Notes on the Cost of Capital

Transcription

1 Notes on the Cost o Capital. Introduction We have seen that evaluating an investment project by using either the Net Present Value (NPV) method or the Internal Rate o Return (IRR) method requires a determination o the irm s cost o capital. Again, the terms cost o capital, required rate o return, hurdle rate, and weighted average cost o capital (WACC) tend to be used interchangeably. This terminological point has been emphasized because it tends to cause conusion when irst learning corporate inance. The important point is that these terms reer to the appropriate discount rate to be used when evaluating investment projects and when attempting to value a irm. In either case, it is necessary to determine the present value o a uture low o net beneits (e.g., proits, cash lows, etc.). The present value calculation requires a discount rate to be used and the question naturally arises as to what the appropriate discount rate should be. The cost o capital is this discount rate. The current set o notes demonstrates how a corporation arrives at its cost o capital. Thinking o cost o capital in terms o the required rate o return, we observe that what is really necessary is to discover what rate o return the current credit-holders and shareholders require. A useul way to visualize the thinking is given below. The Firm Financial Markets Net Operating Assets (NOA) Net Financial Assets (NFA) Credit-holders or Debt issuers Shareholders Source: inancial Statement Analysis and Security Valuation, rd edition, Stephen H. Penman, p. 46.

2 The diagram illustrates that the irm may raise inancing in the inancial markets by issuing debt (liabilities) or new shares (equity). The inancing raised will add to the irm s net inancial assets (in this case, cash). The irm will use the cash raised to invest in additional net operating assets (e.g., property, plant, & equipment). Depending upon the irm, the net operating assets could be new equipment, new manuacturing plants, patents, etc. In short, these are the assets the irm uses to do what it is in business to do. The purchase o the operating assets constitutes a capital expenditure by the irm and outlow o cash. I all goes well, the irm will be able to generate additional earnings rom their operations and capital expenditure, which returns to the irm by increasing their net inancial assets thus, a cash inlow. The irm will use the inancial assets (cash) to make payments to the inancial markets in the orm o interest and principal on debt to credit-holders and/or dividends to shareholders. The goal o the current notes is to understand how the inancial markets signal the cost o capital to the irm, thereby inorming the capital expenditure decision. It is important to keep in mind throughout that this signal will be present regardless o how the additional investment (i.e., capital expenditure) will be inanced. Thus, in our simple story, the signal (cost o capital) will be present even i the irm had chosen to make the capital expenditure in additional net operating assets out o their existing net inancial assets (thus, retained earnings). The cost o capital is determined by the current creditholders and shareholders, not the ones that had made the purchase o the original issue o new shares or debt. This should become clearer as we get into the details o arriving at the cost o capital. We must now begin that process by seeing how to determine the required rate o return rom credit-holders and shareholders. We will begin with creditholders irst and assume the irm has issued bonds as debt (the case o bank loans would be even simpler).. The Cost o Debt --- Bonds Bonds come with a variety o characteristics. The characteristics o bonds typically turn on how repayment and interest will be paid. One o the simplest types o bonds is the discount bond (sometimes reerred to as zeros). A discount bond makes one payment at the end o the loan agreement. For example, a discount bond may state that it will pay the holder o the bond $,000 on November st, 0. The $,000 is the ace value o the bond not to be conused with the value o the bond. The date is reerred to as the date o maturity or, when the loan ends. I, or ease o application, we assume that November st is one year away, then we can set up the ormula or valuing this bond. $,000 V D where, V D is the value o the bond (debt) k is the appropriate discount rate I we believed that an 8% discount rate is appropriate or this bond, then the value o the bond would be roughly $96. On the other hand, i 6% was a more appropriate discount

3 rate, then the value o the bond would be roughly $94. Again, notice the inverse relationship between the discount rate and value o the bond. Suppose the maturity date had actually been November st, 05 thus, ive years away. We can determine the value o the bond or each o the assumed discount rates. V D $,000 (.08) 5 $68 V D $,000 (.06) 5 $747 The time value o money has now come into view. Given the ace value o $,000 and discount rate o 8%, the value o the bond went rom $96 or a one year bond to $68 or a ive year bond. That is, as the $,000 we receive gets pushed urther into the uture we value it less today. How one comes up with the appropriate discount rate to use is only slightly less diicult or a bond than many other assets. Bonds will typically come with a credit rating made my some agency (e.g., Moody s, Standard & Poors, etc.). The credit rating is based on an analysis o the inancial condition (present and uture) o the issuer. A low (high) credit rating will lead people to use a higher (lower) discount rate. We can reverse engineer (a ancy term or rearranging an equation) the valuation in order to discover what discount rate the market is using. For example, suppose our $,000, 5-year discount bond is currently selling or $700, then we can solve or the discount rate. $,000 $700 5 Solving or k we get the ollowing. k 5 $,000 $ % Here, we see that the market is valuing the bond at $700 and discover a 7.9% discount rate being used. Again, one should be careul about the terminology here. It is true that the 7.9% is the interest rate the buyer o the bond would earn i they hold it until maturity. However, this is not necessarily the interest rate the issuer (i.e., the irm) is paying. I this purchase is on the secondary market, then the bond may have been issued many years ago and more important at a price other than $700. Furthermore, or the buyer, the 7.9% may not be the rate o return earned on the bond. Suppose, the buyer turns around and sells the bond a month later or a price o $770. The buyer s rate o return would be 0%.

4 $770 $700 Rate o Return.0 0% $700 Care will need to be taken concerning terminology or a bit. Once we get used to the terminology, then no real harm will be done by using the term interest rate instead o discount rate. Unlike a discount bond, a coupon bond makes periodic interest payments during the lie o the loan. The ace value will still reer to the last payment. There will be a maturity data as well. However, there will also be a coupon rate stating the percentage o the ace value that will be paid out as interest periodically (annually, semi-annually, etc.). We will oten assume that interest (i.e., the coupon payment) is paid annually in order to simpliy the calculations. For example, suppose we want to value the ollowing bond. Face Value $,000 Time to Maturity years Coupon rate 5% The 5% coupon rate implies that the issuer will make annual payments to the holder o the bond in the amount o $50 per year (i.e., 5% o the $,000 ace value). I, given the characteristics o the issuer, we believe a 7% discount rate is appropriate the value o the bond would be the ollowing. V D $50 (.07) $50 (.07) $50 (.07) $,000 (.07) $46.7 $ $86.0 $947.5 We see the time value o money once again as the $50 coupon (interest) payment is received urther in the uture. What would happen i the appropriate discount rate dropped to 4%? The value o the bond would be $, The appropriate discount rate may have dropped because the issuer was more credit worthy than beore (e.g., received a big contract, sold o unproitable parts o the business, etc.). The drop in the discount rate has meant that we value the bond more now. It is possible, but not easy without a inancial calculator or Excel, to reverse engineer a coupon bond. For example, i the bond was currently selling or $980, then we might solve or the discount rate being applied to the bond. $970 $50 ( $50 $50 $,000 k) k ) ( Just by glancing at the above equation we see that it will not be an easy task to solve or the discount rate. In act, we cannot solve or the discount rate directly. We would have to use a trial-and-error process in order to pin down the discount rate. For example, at a 4

5 price o $970, we know that the discount rate will be lower than 7% but higher than 4% (how do we know this?). Most spreadsheets have a unction that will solve or the discount rate. The discount rate or this bond selling at a price o $970 is 6% (you should veriy this by plugging in 6% in the above). Notice how similar this is to the Internal Rate o Return (IRR) rom the previous set o notes. In that case, the internal rate o return was merely the discount rate that made the present value o the uture cash lows rom an investment project just equal to the current cost o the project. In this case, we are attempting to solve or the discount rate that makes the present value o the uture payments (coupon and ace value) just equal to the current selling price o the bond. The discount rate that sets the present value o the uture payments (coupon and ace value) equal to the price o a bond is called the yield to maturity. Typically, what people reer to as the interest rate on a bond is the yield to maturity. Due to the diiculty o calculating the yield to maturity (at least prior to inancial calculators and computers), people have sometimes used an approximation known as the current yield. The current yield is simply the coupon payment divided by the current price o the bond. In the previous case, the current yield would be the ollowing. $50 Current yield % $970 The current yield is still reported in most inancial news publications. However, it should be clear that it is only an approximation to the interest rate o most signiicance (i.e., yield to maturity). The yield to maturity is oten abbreviated as YTM. We have been discussing bonds as i our goal was to value them ourselves. What has this to do with a corporation discovering what rate o return is being required by current credit-holders (or, in our case, bond-holders)? Everything! In act, we have already answered the question. The rate o return required by current bond-holders is the yield to maturity (YTM). To see this, assume a corporation issues (i.e., sells, or loats) a new bond on January, 00. The bond has the ollowing characteristics (note, we assume a single bond just to make the discussion easier, things would be no dierent i it were a thousand bonds). Face Value $,000 Time to Maturity 4 years Coupon rate 4% Furthermore, assume the bond was actually sold or $,000. In this case, the yield to maturity on the bond would be 4%, same as the coupon rate.,000 (.04) (.04) (.04) (.04) $,000 (.04) $ 4 4 $8.46 $6.98 $5.56 $4.9 $ $,000 5

6 Now, suppose a year has gone by and the original purchaser o the bond decides to sell it. I everything had remained pretty much the same, then the purchaser should be able to sell it with the same yield to maturity and or a price o $,000. Double check this in order to see that the three years remaining with coupon payments and a inal payment o $,000 ace value will lead to a value o $,000 as long as the discount rate to be used remained at 4%. But, more interestingly, suppose that during the year the corporation had not done very well. The corporation may have lost an important customer or aced stier than anticipated competition, or all sorts o bad things. The point though is that the original purchaser inds that he/she can only sell the bond or a price o $950. What rate o return does the new holder o the bond require? $950 ( YTM ) ( YTM ) ( YTM ) ( $,000 YTM ) By solving or the yield to maturity (YTM), we discover what the current required rate o return is or the current bond-holder. Using Excel, we ind the yield to maturity to be 5.87%. $950 (.0587) (.0587) (.0587) $,000 (.0587) Thus, when things did not go as well or the corporation and the risk o the debt increased, the price (or, value) o the bond ell causing the yield to maturity to increase rom 4% to 5.87%. I things had gone the other way, and the business prospects looked better than a year ago, we may have observed an increase in the price o the bond and decrease in its yield to maturity. What does this have to do with the corporation? On irst glance the answer would be not much. Ater all, the corporation has merely promised to make the coupon payments and $,000 ace value payment over the course o the 4 year lie o the bond to whomever is holding the bond. The act that the original purchaser o the bond could only sell it or $950 does not change the payments that the corporation must make only to whom it should write the checks, but not the size o the checks. On the other hand, this change does impact the cost o capital speciically, in this case, the cost o debt. Bondholders are now signaling to the corporation that they demand a higher rate o return to rom the corporation due to the changed circumstances. This will impact the cost o capital the corporation uses in the Net Present Value method and Internal Rate o Return method. It will also impact the present value o the irm itsel. Though, we will need to wait to see these implications. For now, we may summarize with the ollowing. Cost o Debt or a corporation is the Yield to Maturity Yield to Maturity is the discount rate that makes the present value o uture payments on a bond just equal to the current selling price o the bond 6

7 Fortunately, the yield to maturity or a bond is easily obtained on a daily basis rom the inancial section o most newspapers. I not, the corporation merely needs to know the characteristics o the bond (e.g., ace value, coupon rate, time to maturity) and the current selling price in order to calculate the yield to maturity and know what its bond-holders require or a rate o return. Thus, the current cost o debt is easily obtainable. What about the cost o equity?. Cost o Equity --- Stocks Stocks tend to be more diicult than bonds to value. The irst diiculty arises rom identiying just what the net beneit should be not just the numerical value. A stock represents part ownership in a corporation. The owners have a claim on the proits (or, net income, earnings) the corporation generates. Understood rom this perspective, the net beneit would be the share o the uture proits the stock represents. On the other hand, the owners have a claim to the equity (or, net wealth) o the corporation at any given time. The net beneit rom owning a stock could be the claim to the uture equity o the corporation. There are a variety o perspectives that lead to diering notions o the net beneit o a stock. The current section develops a simple, but very useul, approach to deining net beneit. One may think o the net beneit o a stock as ultimately residing in the cash low going to stockholders. This cash low comes in the orm o a dividend payment. A dividend is the portion o the proits earned that the corporation pays to its owners (i.e., stockholders). Many corporations choose not to pay dividends, especially in their early or start-up phases. I the corporation, or example, has a better in terms o higher rate o return - place to invest the potential dividends than the stockholder, then it would seem to be appropriate not to pay a dividend. Alternatively, i the corporation suers losses, then a dividend may not be paid. We will look at two alternative ways o arriving at the cost o equity or, the current required rate o return by shareholders in this section. The irst is based on determining the present value o the uture dividends a corporation will pay. This method emphasizes the present value aspect o stocks and makes clear certain important properties. The second method, more oten used, is the Capital Asset Pricing Model or CAPM or short (read as Cap-M).. Dividend Discount Model Valuation o stocks based on deining net beneit as dividend can be accomplished in dierent ways. The approach ollowed here will be the Dividend Discount Model. We can present the basic ormulation very simply. V E 0 D D D Pn K n where, The deinition o cash low to the stock holder could include stock repurchases as well as dividends. 7

8 V E is the value o the stock (equity) at the present time D i is the dividend paid in period i k is the appropriate discount rate P n is the price o the stock when eventually sold First, notice that we have just applied the present value ormula. Second, notice that we have a circularity problem a problem that oten arises in valuation. We are attempting to arrive at the value o an asset independent o price. However, in the above, we are saying that the current value o the stock partially depends upon the expected price in period n (when we sell it). At this point we will gloss over this problem and assume that by the time we wish to sell the stock its price will be the same as its value. Upon making this assumption, we can rewrite the above. V E 0 E D D D Vn K n The Dividend Discount Model takes the above and adds the assumption o constant dividend growth. The assumption may seem unrealistic. It is, though not drastically so. Many corporations keep their dividend the same (zero growth) or long stretches o time or target a particular growth rate. We can now begin to rework the ormulation. First, notice that the value o the stock at time n will be the present value o the uture dividends. The ormula becomes an ininite series. V E 0 D D D D4 D5 4 ( k) 5 K Second, assume the dividend grows at a constant rate (g) orever. V E 0 4 D0 ( g) D0 ( g) D0 ( g) D0 ( g) D0 ( g) K Finally, the above equation can be simpliied to V E 0 D k g and we arrive at a version o the Dividend Discount Model oten reerred to as the Gordon Model. According to this model, in order to value a stock, we need to estimate next period s dividend, the growth rate o the dividend, and arrive at the appropriate discount rate. It is the simplicity o the Gordon Model that makes it useul. Although many investors have moved beyond the model, it can still serve as a useul starting point. For example, i you read the stock tables in a newspaper, then you will mostly likely observe 8

9 a column or the P/E ratio (i.e., price-earnings ratio --- note, in inance, net income is oten reerred to as earnings). Some investors will look to purchase stocks with low P/E ratios. The Gordon Model can help us understood why. We can begin by dropping the notation o value and use the more common price terminology. Next, we recognize that dividends are simply the portion o earnings (E) that get paid out to stockholders deine the portion as b. P 0 be k g P E 0 b k g The P/E ratio depends upon the payout rate (i.e., what portion o earnings are paid out as dividends), the growth rate o dividends (and, assuming a constant payout ratio, the growth rate o earnings!), and the appropriate discount rate. Upon observing a P/E ratio or a particular stock, we can begin to discover what assumptions would need to be made in order to justiy it. One inal rearrangement o the original Gordon Model is most useul or us. The model can be solved or the discount rate. When this is done, the discount rate (k) is reinterpreted as an expected rate o return (r) on the stock. Or, or us, the rate o return required by current shareholders hence, the cost o equity capital. D r P g The rate o return depends upon the dividend yield (D/P) oten reported in stock tables and the expected growth rate o the dividend (and, earnings assuming a constant payout ratio). For example, a stock currently priced at $50 and paying a $5 dividend with expected growth o 4% per year implies that shareholders require a rate o return o 4% (plug in the numbers and see). I the stock price should all to $45 assuming the dividend and growth remaining the same the required rate o return (i.e., cost o equity capital) will rise to just over 5% (the dividend yield rises to.%). A corporation can, thereore, use this model to estimate its cost o equity capital by observing the current market price, the current dividend it will pay, and the expected growth o the dividend. O course, the problem is that the expected growth o the dividend is really inside the head o its shareholders. Though, with guidance rom the corporation itsel, the model might be helpul. Probably the most important thing to note or our purposes is the relationship between the current stock price and the cost o equity capital. When the stock price rises, current shareholders are signaling to the corporation that they require a lower rate o return (hence, the cost o equity capital alls). There are actually two P/E ratios. One is a lagging P/E ratio and uses the past earnings. The second is the orward P/E ratio and uses the estimate or next period earnings. 9

10 . The Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (or, CAPM or short) leads to one o the most amous and heavily used equations in inance. The derivation o this model requires a great deal o work and encompasses many lines o thought. However, the equation embodying the CAPM is airly easy and straightorward. In order to see the intuition behind the CAPM, consider how you would come up with an appropriate discount rate to be used in a present value calculation or determining the value o any asset. The appropriate discount rate would most likely be composed o two parts. The irst component would be something like the interest rate on a U.S. government bond (i.e., Treasury Bond). A Treasury bond would be risk-ree in the sense that the U.S. government is extremely unlikely to deault on its debt. The second component would be an addition to the risk-ree rate o return to take into account the risk o the speciic asset that you were attempting to value. Appropriate Discount Rate Risk-Free Rate Risk Premium Alternatively, you can think o the above as explaining the rate o return on a particular asset. Rate o Return Risk-Free Rate Risk Premium In this case, we explain why a particular asset provides a rate o return above a risk-ree asset because o the risk o the particular asset. For example, suppose the interest rate (i.e., yield to maturity) on a Treasury bond is % and you purchased a stock that gave you a rate o return o 7%. Why did your stock s rate o return exceed the interest rate on the Treasury bond? The answer is that your stock entailed greater risk than an investment in U.S. Treasuries. To be precise, it carried a 4% risk premium. Suppose your stock, or whatever reason, became less risky then investors would increase the demand or the stock and drive up its price. But, when the stock price goes up, the required rate o return alls (take a look back at the Gordon Model). From the above, we would say that the risk premium ell resulting in a lower rate o return (or, lower appropriate discount rate). The CAPM utilizes the basic idea that return is composed o a risk-ree rate and risk premium. The model turns to the issue o just how to precisely arrive at the risk premium o an asset. In order to discuss it urther, we should go ahead and write down the amous equation E( r) r β [ rm r ] where E(r) is the Expected (the E) rate o return on an asset r is the risk-ree rate o return (e.g., interest rate on a Treasury bond) r M is the rate o return on the Market or all risky assets For those students interested in the theory behind the CAPM and its use, you should take the Money & Capital markets course. 0

11 β (pronounced Beta) is a measure o the relationship between variations in the rate o return on an asset and the rate o return on the Market or all risky assets. 4 β[r M - r ] is the measure o the risk premium o the asset. How does one apply the CAPM to arrive at a measure o the cost o equity capital (hence, the current required rate o return by shareholders)? First, it is necessary to deine the risk-ree rate o return. This is normally done by using the interest rate on a government bond (such as a Treasury) with a maturity that comes closest to the length o time o a particular investment project. I the investment project will generate earnings or a corporation over the next 0 years, or example, then the interest rate on a 0-year Treasury bond would be used. Second, it is necessary to arrive at the expected rate o return or the stock market as whole or the next ten years. In practice, historical data is typically used or something like the S&P 500 (a stock index comprised o 500 stock listed on the market). Although we would like to know what the rate o return on the S&P 500 would be or the next 0 years, it is probably saer to use the historical rate o return rather than guess what will happen in the uture. Third, and this is the really interesting part, the beta (β) must be determined. In act, the beta will be the only thing that changes between various stocks the other two variables in the equation remain the same when comparing two dierent stocks. The beta o a stock measures its speciic risk relative to the market or all risky assets (e.g., the stock market as a whole). Beore getting at the intuition, we should keep in mind that risk in inance does not really mean the commonsense deinition. In inance, risk can reer to both the upside (or, possible gain) o an investment as well as its downside (or, possible loss). Normally, we think o risk only in terms o the possible downside impact. In inance terms, it is better to think o the term risk as opportunity, which denotes both upside and downside potential. Technically, risk reers to the variation (or, more precisely, the standard deviation) in the rate o return. The intuition behind the beta term can be seen by comparing a stock the moves up or down twice as much as the market with a stock that moves hal as much as the market. Thus, the irst stock would have a beta o, whereas the second stock would have a beta o one-hal. For example, i the stock market as a whole went up or down by 6%, then the rate o return on the irst stock would go up or down by %. In contrast, the rate o return on the second stock would go up or down by only %. Let s lesh this out a little more by assuming a risk-ree rate and market rate o return. 4 To be precise, beta is equal to the covariance o the asset and market returns divided by the variance o the market, σ M Cov( r, rm ) β where σ M is the covariance between the asset and the market. σ σ M M

12 Stock Stock risk-ree rate % % market rate o return 7% 7% beta 0.5 E r) r β [ r r ] % 4.5% ( M Thus, the stock that varies more will have a higher required rate o return (i.e., cost o equity capital) according to CAPM. Briely, what would happen i the rate o return on an asset did not vary at all? Thus, when the stock market as a whole moved up or down, this stock s rate o return would not change. The beta or this stock would be zero. In this case, we would say that the stock s rate o return carried no risk. Hence, its rate o return should be equal to the risk-ree rate o return. E ( r) r β [ r r ] r 0[ r r ] r M M On the other hand, suppose there was a stock that moved exactly with the market as a whole. When the market went up by %, the rate o return on this stock s rate o return went up by precisely % as well. Or, when the market went down by 8%, the rate o return on this stock went down by exactly 8% as well. I the stock s rate o return moved exactly with the market, then the beta would be exactly one. Now, i there were such a stock, what should be its rate o return? According to CAPM, the rate o return should be exactly equal to the rate o return on the market or all risky assets (e.g., the stock market as a whole). E ( r) r β [ r r ] r [ r r ] r M M M Thus, when a stock s return moves more than the market (either up or down), then beta will be greater than one and the holder o the stock will be rewarded (or, penalized) with an expected rate o return greater than the market as a whole. I, on the other hand, a stock s rate o return tended to move less than the market, then the beta will be less than one and the expected rate o return will be less than that expected on the market as a whole. The underlying idea is that the market rewards one or taking on greater risk holding stocks that move up and down more than the market as a whole. In practice, the beta is calculated using the statistical technique known as regression analysis. It is easy enough to perorm a regression with Excel. One simply gets historical data on the rate o return or the particular stock and the market as a whole (again, the S&P 500 or some other broad index measure is used) and hits a ew keys in

13 Excel to arrive at the beta. Fortunately or us, betas have become so popular that they are widely publicized. You can ind a stock s beta, or example, on Yahoo!Finance and MSN money central. You will ind, however, that any two sources will typically present dierent measures o beta or the exact same stock. Why? One reason or this is that historical data must be used, which brings up the question o just what historical data to be used (e.g., , , , or what?). A second reason is the index to be used (Dow Jones, S&P 500, Russell 000, or what?). There are other reasons or the dierent estimates o beta, but we seem to have enough o an idea already. The point is to know what the beta is telling you and just how to use it. The CAPM provides a useul way to arrive at the cost o equity capital. The expected rate o return in the CAPM is the appropriate discount rate used to apply to stocks. Thus, i one were using the Gordon Model in order to value a stock, they could ind the dividend payment and estimate the growth rate o that dividend, then use the CAPM rate o return as the proper discount rate to apply. For example, suppose we have the ollowing inormation on a particular stock. D $ per share g 4% annually r % r M 8% β.5 According to the Gordon Model, the value o the stock would be the ollowing. $ P r.04 O course, we need the discount rate to use. We get this rom the CAPM. E( r) r β [ r r ].0.5[.08.0] % M Notice in the above that the risk premium or this stock is 6.5%. Now, we can value the stock. $ P $8.0 What i the beta had been 0.75 with everything else the same? E( r) r β [ r r ] [.08.0] % M The risk premium would drop to only.75%, the cost o equity capital alls to 6.75%, and the stock price would rise. $ P $7.7

14 Thus, since the rate o return on the stock does not vary as much now (i.e., beta is lower) the value o the stock should increase. In other words, investors should be willing to pay more or a stock when its rate o return does not change much. We will use the CAPM to arrive at the cost o equity capital or a corporation. The cost o debt capital has already been shown to be simply the yield to maturity (or, interest rate) on a corporation s debt (e.g., bonds). The two costs then tell us what those people currently holding our debt and equity require in terms o a rate o return. We have deciphered the signals originating in the bond and stock markets to undercover the inormation we needed in order to evaluate investment projects using either the Net Present Value Method or Internal Rate o Return Method. Now, what do we actually do with these numbers? We want one number to use as our cost o capital. At this point we have two numbers. In the next section we see that we will simply take a weighted average o the two numbers to arrive at the cost o capital (or, now it will make more sense to call it the weighted average cost o capital). 4. Weighted Average Cost o Capital (WACC) In order to determine a corporation s cost o capital we will take a simple weighted average o the cost o debt and cost o equity capital. With only a couple o exceptions, there is really not much more to do to arrive at the cost o capital. The current section will demonstrate how to compute the weighted average and make a couple o adjustments to what has been said already. Anyone that has computed their grade point average (GPA) or a semester knows how to calculate a weighted average. To illustrate, suppose a student received the ollowing grades in a semester. Course Credit Hours Letter Grade Point Grade Intro to Organizations A 4.0 Calculus 5 C.0 Field Experience Seminar B.0 What is the student s GPA or this semester? I we just look at the last two columns then we might initially answer.0. However, we need to take into account the credit hours or each course, and weigh the grades accordingly. Ater doing so, we see that the GPA is actually.8 rather than.0. The calculus course in which the student received a C represented hal o the credit hours taken and thereore weighed heavily in determining the GPA. 4

15 Course % o Total Credits Point Grade Intro to Organizations 0% x 4.0. Calculus 50% x.0.0 Field Experience Seminar 0% x GPA Calculating the weighted average cost o capital is no dierent than calculating your GPA. We simply weight the cost o debt and equity capital according to the percentage that each type o inancing represents in the total capital o the corporation. As a very simple example, suppose we have the ollowing or a corporation. Source Market Value Cost Debt (bonds) $00 5% Equity (stocks) $800 0% I we took the simple average, we would arrive at a cost o capital o 7.5%. However, it is clear that the cost o equity capital should be weighed more than the cost o debt. Source % o Total Value Cost Debt (bonds) 0% x 5% % Equity (stocks) 80% x 0% 8% 9% WACC The weighted average gets pulled above the simple average because stocks represent a higher percentage in this corporation s total market value. Notice, we are using the market value o the sources o inancing. This will typically dier rom what is actually on the balance sheet. For example, the shareholder equity section o the balance reports the amount o equity raised in the initial oering o the stock hence, the historical value. We are interested in the current market value o the stock. The market value o the stock o a corporation is called its market capitalization and is ound by multiplying the current stock price by the number o shares outstanding. The market capitalization is typically provided by Yahoo!Finance and MSN money central. The market value o the debt outstanding can be a bit more diicult to actually ind online, but will oten be provided in a corporation s 0K iling with the SEC. The market value o the debt is simply the current value o the bonds outstanding. In applications, this can create an additional step or us i the corporation has more than one type o bond outstanding but, we ll see that this will mean calculating another weighted average. 5

16 The most signiicant modiication we need to make in order to arrive at the WACC is to adjust or the tax impact o interest. Interest expense is deducted rom Earnings beore Interest & Taxes (i.e., EBIT) prior to calculating the tax payment. We need to take this into account when using the interest rate as the cost o debt. In order to see the implications, consider the ollowing two irms, identical in all ways except or the capital structure (i.e., their debt and equity). Firm has been all equity inanced and carries no debt, and thereore no interest expense. Firm had used some debt to inance its assets. In the current period suppose interest expense had been say $00 please note, the numbers here are used just to illustrate the tax impact. Firm Firm EBIT $,000 $,000 - Interest 0 00 EBT $,000 $700 - Tax Net Income $ 650 $455 Now, what did the interest expense actually cost Firm? The net income or Firm was only $95 less than Firm, not $00 less. The reason is that the total taxes were lower or Firm even though they both made the same EBIT. The interest expense was deducted prior to calculating the taxes to be paid. In this case, we have used a 5% tax rate or both irms. Now, let s see how to come up with that $95 dierence between the Net Incomes o the two irms. This, ater all, is the true cost to Firm or taking on debt and paying interest. Interest x ( t) $00 x ( -.5) $95 The true cost o interest is ound by multiplying interest by one minus the tax rate (t). With a tax rate o 5%, Firm loses only 65% o the interest expense compared with a situation in which it paid no interest at all. This means that the true cost o debt is not the interest rate, but the interest rate adjusted or the tax beneit. Cost o Debt i x ( t) The above is called the ater-tax interest rate, or ater-tax cost o debt. Using a 5% tax rate, we can redo our previous calculation o the WACC. 6

17 Source % o Total Value Cost Debt (bonds) 0% x 5%(-5%).5%.65% Equity (stocks) 80% x 0% 8% 8.65% WACC The WACC has decreased because the true cost o debt is not the interest rate o 5% but rather the ater-tax interest rate o.5% (assuming a 5% tax rate). A more complete example should be useul at this point. Example: B.B. Lean Co. The B.B. Lean Co. has.4 million shares o common stock outstanding. The stock currently sells or $0 per share. The market value o the irm s debt is $4.65 million with a current yield to maturity o % (i.e., the current interest rate). The risk-ree rate is 8%, and overall market rate o return is 5%. The historical CAPM beta or Lean is.74. The corporate tax rate is 4%. What is B.B. Lean Co. s WACC?. Calculate the CAPM required rate o return (or, cost o equity capital). r r β ( r r ) 8%.74 [5% 8%].8% E M. Calculate the total market value o the equity (or, market capitalization) (Equity) Market Capitalization $0 x.4 million $8 million. Calculate the market value o the debt Market Value o Debt $4.65 million (this has been given to us in the problem) 4. Calculate the total market value o debt and equity V $8 million $4.65 million $.65 million 5. Calculate the percentage o equity and debt in the total market value Equity Percent $8/$ % Debt Percent $4.65/$ % 6. Calculate the WACC (cost o capital) WACC ( ) (.44. (.4) ).4.4% 7

18 Quick Reerence. Weighted Average Cost o Capital (WACC) --- with Debt and Common Stock D WACC i( t) V E V D is the Market Value o Debt E is the Market Value o Equity V is the Total Market Value i is the yield to maturity (or, cost o debt) t is the tax rate r is the cost o equity. WACC --- with Debt, Common Stock, Preerred Stock D C F WACC i( t) r V V V r C r F D is the Market Value o Debt C is the Market Value o Common Stock F is the Market Value o Preerred Stock V is the Total Market Value i is the yield to maturity (or, cost o debt) t is the tax rate r C is the cost o common equity r F is the cost o preerred stock Total Equity Capital Common Stock Preerred Stock Preerred Stock is a hybrid o debt and equity, meaning it has characteristics o both. However, it is listed within the shareholders equity portion o the balance sheet. It is a title o ownership, but normally without any voting rights (thus, no control). It is like debt in the sense that preerred stock normally promises a particular dividend payment each year, unlike common stock where the dividend may go up or down depending upon proitability. Since preerred stock promises a set dividend each year, and it is assumed to last orever the required rate o return (or, cost o this orm o equity) is easy to calculate --- it uses our orever assumption. D r F where D is the annual dividend, and P the current market price. P 8

19 4. Cost o Debt (or, yield to maturity --- YTM) C C P L ( YTM ) ( YTM ) ( C YTM ) T ( FV YTM ) T P is the current market price o the bond C is the annual coupon payment FV is the ace value o the bond T is the year the bond matures 5. Cost o Equity (r, using Gordon Model) D r P g D is the annual dividend payment P is the current market price g is the expected annual growth rate o the dividend 6. Cost o Equity (r, using CAPM) r r β [ rm r ] r is the risk-ree rate (e.g., interest rate on government bond) r M is the rate o return on the market or risky assets as a whole (e.g., S&P 500) β is beta (see text or explanation) 7. Net Present Value (NPV) NPV CF ( WACC) CF ( WACC) CFT L ( WACC) T Cost WACC is the cost o capital (weighted average cost o capital) CF is the expected cash low or a particular year Cost is the initial cost o the investment project T the economic lie o the investment project 8. Internal Rate o Return (IRR) Cost CF ( IRR) CF ( IRR) CFT L ( IRR) T 9