||||
| been a good predictor of growth through 2000. This is generally true for any company. | |||||||||||
| 2. In 2001, Value Line forecasted a 5-year growth for EPS of 11% and 6.5% for DPS. Others | |||||||||||
| made different forecasts. The retention growth forecast (g = ROE*RR) was 0.72*33.5% | |||||||||||
| = 24.2%, again based on Value Line's predicted ROE and retention rate. | |||||||||||
| 3. In 1996 Value Line predicted that A-B's earnings would grow at a 10% rate over the next 5 | |||||||||||
| years, and that dividends would grow at an 8% rate. Those rates are reasonably close to what | |||||||||||
| actually happened, and much better predictors than historical rates up to 1995. | |||||||||||
| 4. Our conclusion is that historical data are useful as a starting point for predicting future | |||||||||||
| growth, but even for an extremely stable company, historical data alone are not likely to | |||||||||||
| result in a good forecast of future growth. Therefore, for DCF purposes, one should rely | |||||||||||
| more on analysts' forecasts than on historical growth rates. Analysts bring in other factors | |||||||||||
| besides time and thus make better predictions of future earnings, I.e., growth in earnings. | |||||||||||
| All of the above demonstrates that the DCF method, like the CAPM method, requires a lot of | |||||||||||
| judgment, and is not nearly as precise as it might first appear. | |||||||||||
| Question 4-c. Own bond-yield-plus-risk premium rs | |||||||||||
| Data for an illustrative company: | |||||||||||
| Bond rating and interest rate: | Baa | 7.8% | |||||||||
| Risk premium range: | Low: | 3.0% | |||||||||
| High: | 5.0% | ||||||||||
| rs range: | Low: | 10.8% | |||||||||
| High: | 12.8% | ||||||||||
| For more on the risk premium used here, click the tab labeled RP Study. | |||||||||||
| SUMMARY OF THE CALCULATIONS FOR COMPANY: | |||||||||||
| High | Average | Low | |||||||||
| CAPM: | 13.2% | 12.1% | 11.0% | ||||||||
| DCF: | 13.8% | 12.8% | 11.8% | Found as average +/- 1.0%. | |||||||
| Risk Premium: | 12.8% | 11.8% | 10.8% | ||||||||
| Averages: | 13.3% | 12.2% | 11.2% | ||||||||
| Based on these data, we would conclude that the cost of equity is probably in the range of | |||||||||||
| 12% to 13%, with a best point estimate of 12.2%. | |||||||||||
| We might have less confidence in the DCF estimates in this particular example, because the growth rates are so | |||||||||||
| awfully high, as is true for many high tech companies when the economy is strong. If we were analyzing a stable | |||||||||||
| company like Anheuser-Busch, we would be much more confident in the growth rates, but we would also be more | |||||||||||
| confident about the other estimates. | |||||||||||
| Question 5. FLOTATION COST ADJUSTMENT | |||||||||||
| Assume the flottion cost for issuing new common stock is: | 10% | ||||||||||
| The DCF method can be used to estimate a flotation cost adjustment, which can then be | |||||||||||
| applied to the costs of retained earnings as found by the CAPM and RP methods. | |||||||||||
| Go to the DCF section and change the stock price to the base price times (1-F) or 0.9. This produces a price of $36. Use | |||||||||||
| that price as the "To value" price in Goal Seek to get the with-flotation DCF cost of equity. Subtract the base DCF cost | |||||||||||
| from the higher cost to get the flotation cost adjustment factor. Use this adjustment for the base case situation to get a | |||||||||||
| "reasonable" flotation cost adjustment factor, and then add that factor to the average estimated cost of retained | |||||||||||
| earnings. | |||||||||||
| Adjustment factor: | DCF cost of new common stock, re: | 13.4% | |||||||||
| DCF cost of retained earnings, rs: | 12.8% | ||||||||||
| Flotation cost adjustment factor: | 0.6% | ||||||||||
| Estinated cost of equity from new common stock: | rs | 12.2% | (the average) | ||||||||
| Factor | 0.6% | ||||||||||
| re | 12.8% | ||||||||||
| Question 2. WEIGHTED AVERAGE COST OF CAPITAL (WACC) | |||||||||||
| Compant's target capital structure: | Debt | 40% | @ | 7.8% | |||||||
| Equity | 60% | @ | 12.2% | ||||||||
| WACC with Ret. Earnings | 10.4% | ||||||||||
| WACC with New Stock: | 10.8% |
Copyright (c) 2002 by Harcourt, Inc.
0.1 0.11 0.12 0.128446 0.14000000000000001 99.254120686149022 65.595616259373003 48.782938882640259 39.999799354408196 32.001211032836565Equity Cost
Stock Price
RP Study
| Cost of Equity Estimates for Selected Companies | (CofC-Studies) | 1/25/15 | |||||||
| The family of Roger Maris, the baseball player who broke Babe Ruth's home run record, sued Anheuser-Busch, the brewers of Budweiser and other beers, and a trial was held in 2001. Maris was given an A-B distributorship after helping the St. Louis Cardinals, which was then owned by A-B, win a World's Series. After Roger dies, A-B took the distributorship away from the family. The business was generating over $6 million of profits per year, so losing it was quite a blow. Consequently, the family sued A-B and asked for the value of the business, plus penalties. To find the value of the business, it was necessary to estimate future cash flows and then discount them at a risk-adjusted discount rate. Since the business was not publicly owned, it was not possible to find a beta for the CAPM or a stock price for the DCF method, so the cost of capital estimating procedure was based on the bond-yield-plus-risk-premium method. The following information was used in the case as part of the support for the 3-to-5 percent risk premium. The Maris family was awarded $72 million, but they appealed and eventually settled 4 years later for at least $120 million. | |||||||||
| Industrial Companies' | |||||||||
| Risk-free rate | 5.3% | March 2001 per | Interest rates, March 2001, | ||||||
| FRB Web site | Per Moody's: | ||||||||
| Aaa | 6.6% | ||||||||
| Market risk premium | 6.0% | (used 5% to 7% range) | Aa | 6.9% | |||||
| A | 7.6% | ||||||||
| Baa | 7.8% | ||||||||
| Beta | CAPM rs | rd, 3/01 | Risk Prem. | Bond | |||||
| ValueLine | Yahoo | ValueLine | Yahoo | (Moodys) | V-L | Yahoo | Rating | Ticker Sym | |
| Intel | 1.1 | 1.6 | 11.9% | 14.8% | 6.6% Gene Brigham: INTC has only 2% debt, and it is not rated. Would be AAA if rated, so assumed AAA. | 5.3% | 8.1% | no rating Gene Brigham: Only a trivial amount of debt is outstanding, hence it is not rated. Assumed it would be rated AAA given strength of company and very small amount of debt outstanding. | INTC |
| GE | 1.3 | 1.2 | 12.8% | 12.4% | 6.6% | 6.2% | 5.8% | AAA | GE |
| Coca-Cola | 1.0 | 0.7 | 11.0% | 9.8% | 6.9% | 4.1% | 2.9% | AA3 | KO |
| Walt Disney | 0.9 | 0.9 | 10.7% | 10.4% | 7.6% | 3.2% | 2.9% | A2 | DIS |
| Motorola | 1.3 | 1.5 | 12.8% | 14.0% | 7.6% | 5.3% | 6.5% | A2 | MOT |
| H.J. Heinz | 0.7 | 0.4 | 9.2% | 8.0% | 7.6% | 1.7% | 0.4% | A1 | HNZ |
| Wal-Mart | 1.2 | 0.9 | 12.2% | 10.7% | 6.9% | 5.3% | 3.8% | AA2 | WMT |
| AT&T | 1.0 | 1.0 | 11.3% | 11.5% | 7.6% | 3.8% | 3.9% | A2 | T |
| Exxon Mobil | 0.8 | 0.8 Gene Brigham: Yahoo does not report a beta for XOM due to recent merger. Used VL beta. | 10.1% | 10.1% | 6.6% | 3.5% | 3.5% | AAA | XOM |
| BellSouth | 0.9 | 0.5 | 10.4% | 8.2% | 6.9% | 3.5% | 1.2% | AA2 | BLS |
| Average | 1.0 | 0.9 | 11.3% | 11.0% | 7.1% | 4.2% | 3.9% | ||
| Std Dev | 0.2 | 0.4 | 1.2% | 2.2% | 0.4% | 1.3% | 2.2% | ||
| Avg k VL+Yah | 1.0 | 11.1% | 4.0% | ||||||
| Avg SD, VL+Yah | 0.3 | 1.7% | 1.7% | ||||||
| Data Table: Risk Premium as Function of Market Risk Premium | |||||||||
| D7 | Own-Bond | The companies in the sample were brought up by A-B's attorneys and | |||||||
| MRP | RP | then used for various illustrative purposes. The RP results found for | |||||||
| 4.0% | these companies were consistent with other earlier PR studies, but it | ||||||||
| 5.0% | 3.1% | is possible that the RP's of smaller, weaker companies over their own | |||||||
| 6.0% | 4.0% | debt yields would be different. Note, though, that weaker companies | |||||||
| 7.0% | 5.0% | would have higher debt costs, so their estimated equity cost would | |||||||
| be higher than the ones for the companies in this sample. | |||||||||
Copyright (c) 2002 by Harcourt, Inc.