# Capital Asset Pricing Model and Cost

9 September 2016

What is the WACC and why is it important to estimate a firmâ€™s cost of capital? Do you agree with Joanna Cohenâ€™s WACC calculation? Why or why not? Answer: 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.

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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 Cohenâ€™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.

The cost of debt should not be calculated by â€śtaking total interest expense for the year 2001 and dividing it by the companyâ€™s average debt balance. These historical data would not reflect Nikeâ€™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 Cohenâ€™s analysis, calculate your own WACC for Nike and be prepared to justify your assumptions. Answer: 1)Weights of equity and debt:

Systematic risk canâ€™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. Disadvantages: -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.

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% Advantages: -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 shareâ€™s true value in present terms. Disadvantages: -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 canâ€™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? Answer: 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%, Nikeâ€™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 Nikeâ€™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 Nikeâ€™s shares are currently under-valued in the market.

We believe that Nikeâ€™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. 03/03/2011 CASE OVERVIEW 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. Nikeâ€™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 Nikeâ€™s revenues plateaued around \$9 billion while net income had fallen from around \$800 million to \$580 million. Also, from 1997-2000 Nikeâ€™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 analystsâ€™ 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 companyâ€™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 FIRMâ€™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 profitabilityâ€™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 COHENâ€™S WACC CALCULATION? WHY OR WHY NOT? We do not completely agree with Joanna Cohenâ€™s calculation of WACC. There are several problems in her calculation; * In Cohenâ€™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 Nikeâ€™s capital structure so it doesnâ€™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 companyâ€™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.

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.

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