WACC Explanation and Answers PDF

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WACC Explanation and Answers...

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The Weighted Average Cost of Capital (WACC) What is WACC? The incremental Weighted Average Cost of Capital (WACC) identifies the average cost of all sources of raising new funds (capital). The sources of capital raised in the past can be identified on the right side of the balance sheet, although the numbers represent book values (historical). The WACC is an important number because it identifies the cost of raising new capital to be used to fund new projects. In order to increase the value of the firm, any new projects must earn more than the cost of new capital. Therefore, the cost of capital identifies a required rate of return for new projects (sometimes referred to as the hurdle rate). This is the discount rate used to calculate the Net Present Value (NPV) of proposed new projects.

How do you calculate WACC? The formula for calculating WACC is WACC = w k E

E

+ w k P

P

+

w k D

D

(1 − t )

where wE = wP = wD = kE = kP = kD = t =

the market value weight for equity, the market value weight for preferred stock, the market value weight for debt, the expected or required return for equity, the expected or required return for preferred stock, the expected or required return for debt, and the expected corporate tax rate.

The WACC should be calculated on an after tax basis. Dividend payments to common stockholders and preferred stockholders are already on an after tax basis, so no correction is needed for these two sources of capital. In contrast, interest payments to the creditors are on a before tax basis. Since interest is a tax deductible expense, the effect of this tax reduction (more interest expense will result in lower taxes) must be included in the calculation of the required return. Therefore, the cost of debt must be multiplied times one minus the corporate tax rate, (1-t). As a clarifying issue, recall that in calculating the cash flows we did not include the effect of the tax deductibility of interest. To do so would be counting the effect twice since the effect is already included within WACC, the discount rate. The formula for calculating operating cash flow is OCF

= EBIT (1 − t ) + Depreciati on

where EBIT

= the Earnings Before Interest and Taxes.

Notice that the operating cash flow is not the same thing as net income plus depreciation because net income does not equal EBIT (1-t), except in the trivial case where interest is equal to zero. This is because EBIT (1-t) is independent of and not affected by the level of interest expense. The effect of the reduction in taxes due to the deductibility of interest should only be reflected in the after tax cost of debt, which is included within the calculation of WACC.

How do you determine the weights in the calculation of WACC? The formula for calculating the weights are = E + P

V

w

E

=

w

P

=

w

D

=

+ D

E V P V D V

where V = E = P = D = wE = wP = wD =

the market value of the firm, the market value of the equity, the market value of the preferred stock, the market value of the debt, the market value weight for equity, the market value weight for preferred stock, and the market value weight for debt.

In the calculation of WACC, the weights should be determined on a market value basis. This is because the current market values would be used to determine the current financing costs. Notice that you would not use book values because they reflect what the market values were at some historical point in time. A quick example may help to clarify this concept. Suppose you purchase a “fixer upper” house for $100,000 using 100% debt financing (i.e., you borrow the entire $100,000 from a bank to purchase the property). Your personal net worth balance sheet would show $100,000 in assets on the left side and $100,000 in debt on the right side. Suppose with a little paint and a lot of sweat (but not very much cash) you are able to clean up the appearance and liveabililty of the house such that the market value becomes $200,000. However, the book value of your house would still show a $100,000 asset and $100,000 in debt indicating 100% debt financing. If you then approached a bank to see if you could raise additional funds, the bank would re-state your balance sheet on a market value basis. They would first determine that your house is currently worth $200,000 (market value of the asset). Then they would ask you

how much you owe on the property, or $100,000. This means on a market value basis you have $100,000 in equity. The bank would very likely be willing to loan additional funds based on the market value of your equity, ignoring the historical book value of your personal balance sheet (which still indicates 100% debt financing). This is because new financing is determined on a market value basis.

How do you calculate the market values? As stated before, the market value of the total firm is equal to the sum of the market values of equity, preferred stock, and debt.

V

= E + P

+ D

The market value of equity is determined by multiplying the number of common shares times the most recent price per share. For example, if there are 287 million shares outstanding and the most recent stock price is $25, then the market value of equity is $7175, as follows: (Shares Outstanding) (Price) = 287 (25 )

= 7175

The market value of preferred stock can be determined in a similar manner to equity by multiplying the number of preferred shares outstanding times the price per share of preferred stock. Sometimes you may have to back into an estimate for the market value of preferred stock. For example, suppose you know that in the past preferred stock had been issued with a 5% coupon rate, and now you know that preferred stock is currently yielding 5.9%. The definition of the current yield is the dividend divided by the price. Since we know the dividend is 5% of par value, the current price of preferred stock relative to the par value (or issue value) can be solved as follows: Dividend = 5% of par Dividend 5% of par Current Yield == == Price Price 5% of par Price == = 84.75% of par 5.9%

= 5.9%

As it turns out, the book value of preferred stock on the balance sheet is usually very close to the par value because the market value of preferred stock at the time of issuance is normally near the par value. Thus, in this case, an estimate for the current market value of preferred stock would be the book value times 84.75%. If the book value of preferred stock is 70 million, then an estimate of the market value of preferred stock is .8475 (70) = 59.32.

The market value of debt can be determined by observing the average price of debt outstanding. For example, if you know that the average long-term debt outstanding is priced at 118% of par, this means that a $1000 face value bond would be priced at $1180. If we assume that the book value of long-term debt is near par value, then the market value of long-term debt would be 118% of book value. For example, if the book value of long-term debt is 3328, then an estimate of the market value of long-term debt would be 1.18 (3328) = 3927. Often a firm will persistently maintain levels of both short-term (notes payable) and longterm (bonds) debt. If a firm is repeatedly refinancing the short-term debt as a long-term financing strategy, then the market value of short-term debt must also be included in the weight for debt. As it turns out, short-term debt does not change in value very much from the original issuance value because of a very short duration (i.e., the price is not very sensitive to changes in interest rates). Therefore, it is common practice to estimate the market value of short-term debt by using the book value of short-term debt. For example, if the book value of short-term notes payable is 5033, then this would also be an estimate of the market value of short-term debt. In many cases, the value of long-term debt also does not change much from book value to market value, at least relative to equity. As a result, many practitioners also assume that the market value of long-term debt is nearly equal to the book value.

How do you determine the cost of debt? The cost of debt is the expected yield to maturity if new debt is issued. An easy way to estimate this is to observe the current yield to maturity on existing debt. Sometimes you may have to calculate the yield to maturity if you are given other facts about the debt. For example, if you are given the coupon rate, the years to maturity, the face value, and the current price you can calculate the yield to maturity on a financial calculator. An example problem can illustrate this calculation, Suppose a bond has a coupon rate of 11% with 15 years left to maturity, and is currently priced at 118% of par. If interest is paid semiannually, what is the yield to maturity. In a financial calculator, N=2*15 or 30, PV=-1180, PMT=.11*1000/2 or 55, and FV=1000 par value. If you compute the interest rate, the answer is 4.407% every 6 months. Multiplying by two yields an annual yield to maturity of 8.81%. Sometimes there is a flotation cost (a cost for issuing securities) of around .5% for debt. Therefore, a complete estimate for the cost of debt including flotation cost might be 8.81% + .5% = 9.31%. One complication arises if there is both short-term (notes payable) and long-term debt (bonds). Generally, interest bearing debt that will persist over the life of a potential project (say for 10 years or so) should be included in the cost of the debt. In other words, if a firm is repeatedly refinancing the short-term debt as a long-term financing strategy, then the cost should be included within WACC. Also, if the yield to maturity is different for short-term and long-term debt, just determine the weighted average yield to maturity (on a market value basis) to obtain a composite yield to maturity for all debt. For example, suppose that the estimated market value of long-term debt is 3927 and the

estimated market value of short-term debt is 5033. If the average yield to maturity of long-term debt is 9.31% and the average yield to maturity of short-term debt is 5.86%, then a weighted average yield to maturity would be 3927 9.31% + 3927 + 5033

Average Yield to Maturity =

5033 5.86% 3927 + 5033

== 7.37%

How do you determine the cost of preferred stock? The cost of preferred stock is simply the current yield, or k

= Current Yield =

P

Preferred Dividend Preferred Price

For example, if you know that existing $100 par value preferred stock currently pays a dividend of $5 per year and is currently priced at $84.75, then the cost of preferred stock is 5/84.75 or 5.9% per year. Suppose the issuance cost for preferred stock is about $4 per $100 par value, or 4%. Then the cost of preferred stock including flotation costs would be k

P

5.9 % 1.00 − .04

=

=

5.9 % .96

= 6.15 %

How do you determine the cost of equity? The most common way to find the cost of equity is to use the CAPM formula, as follows: k

E

k

E

== k == k

RF

RF

+ β [k − k or M

RF

]

+ β [E(MRP) ]

where kE = kRF = kM =  = E(MRP)

the expected return on equity, the expected return on the risk-free asset, the expected return on the market portfolio, the beta of a particular stock, and = the expected market risk premium.

A frequent student error occurs when trying to use the first CAPM equation. Suppose the current rate on intermediate treasury bonds is 15% and you have decided to use this as the risk free rate. The Beta for a particular company has been measured at 1.20 using the last 60 months of historical data, and this beta is assumed to be the risk factor for the next 5 to 10 years. You also have historical averages over the last 75 years for the stock market in general (13%) and for intermediate treasury bonds (7%). What is the required rate of return of equity for this company using the CAPM? Suppose you plug the following numbers into the first equation for CAPM: k k k

+ β [k − k

]

E

== k

E

== 15% ++ 1.20 [13% − 15%]

E

=

RF

M

RF

12.6%

This is of course incorrect because the 12.6% expected return on stocks (which contain risk) is less that the 15% current risk free rate (an implausible scenario). In this case, 15% was used for the risk free rate in both places in the equation, the expected return on the market was assumed to be the historical average over the last 75 years, and the beta was given as calculated from the last 5 years of monthly data. This does not result in a sensible answer – so what went wrong? The problem is that the term in the brackets is the expected market risk premium. The estimate for the risk free rate in this term needs to be consistent with the expected return on the market. The mistake is that we incorrectly assumed a negative market risk premium by using the average of the last 75 years inconsistently with the current risk free rate (which may be temporarily high or low). If we use the second equation for CAPM, the problem becomes more apparent, and much less likely to fall into this trap of inconsistency. + β [E(MRP) ]

k

E

= k

k

E

= 15% + 1.20 [13% −− 7%]]

k

E

=

RF

22.2%

Notice that now we must estimate the market risk premium. If we again choose to use the last 75 years of data to estimate the future expected market risk premium, we subtract the 75 year average for the risk free rate from the 75 year average for the general stock market. This is a consistent estimate of the expected market risk premium. However, notice that the current rate for the risk free asset is normally used in the first part of the equation. This is because the current level of interest rates is often the best estimator of what you expect the risk free rate to be in the future period comparable to the term of the projects that you are evaluating. The ending result is now sensible – the expected return on stocks is higher than the expected risk free rate. So to avoid this common error, make sure that consistent numbers are used to estimate the expected market risk premium whether it is stated as E(k M) – E(kRF) or as E(MRP).

The previous example used a very high rate of interest for the risk-free rate to demonstrate a point. However, suppose the interest rate on intermediate term U.S. Treasury securities is a more reasonable 5.82% and the beta of a particular company stock is 0.75. If the 75 year average for the stock market (using a geometric mean) is 11% and the 75 year average for intermediate U.S. Treasury securities is 5.3%, then the required rate of return for a particular company would be k

S

= k

RF

++ β [E(MRP) ] = 5.82%

++ 0.75 [11% − 5.3% ] = 10.1%

Suppose also that the cost of issuing common stock is in the order of 7% of the issuance value. Then the composite cost of equity would be k

S

=

10.1% 1.00 − .07

=

10.1% .93

= 10.9%

How do you put it all together and calculate WACC? The equation to calculate the Weighted Average Cost of Capital (WACC), as stated before, is WACC = w k E

E

+ w k P

P

+

w k D

D

(1 − t )

Given all the previous facts plus an expected corporate tax rate of 40%, the WACC would be WACC =

8960 59 7175 (7.37%) (1 − .40 ) (6.15%) + (10.9%) + 7175 ++ 59 + 8960 7175 + 59 + 8960 7175 + 59 + 8960

WACC = 4.83% ++ .02%

+ 2.45%

= 7.30%...