Capm Vs Dividend Growth Model Essays
1.What is the WACC and why is it important to estimate a firm’s cost of capital? Do you agree with Joanna Cohen’s WACC calculation? Why or why not?
The cost of capital refers to the maximum rate of return a firm must earn on its investment so that the market value of company’s equity shares will not drop. This is a consonance with the overall firm’s objective of wealth maximization. WACC is a calculation of a firm’s cost of capital in which each category of capital is proportionately weighted. All capital sources – common stock, preferred stock, bonds and any other long-term debt – are included in a WACC calculation. All else equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk. The WACC of a firm is a very important both to the stock market for stock valuation purposes and to the company’s management for capital budgeting purposes. In an analysis of a potential investment by the company, investment projects that have an expected return that is greater than the company’s WACC will generate additional free cash flow and will create positive net present value for stock owners. Thus, since the WACC is the minimum rate of return required by capital providers, the managers in the company should invest in the projects which generate returns in excess of WACC.
We do not agree with Joanna Cohen’s calculation regarding the WACC from 3 aspects: 1) When Joanna Cohen computed the weights or proportions of debt and equity, she used the book value rather than the market value. The book values are historical data, not current ones; on the contrary, the market recalculates the values of each type of capital on a continuous basis, therefore, market values are more appropriate. 2) The cost of debt should not be calculated by “taking total interest expense for the year 2001 and dividing it by the company’s average debt balance. These historical data would not reflect Nike’s current or future cost of debt. 3) She mistakenly used the average Beta from year 1996 to 2001. The average Beta could not represent the future systemic risk, and we should find the most recent Beta as Beta estimate in this situation.
2.If you do not agree with Cohen’s analysis, calculate your own WACC for Nike and be prepared to justify your assumptions.
1)Weights of equity and debt:
Market value of equity = Current share price x Current shares outstanding = $42.09 x 271.5m = $11,427.44m
Due to the lack information of market value of debt, we could use the book value for calculation: Market value of debt = Current portion of long-term debt + Notes payable + Long-term debt = $5.4m + $855.3m + $435.9m = $1,296.6m We = $11,427.44m/($11,427.44m +$1,296.6m) = 89.81%
Wd = $1,296.6m/($11,427.44m +$1,296.6m) = 10.19%
2)Cost of Debt:
We can calculate the current yield to maturity of the Nike’s bond to represent Nike’s current cost of debt. Po=$95.6 N=20×2=40 PAR=$100 PMT=$100×6.75%/2=3.375
By using financial calculator: r=3.58%(semiannual)
So Rd=3.58% x 2 = 7.16%
3)Cost of Equity:
Use 20-year T-bond rate to represent risk-free rate, as the rate of return of a T-bond with 20 years maturity is the longest rate which is available right now. So Rf=5.74% Use a geometric mean of market risk premium 5.9% as Market Risk Premium As we mentioned in Q1, the most recent beta will most relevant in this respect, so we will use B=0.69 Re=Rf+B(Market Risk Premium)
=0.0574 + 0.69×0.059 = 9.81%
Use tax rate = US statutory tax rate + state tax
= 35% + 3% = 38%
WACC=Wd x Rd x (1-T) + We x Re
= 10.19% x 7.16% x (1- 38%) + 89.81% x 9.81% = 9.26%
3.Calculate the costs of equity using CAPM, and the dividend discount model.
What are the advantages and disadvantages of each model?
1)Cost of Equity using CAPM:
Market Risk Free Rate (Rf)= 5.74% (20-year yield on US Treasuries) Beta (B) = .69 (most recent beta used as most relevant beta to calculate Nike’s valuation) Market Risk Premium = 5.9% (Geometric Mean used as Historic Equity Risk Premium) Cost of Equity using CAPM = Re = Rf + B(Market Risk Premium) Re = 9.81% = 5.74% + .69(5.9%)
-CAPM includes systematic risk by incorporating Beta in the Cost of Equity formula. Using the stock’s Beta to calculate equity will provide a return rate based on how risky the stock is perceived by investors. The higher the risk, the higher the Beta will be and will result in a higher required rate of return on the investment. Systematic risk can’t be diversified away, while unsystematic risk can be diversified away by maintaining a diversified portfolio. -CAPM proves to be a better model than others such as the Dividend Discount Model, because the valuation behind CAPM is based on risk and rates of return while the Dividend Discount Model relies heavily on dividends and a growth rate.
-When using CAPM, it can be difficult determining the estimate of Beta. Different investments may involve different risks and the Beta used in calculating CAPM should reflect the appropriate amount of risk relating to the specific investment. -The risk free rates used in calculating CAPM are continually changing as with the values of the investments in the market which make up the market risk premium. The constant changes in the market can have negative impacts on the valuation of CAPM. -Another disadvantage in using the CAPM in investment appraisal is that investment appraisal is premised on a long-term time horizon, whereas CAPM assumes a single-period time horizon, i.e. a holding period of one year. While CAPM variables can be assumed constant in successive future periods, market reality often shows that this is not the case.
2)Cost of Equity using the Dividend Discount Model:
Growth (g) = 5.5%
Dividend (D0) = $.48
Share Price (P0) = $42.09
Cost of Equity using Dividend Discount Model = Re = (D0 x (1+g)/P0) +g Re = 6.7% = (.48 x (1+5.5%)/42.09+5.5%
-Using the Dividend Discount Model is very easy to calculate because the formula is not complicated. There are no real technical or difficult calculations involved with using this method. -The inputs that are used in the calculations of this model are market information and can be easily obtained. -The Dividend discount model attempts to put a valuation on shares, based on forecasts of the sums to be paid out to investors. This should, in theory, provide a very solid basis to determine the share’s true value in present terms.
-The Dividend Discount Model relies heavily on the growth rate to calculate the rate of return. If growth slows or becomes temporarily negative, it can result in calculations which may not truly represent future expected returns. -This model is calculated using dividends and can’t be used in instances where a company is not paying dividends. This is also a disadvantage for any investment without a reasonably constant growing dividend stream. -The Dividend Discount Model is very sensitive to minor changes in input figures. If the growth rate changes by 1 % the cost of equity will also change by that rate. -The Dividend Discount Model does not explicitly consider the risks which the company faces.
4.What should Kimi Ford recommend regarding an investment in Nike?
In order for Kimi Ford to make a decision regarding an investment in Nike, she must compare an accurately calculated WACC to the sensitivity of equity value to discount rate chart shown in Exhibit #2. The sensitivity chart in Exhibit #2 states that at a discount rate of 11.17%, Nike’s current share price is fairly valued at $42.09. If a discount rate were to be calculated below 11.17% then the Nike shares would be under-valued in the current market, but if their discount rate were higher than the 11.17% Nike share price would be considered over-valued when compared to the current share price. When we calculated Nike’s discount rate, we determined that their appropriate WACC should be 9.26%. Since this WACC of 9.26% is below 11.17%, we believe that Nike’s shares are currently under-valued in the market. We believe that Nike’s equity value based on the WACC of 9.26% should fall somewhere between $55.68 and $61.25. Kiki Ford should recommend adding Nike shares to the NorthPoint Large-Cap Fund based on our analysis.
Kimi Ford is a portfolio manager at a large mutual-fund management firm called, NorthPoint Group. Ford is considering the addition of Nike Inc. to the Large-Cap Fund at NorthPoint Group. Nike’s share price has notably declined since the beginning of the year. Her decision whether or not to add Nike to the portfolio should be made by looking at the 2001 fiscal year end 10-K report.
In 1997 Nike’s revenues plateaued around $9 billion while net income had fallen from around $800 million to $580 million. Also, from 1997-2000 Nike’s market share in U.S. athletic shoes fell from 48% to 42%. Supply-chain issues and the adverse effect of a strong dollar had negatively affected revenue in recent years. At the June 28, 2001 analyst meeting Nike planned to add both top-line growth and operating performance. One goal was to develop more mispriced ($70-$90) athletic shoes and the other to push its apparel line. At this meeting a target long-term revenue growth rate between 8%-10% was given and an earnings-growth target above 15%.
After reviewing all the analysts’ reports about the June 28th meeting Ford still did not have a clear picture of how to value Nike. Ford then performed her own sensitivity analysis which revealed Nike was undervalued at discount rates below 11.17%.
WHAT IS THE WACC?
A firm derives its assets by either raising debt or equity or both. There are costs associated with raising capital and WACC is an average figure used to indicate the cost of financing a company’s asset base. More formally, the weighted average cost of capital (WACC) is the rate that a company is expected to pay to debt holders and shareholders to finance its assets. Companies raise money from a number of sources so the WACC is the minimum return that a company must earn on existing asset base to satisfy its creditors, owners, and other providers of capital.
WACC is calculated taking into account the relative weights of each component of the capital structure which means it is the proportional average of each category of capital inside a firm. This rate, also called the discount rate, is used in evaluating whether a project is feasible or not in the net present value (NPV) analysis, or in assessing the value of an asset.
WACC = [Wdebt * Kdebt * (1-t)] + [Wequity * Kequity] + [Wpreferred * Kpreferred]
K = component cost of capital
W = weight of each component as percent of total capital
t = marginal corporate tax rate
WHY IS IT IMPORTANT TO ESTIMATE A FIRM’S COST OF CAPITAL?
The cost of capital is an important issue from the perspective of management while taking a financial decision. We can list some basic issues related to the importance of WACC and its interpretation by firms:
* The importance of the WACC is in its relation to the evaluation of
projects. For a project to be feasible, not just profitable, it must generate a return higher than the cost of raising debt (Kd) and the cost of raising equity (Ke). WACC is affected not only by Re and Rd, but it also varies with capital structure. Since Rd is usually lower than Re, then the higher the debt level, the lower the WACC. This partly explains why firms usually prefer issuing debt first before they raise more equity. As part of their risk management processes, some companies add a risk factor to the WACC in order to include a risk cushion in their project evaluation.
* The cost of capital is also important for the management while taking a decision about capital budgeting. Naturally, the project which gives a higher (satisfactory) return on investment compared to the cost of capital incurred for its financing would be chosen by the management. Cost of capital is the key factor in deciding which project to undertake out of different opportunities.
* The cost of capital is significant in designing the firm’s capital structure. It will direct the management about adopting the most appropriate and economical capital structure for the firm which means the management may try to substitute the various methods of finance to minimize the cost of capital so as to increase the market price and the earning per share.
* The cost of capital is also an important factor for taking a decision about the soundest method of financing for the company whenever the company requires additional finance. The management may try to catch the source of finance which bears the minimum cost of capital.
* The cost of capital can be used to evaluate the financial performance of the top management by comparing actual profitability’s of the projects and the projected overall cost of capital and an appraisal of the actual cost incurred in raising the required funds.
DO WE AGREE WITH JOANNA COHEN’S WACC CALCULATION? WHY OR WHY NOT?
We do not completely agree with Joanna Cohen’s calculation of WACC. There are several problems in her calculation;
* In Cohen’s calculation, she used the book value for the weights of each capital structure component (debt and equity). Book value of equity should not be used when calculating cost of capital. Instead she should have calculated the market value of equity. Also, she should have discounted the value of long-term debt that appears on the balance sheet to find the market value of debt (even if the book value of debt is accepted as an estimate of market value).
* Also, she should have considered the preferred stock while calculating the weights of the components of capital structure (the redeemable preferred stock is relatively small in Nike’s capital structure so it doesn’t affect the weights).
* Another problem with her calculation is about the cost of debt. Cohen used a cost of debt which is even lower than treasury yield. In common sense, a company, even it might be a large AAA firm, should be risky than US government. Cost of debt should be calculated by finding the yield to maturity on 20-year Nike Inc. debt with current coupon rate paid semi-annually instead of by taking total interest expense for 2001 and dividing it by the company’s average debt balance.
USING SINGLE OR MULTIPLE COSTS OF CAPITAL IS APPROPRIATE FOR NIKE INC.?
Even Nike Inc. has multiple business segments such as footwear, apparel, sports equipment and some non-Nike-branded products (which accounts for relatively small fraction of revenues), we assumed Nike Inc. to have a single cost of capital since its multiple business segments are not very different and would experience similar risks and betas.
WHICH EQUITY RISK PREMIUM SHOULD BE USED TO DETERMINE THE COST OF CAPITAL?
For the cost of capital, the geometric mean is a better alternative to the arithmetic mean. Furthermore, the geometric mean is a more conservative measure to use compared to the arithmetic mean. The average market risk premium has fluctuated by large amounts in short time periods from 1926-1999. 1926-1929 saw high market risk premiums; however, the 1930s and 1970s saw very low market risk premiums. Therefore, we use the geometric mean since it is a better measurement compared to arithmetic mean when the measured period is longer and contains more fluctuations.
VALUE OF EQUITY, VALUE OF DEBT AND WEIGHTINGS OF EACH COMPONENT
| Value(in millions $)| Weight|
Current Portion of Long term Debt| 5.40| 0.04%|
Notes Payable| 855.30| 6.73%|
Long-Term Debt| 416.72| 3.28%|
Total Debt| 1,277.42| 10.05%|
Equity| 11,427.44| 89.95%|
Table 1. The weight of debt and equity in total capital of Nike
CALCULATION OF THE COST OF EQUITY UNDER DIFFERENT METHODS AND ADVANTAGES AND DISADVANTAGES OF EACH METHOD
1. Capital Asset Pricing Model (CAPM)
Under CAPM we can find the cost of equity as;
Ke = Rf + Betai * Equity Risk Premium
The first issue is to find an appropriate risk-free rate. We think the 20-year yields on treasures would be the one because NIKE is assumed to be operated for such long time, according to the revitalizing strategy proposed by the management and the long-term debt issued.
Next is to determine the beta. The historic betas has been generally decreasing, and we assume it is the market condition and management`s purpose that make NIKE to be a defensive company. Furthermore, we find that the competitors such as K-Swiss and Lacrosse also have beta less than one. So rather than the average, we use the YTD beta into calculation. On the other hand, since the beta has been found to be on average closer to the mean value of 1, which is the beta of an average-systematic-risk security, we calculate the adjusted beta, giving two-third weight to the YTD beta and one-third weight to 1.
Regarding the risk premium, we use the geometric mean since it is a better measurement compared to arithmetic mean when the measured period is longer and contains more fluctuations.
Combining the above information, we calculate the cost of equity as follows:
Using YTD Beta => 5.74% + 0.69*5.9% = 9.81%
Using Adjusted Beta => 5.74% + [(2/3)*0.69 + (1/3)*1)]*5.9% = 10.42%
* It provides an economically grounded and relatively objective procedure * It concentrates on the systematic risk that investors can`t avoid, rather than unsystematic risk that can be avoided through diversification * It is suitable for company that doesn`t pay dividend
* It is widely used.
* The assumptions may not be realistic. For example, investors may not be all risk averse and rational that holds efficient portfolio * Investors may concern more than just market risk.
2. Dividend Discount Model (DDM)
Under DDM we can find the cost of equity as;
Ke = (D1/P0) + g
Ke = (0.48*1.055/42.09) + 5.5% = 6.70%
Here we assume NIKE will pay dividend at constant growth rate of 5.5% which forecasted by Value Line, so we use the Gordon growth model to derive required rate of return.
* It is simple and widely used
* Can be used to infer implied required rate of return
* It is helpful to perform a sensitivity analysis on the inputs
* It is not suitable for company that doesn`t pay consistent dividends or the dividends are not tied to profitability * It is suitable for only matured company
3. Earnings Capitalization Ratio (ECM)
Under ECM we can find the cost of equity as;
Ke = E1/P0
Ke = 2.32/42.09 = 5.51%
* It assumes the earnings would be the same in the future, which may not be true * It doesn`t take the growth of company into consideration.
Cost of Equity| | |
CAPM| | |
| Risk-free Rate| 5.74%|
| Equity Risk Premium| 5.90%|
| Year-to-Date Beta| 0.69|
| Adjusted Beta| 0.79|
| Cost of Equity with YTD Beta| 9.81%|
| Cost of Equity with Adjusted Beta| 10.42%|
| | |
DDM| | |
| Current Dividend| 0.48|
| Growth Rate| 5.50%|
| Current Stock Price| 42.09|
| Forecasted Dividend| 0.5064|
| Cost of Equity| 6.70%|
| | |
ECM| | |
| Consensus Earnings Estimate| 2.32|
| Current Stock Price| 42.09|
| Cost of Equity| 5.51%|
| | |
Build-up Method| | |
| Risk-free Rate| 5.74%|
| Equity Risk Premium| 5.90%|
| Cost of Equity| 11.64%|
Table 2. Cost of Equity under different methods
WHICH RATE AS RISK FREE RATE IS BEST FOR NOTES PAYABLE AND LONG-TERM DEBT?
For long term debt, the 20-year yield on U.S. Treasuries is best as the risk free rate. Considering the long time horizon of Nike, a 20-year bond is property. And also, it is comparable to the current 25-year bond which Nike issued 5 years ago. Although Nike’s current bond is 25 years, we could consider it as a 20-year bond issued this year, and use the current price to calculate the 20-year bond YTM.
And for short term debt, because the note payable was a major portion in the debt structure, the 1-year treasuries would be preferred as risk free rate.
COST OF DEBT CALCULATION FOR NIKE
We could not agree with Cohen’s analysis. Because Cohen used a cost of debt
which is even lower than treasury yield. In common sense, a company, even it might be a large AAA firm, should be risky than US government.
First, Cohen’s emphasis that last year, the effective cost of debt of Nike was less than treasury yield due to its Japanese Yen notes. However, the rates of debt based on currency change are unstable and non-repeatable. We could reasonable consider that Nike’s last year’s low cost of debt is a kind of arbitrage by chance.
Second, to calculate the cost of debt, market value of debt should be used rather than the book value used by Cohen. The market value of debt is compounded by the current portion of long-term debt, notes payable, and long- term debt discounted at Nike’s current coupon.
Therefore, we would like to recalculate the cost of debt. Cost of debt was calculated by using the current liquidated 20-year bond of Nike, Inc. with a 6.75% coupon semi-annually. Then we obtain a cost of long term debt before tax as 7.17%, and cost of short term debt before tax as 5.02%.
As shown above in Table 1, short term debt took a significant portion in Nike’s debt structure; therefore, we use a weighted cost of debt to combine both long term and short term debt effects as in following equation:
Here is the weight of short-term debt, while is the weight of long-term debt. And both cost of short-term and long-term debt are after tax.
Cost of Debt| | |
Long Term Debt| | |
| Coupon Rate| 6.75%|
| Time to Maturity| 40|
| Current Stock Price| $95.60|
| Cost of Debt| 7.17%|
| After Tax Cost of Debt| 4.44%|
Short Term Debt| | |
| 20-year Yield| 5.74%|
| 1-year Yield| 3.59%|
| Risk Premium| 1.43%|
| Tax Rate| 38.00%|
| Cost of Debt| 5.02%|
| After Tax Cost of Debt| 3.11%|
Final Weighted Cost of Debt After Tax| 0.36%|
Table 2. Cost of debt
WHAT IS OUR WACC CALCULATION FOR NIKE?
Under different methods, we would obtain different cost of equity, then, definitely different WACCs which range from 5.31% to 10.83%. However, no matter which method we use, the stock price of Nike is undervalued currently.
WACC| | |
| Under CAPM with Adjusted Beta| 9.73%|
| Under CAPM with YTD Beta| 9.18%|
| Under DDM| 6.39%|
| Under ECM| 5.31%|
| Under Build-up Method| 10.83%|
Table 4. Weighted Average Cost of Capital
As shown in Table 5, the actual implied discount rate by current price is 11.17%, which is significantly beyond the range of WACCs we calculated and presented in Table 4. Therefore, in our analysis, Nike’s price would be considered as undervalued.
Discount Rate| Equity Value|
8.00 %| $ 75.80|
8.50 %| 67.85|
9.00 %| 61.25|
9.50 %| 55.68|
10.00 %| 54.92|
10.50 %| 46.81|
11.00 %| 43.22|
11.17 %| 42.09|
11.50 %| 40.07|
12.00 %| 37.27|
Table 5. Sensitivity test on WACCs
This graph shows the estimated value provided under different WACCs, and NIKE is currently trading at 42.09 with corresponding 11.17% WACC. So if the calculated WACC is below 11.17%, the estimated value would be higher than the current price and NIKE is undervalued; if the calculated WACC is beyond 11.17%, the estimated value would be lower than the current price and NIKE is overvalued.
After adjusting the possible mistakes that Joanna made, the table shows the calculated WACC under each method:
CAPM (Adjusted Beta)| 9.73%|
CAPM (YTD Beta)| 9.18%|
We can see none of them is above 11.17%, indicating NIKE is currently undervalued and Ford should add NIKE to the NorthPoint Large-Cap Fund. However, it is important to keep monitoring the revitalizing strategy that the management offered, since the future market condition may have huge impact on this strategy and hence, predicted future economic income.
NorthPoint Group is a mutual fund management firm who has the preference on investing in Fortune 500 companies, such as EXXONMobil, GM, McDonald’s 3M and other large-cap. If we look back to a decade ago, the fund had performed extremely well compared to the market in general (we refer S&P500 to represent the market).
Kimi Ford was the portfolio manager in NorthPoint Group, who was concerned about whether or not to add Nike, Inc. shares into her fund. Since net income and market share had been fallen from 1997, a new strategy was proclaimed by the Nike management team during the meeting held in June, 2001:
First, highly priced products are no longer their only target, now they would develop the midpriced segment so that more customers will be able to afford it.
Second, another way to boost the revenue is to focus on its apparel line, which they found out to be profitable. Finally, Nike needs to reduce its costs by exerting more effort on expense control. Company executives were optimistic about the long-term revenue, expecting an 8%~ 10% growths and earnings growth above 15%.
Analysts had different opinion about the company prospects; Lehman Brothers suggested a strong buy while UBS and CSFB recommended a hold. Meanwhile, Ford wanted to make her own forecast so she developed a discount cash flow to determine that, at a discount rate of 12%, Nike was overvalued at its current price $42.09 and undervalued if the discount rate was below 11.17%. She asked her assistant, Joanna Cohen, to calculate the company’s cost of capital precisely.
On the report, Joanna Cohen used WACC to calculate the cost of capital, where she adopted book values to obtain a proportion of 27% of debt and 73% of equity. For cost of debt, she took total interest expense divided by average debt balance which resulted lower than treasury yields. For cost of equity, she used 20-year Treasury bond as risk-free rate and 5.9% as market premium. Moreover, she divided each division by revenue, deciding to use one overall WACC. At the end, she came to a conclusion that the cost of capital for Nike, Inc was 8.4%.
To manage your portfolio, you need a way to compare your different investments and decide which are worth keeping. The dividend discount model and the capital asset pricing model are two methods for appraising the value of your investments. DDM is based on the value of the dividends a share of stock brings in, whereas CAPM evaluates risks and returns compared to the market average.
The dividend discount model bases the current value of your stock shares on the total future value of their dividends. To value a stock using DDM, you combine a company's announced dividends with detailed financial projections to measure the dividend value over the next five years. Beyond that point, you have to make do with less detailed projections. Then you use the model's mathematical formula to discount the value of the future dividends to the present, giving a value for the stock now.
Capital asset pricing models base their evaluation on a different set of factors: the expected rate of return, the risk-free rate of return, the market's average rate of return and the sensitivity of the investment to market conditions. Sensitivity is measured based on how past performance compared to the market. With CAPM you can compare your portfolio or your individual investments to the market and see if they come off as high risk or underperforming.
CAPM Vs. DDM
You can use CAPM and DDM together: most DDM formulas employ CAPM to help figure out how to discount future dividends and derive the current value. CAPM, however, is much more widely useful. DDM can't do anything for you if your investments aren't dividend-issuing stocks but you can apply CAPM to any sort of investment. Even on specific stocks, CAPM has an advantage because it looks at more factors than dividends alone.
Neither DDM nor CAPM is a perfect investment tool, because both rely on assumptions about the future. Long-term financial forecasts are always challenging and DDM is especially so: to be accurate, you have to predict dividend policy five or 10 years down the road. CAPM also makes assumptions. For example, when it measures the relationship between returns and risks, it ignores unsystematic risks -- risks that only affect stocks in one particular industry. If you have a highly specialized portfolio, CAPM may not be as effective a predictor.
About the Author
A graduate of Oberlin College, Fraser Sherman began writing in 1981. Since then he's researched and written newspaper and magazine stories on city government, court cases, business, real estate and finance, the uses of new technologies and film history. Sherman has worked for more than a decade as a newspaper reporter, and his magazine articles have been published in "Newsweek," "Air & Space," "Backpacker" and "Boys' Life." Sherman is also the author of three film reference books, with a fourth currently under way.