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Weighted Average Cost of Capital

By Amy Simmons,2014-04-06 20:04
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Weighted Average Cost of Capital

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    Weighted Average Cost of Capital

    The weighted average cost of capital (WACC) of a firm simply refers to how much, on

    average, it costs the firm to raise money. That is, it is the average rate that the firm must pay on any new capital that it raises. The importance of the WACC is in its relation to the evaluation of projects. For a scale-enhancing project (see definition below), the WACC is the appropriate discount rate at which to evaluate the project.

    Definition: A scale-enhancing project is a project that is similar to the firm as a whole. It has a similar level of risk to the existing assets of the firm.

    The use of the WACC as the discount rate should make intuitive sense. If, for example, the firm must pay an average of 8% on capital that it raises then projects that return less than 8% should be rejected. Projects returning less than the cost of capital will certainly lose money as they will not even cover the payments required to finance the project. This will be reflected in those projects having NPV<0 when 8% is used as a discount rate. The use of the cost of capital as a discount rate is the reason that the costs of financing are never included as cashflows when evaluating a project. For instance, if the firm will have to borrow money in order to finance the project, the cashflows of the loan (receiving the loan, making interest payments and repaying principal) are never considered when estimating the cashflows to an investment. This is because the costs of financing are taken account of in the discount rate, and putting them in as cashflows would mean double-counting them. When a project is not scale-enhancing, practitioners tend to use ad hoc adjustments to the WACC in order to determine the appropriate discount rate. For instance, one would use a slightly higher discount rate if the project is slightly riskier than the current assets of the firm. These adjustments are based upon “best guesses”, but these guesses are based upon analysis of the risk of the project through things such as sensitivity analysis.

    The basis of determining WACC is to determine the costs of each of the individual sources of long term financing for the firm, weight those costs by the degree to which the firm uses the different sources, and simply add up the weighted costs.

    Example: Assume that the firm makes use of only two sources of financing, debt and equity. Let S be the market value of all of the common stock of the firm and D be the market value of all of the debt of the firm. Thus S+D must be the total value of the firm. Let r be the cost d

    of debt financing for the firm and let r be the costs for equity financing for the firm (these s

    will be defined later). The WACC for this firm will be:

    SD?? WACCrr~?~?sd????SDSD

    This equation is the same as saying:

    WACC = (percent of the firm that is equity) times (cost of equity)

     plus (percent of the firm that is debt) times (cost of debt)

    (Note that this example ignored the tax effect of debt.)

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    Conceptually, it is easy to think of the cost of debt. The return to the holder of the debt is the same as the cost to the firm. If the holders of the firm’s debt are earning 5% on their investment, then the debt must be costing the firm 5%. The cost of equity is a little more difficult concept, although the effect is the same as that of debt. It turns out that the cost of equity financing is simply equal to the expected return of the firm’s stock. An expected return of r is required in order to induce new investors to buy the stock of the firm. From the s

    opposite viewpoint, r is the return that the current shareholders (who own the firm) must s

    give in order to attract new equity capital. Issuing new equity entails a cost to the current shareholders as they give up a portion of the firm and the right to a portion of the future dividends. This cost is measured by the expected return on the stock, which is also the cost of equity capital.

    The weights used in the WACC for the various sources of capital are based on their market values (although book values are sometimes used because they are easier to obtain). The weights are based upon the capital structure of the firm as a whole, not on the financing used for any particular project. The general view here is that the financing mix used for a particular project is coincidental. Consider two projects that are identical except that one will be financed through debt and the other through equity. It does not make sense to apply different discount rates to identical projects simply because of the choice of financing. Generally, if the firm has set goals for their capital structure (e.g. a target debt/equity ratio), then these goals are used to determine the weights. The view on this is that the firm will reach these goals eventually and therefore they are the appropriate weights to use for determining the cost of long term financing.

    Up to now, we have viewed the appropriate discount rate for a project as the opportunity cost of capital, the expected rate of return on an investment of equal risk. How can this be reconciled with the use of the WACC as a discount rate? It turns out that the two things are exactly the same.

Proof that WACC and Opportunity Cost of Capital are the Same

    Assume that the CAPM holds (this is not necessary to prove that the two things are the same, but it means the proof is relatively straight forward). We want to use the expected return an asset of equal risk (the opportunity cost of capital) as the discount rate. The risk of the project is the same as the risk of the rest of the assets of the firm (because it is scale-enhancing). Thus, the risk of the project is measured by . asset

    Because the bonds and the equity if the firm are both securities, each will have a beta associated with it, and . debtequity

    There are two ways to “purchase” the firm:

    1) purchase all of the assets of the firm (create an identical firm)

    The risk of this investment would be represented by . asset

    2) purchase all of the equity and all of the debt of the firm (so that you own the firm

    free and clear of debt)

    The risk of the investment would be represented by the weighted average:

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    DS??;; ~?~?debtequity????DSDS

    Both methods would give the same result, therefore the two measures of risk must be the equal:

    DS?? ;;;~?~?assetdebtequity????DSDS

    Now, the opportunity cost of capital will be found from:

    DiscountRateRERR,??!(fassetMf

    DS?? ,?R;;ERR??ERR~?~?!(!(fdebtMfequityMf????DSDS

    DS??RERR???;;RERR??~?~?!(!(;;;;fdebtMffequityMf????DSDS

     expected cost of expected cost of debt=r dequity = r s

    Thus, the opportunity cost of capital is simply a weighted average of the costs of debt and equity and is equivalent to the WACC. Hence, WACC is the appropriate discount rate. The reason that the WACC is used instead of directly applying the CAPM with the asset beta is that is unobservable, but the costs of financing are observable. asset

Determining the Costs of Financing

    In order to determine the WACC, the costs of the individual sources of long term financing must be determined.

    In reality, there are four sources of capital:

     1) Debt

     2) Preferred Stock

     3) Common Stock

     4) Internally generated funds (retained earnings)

1) Debt: Generally, the cost of debt is the yield to maturity on the bonds of the firm. It is not

    the coupon rate, but the yield that is important. This is because the yield is the rate the firm would have to pay if it issued new debt now. That is, it is not the rate that the firm had to pay on old debt that matters but the rate that is prevailing in the market today. This current market rate is measured by the current yield on the bonds of the firm.

    Note that flotation costs will often affect the cost of debt. This might include things such as the legal fees, administrative fees et cetera of floating a new issue. These reduce the proceeds realized by the firm on a bond issue. (They get less money, but make the same interest payments).

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    Example: A firm issues one million in face value of new bonds with a coupon rate of 6%. These bonds have ten years to maturity and coupon payments are made annually. In order to sell all of the bonds, the firm prices them at $950,000. It pays $40,000 on flotation costs. In this case, the yield of the bonds is: 9600001060000950000i10 ()()yy11i1

    y.670%

    But, the actual debt to the firm is y*:

    9600001060000910000i10 (*)(*)yy11i1

    y*.730%

    Note that interest payments on debt are tax deductible for corporations. Thus, it is really only the after -tax cost of debt that is of concern. In this case, if the effective corporate tax rate on the firm is 34%, then the after tax cost of debt is:

    7.3%(1-0.34) = 4.818%

    Note: The greater the number of years to maturity of the bonds in question, the less the effect of flotation costs. The intuitive reason for this is that with longer lived debt, the effect of the flotation costs are spread out over a longer period (even though they are, of course, actually paid up front).

    2) Preferred Stock: Preferred stock is like a cross between debt and equity as it is equity that requires a fixed dividend payment. The cost of preferred equity is simply defined as the dividend yield on the stock.

Let:

    d= fixed annual preferred dividend. p

    P=price of preferred p

    r=cost of preferred equity p

    dp rpPp

    Note that it is actually the net issuing price that should be used in this equation. That is, the price of the preferred stock net of any flotation costs that would have to be incurred in order to issue new shares.

    3) Common Stock: There are two main methods used to calculate a cost of equity capital for common stock:

    a) Capital Asset Pricing Model

    b) Gordon Dividend Growth Model

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    a) The use of the CAPM simply involves estimating the expected return on the firm’s common stock through CAPM and using that estimate as the cost of common equity capital.

b) Gordon Dividend Growth Model:

    The Gordon Dividend Growth Model is based upon the price of a stock being the discounted value of all the future dividends: dt P0t()1rt1

    If we know all of the future dividends then we can solve for the discount rate in the above equation. This rate (the IRR of the stock) would be analogous to the yield on a bond. This rate would be the “yield” of the stock. In other words, it the expected return that is required in order to make the present value of the future dividends equal to the current price. Another way of saying the same thing is that new investors require this return to induce them to invest in the firm’s shares.

    The rate that one solves for in the above equation is the cost of equity (r) in the Gordon s

    Model. The question is, how does one estimate this rate given that one cannot know all future dividends?

Consider the case where dividends are constant forever:

     dtP0t()1rt1

    d tr()1t1

    drs

    d ,,rsP0

    Thus, given constant dividends, the cost of equity is simply the current dividend yield on the stock (the cost of preferred equity can thus be seen as an application of this approach).

    However, the following should make clear that perpetually constant dividends implies that all profits of the firm are paid out as dividends (which is not a very common real world phenomenon).

    Let E be the earnings per share in year t (total firm profit divided by the number of shares). t

    Most firms will pay some of E out as dividends, but will retain some for re-investment in the t

    firm. Assume that the firm retains a constant percentage of E each period, b. This number, b, t

    is the retention ratio.

    The idea is that the firm retains some earnings and re-invests them in the company so that future earnings are higher. Let R be the return generated on the re-invested earnings.

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    EE11

    EERbE,?211

    ,?()1EbR1

    ,?EERbE322

     ,???EbRRbEbR()()1111

    2,?()1EbR1

    ;

    ;

    t1,?()1EEbRt1

    Thus, earnings per share is a perpetually increasing series that is growing at the rate bR each period.

    Let g=bR be the growth rate.

    Since the fraction b of earnings per share is retained each period, (1-b) of earnings must be paid out as dividends. Thus:

    dbE,?()111

    dbEg,??()()1121

    ,?dg()11

    ;

    ;

    t1dbEg,??()()11t1

    t1,?dg()11

    Therefore, it can be seen that g represents the growth rate in earnings per share and in dividends. G is determined by how much the firm re-invests in itself and the rate of return on those investments.

    Now, set the present value of future dividends equal to the current stock price and solve for r: s

    t1()1dg1P0t()1rst1

    d1P 0rgs

    d1r,?gsP0

    This is the cost of equity capital by the Gordon Dividend Growth Model.

    The first term in the equation is the current dividend yield on the stock. This can easily be calculated. However, the growth rate, g, must be estimated. There are two usual methods for this:

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    i) If the firm has a policy regarding the retention rate of earnings then this rate

    can be used to estimate b. R can be estimated by last period’s Return on

    Equity figure, or an average of the last few years’. Since g=bR, you now

    have an estimate of g.

    ii) Remember that g is also the growth rate of EPS, for which figures are

    available. Simply take the percentage increase in EPS over a number of years,

    convert this into a yearly rate and use this as an estimate of the growth rate.

    Warning: Basing estimated growth rates on historical data can sometimes lead to conclusions that do not make sense. This will tend to happen of the firm has recently gone through a period of very high growth (that cannot be expected to last forever) or if the firm has had decreasing EPS (which cannot be expected to last forever).

    4) Internally generated funds: In most ways, internally generated funds are the same as equity. Using internal funds to finance and issuing new stock to finance have (almost) the same cost to current shareholders.

    Internal funds are simply cashflows generated by the firm’s operations that have not been paid out as dividends. Management is faced with a choice: should they retain these funds and invest them inside the firm, or pay the funds out to shareholders as dividends and let shareholders invest the funds themselves outside of the firm? In order for it to be optimal to retain the funds, the firm must expect to earn more than shareholders could earn investing the money on their own (given the same level of risk). Thus, there is a cost to using internally generated funds, equal to the expected return on the outside investment opportunities not taken by shareholders. The return expected by shareholders on an investment of equal risk to their investment in the firm is the expected return on the stock itself. In other words, the cost of internal funds is equal to the cost of common equity (and can be calculated as in (3) above).

    Internal cash on hand is (as you know from accounting) part of the equity of the firm. Thus, there is no separate term within the WACC calculation that represents internal funds. It would seem that internal funds, although an important source of funding for firms, have no effect on the cost of capital. This would be true except for one thing. The cost of internal funds is the same as the cost of new equity capital except for flotation costs. There are no flotation costs for the use of retained cashflow, while there are for new issues of stock. Thus, the cost of using retained cashflows is actually slightly lower.

    Since internally generated funds and issues of stock are basically the same, the cost of equity capital without flotation costs is put into the WACC formula if all of the projects that the firm is considering can have their equity portion financed through retained earnings. If retained earnings would not be enough to cover the required equity financing, then the WACC will increase because a new stock issue will be needed and this involves flotation costs which are now included in the cost of equity.

    Therefore, there is a discontinuity in the WACC. Considering one additional project may raise the discount rate for all projects because the additional project may require a new issue

    MFIN 6663

    Sobey School of Business

    Saint Mary’s University

    Greg MacKinnon

    of stock. The discount rate for all projects is affected because, in reality, all projects should

    be evaluated using the marginal cost of capital.

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