Copyright 2012 Pearson Prentice Hall. All rights reserved.Chapter 9The Cost of Capital 2012 Pearson Prentice Hall. All rights reserved. 9-2Learning GoalsLG1 Understand the basic concept and sources of capital associated with the cost of capital.LG2 Explain what is meant by the marginal cost of capital.LG3 Determine the cost of longterm debt! and explain why the aftertax cost of debt is the rele"ant cost of debt. 2012 Pearson Prentice Hall. All rights reserved. 9-3Learning Goals (cont.)LG# Determine the cost of preferred stoc$.LG% &alculate the cost of common stoc$ e'uity! and con"ert it into the cost of retained earnings and the cost of new issues of common stoc$.LG( &alculate the weighted a"erage cost of capital )*+&&, and discuss alternati"e weighting schemes. 2012 Pearson Prentice Hall. All rights reserved. 9-4Overview of the Cost of Capital-he cost of capital represents the firms cost of financing! and is the minimum rate of return that a pro.ect must earn to increase firm "alue./inancial managers are ethically bound to only in"est in pro.ects that they expect to exceed the cost of capital.-he cost of capital reflects the entirety of the firms financing acti"ities. 0ost firms attempt to maintain an optimal mix of debt and e'uity financing. -o capture all of the rele"ant financing costs! assuming some desired mix of financing! we need to loo$ at the o"erall cost of capital rather than .ust the cost of any single source of financing. 2012 Pearson Prentice Hall. All rights reserved. 9-5Overview of the Cost of Capital (cont.)+ firm is currently faced with an in"estment opportunity. +ssume the following12est pro.ect a"ailable today&ost 3 4155!555Life 3 25 yearsExpected 6eturn 3 78Least costly financing source a"ailableDebt 3 (82ecause it can earn 78 on the in"estment of funds costing only (8! the firm underta$es the opportunity. 2012 Pearson Prentice Hall. All rights reserved. 9-6Overview of the Cost of Capital (cont.)9magine that 1 wee$ later a new in"estment opportunity is a"ailable12est pro.ect a"ailable 1 wee$ later&ost 3 4155!555Life 3 25 yearsExpected 6eturn 3 128Least costly financing source a"ailableE'uity 3 1#89n this instance! the firm re.ects the opportunity! because the 1#8 financing cost is greater than the 128 expected return. 2012 Pearson Prentice Hall. All rights reserved. 9-Overview of the Cost of Capital (cont.)*hat if instead the firm used a combined cost of financing:+ssuming that a %5%5 mix of debt and e'uity is targeted! the weighted a"erage cost here would be1)5.%5 (8 debt, ; )5.%5 1#8 e'uity, 3 158*ith this a"erage cost of financing! the first opportunity would ha"e been re.ected )78 expected return < 158 weighted a"erage cost,! and the second would ha"e been accepted )128 expected return = 158 weighted a"erage cost,. 2012 Pearson Prentice Hall. All rights reserved. 9-!Overview of the Cost of Capital"#o$rces of Long-%er& Capital 2012 Pearson Prentice Hall. All rights reserved. 9-9Cost of Long-%er& 'e(tNet proceeds are the funds actually recei"ed by the firm from the sale of a security.Flotation costs are the total costs of issuing and selling a security. -hey include two components11. Underwriting costscompensation earned by in"estment ban$ers for selling the security.2. +dministrati"e costsissuer expenses such as legal! accounting! and printing.Floatation costs reduce the net proceeds. 2012 Pearson Prentice Hall. All rights reserved. 9-)*Cost of Long-%er& 'e(t (cont.)Duchess &orporation! a ma.or hardware manufacturer! is contemplating selling 415 million worth of 25year! >8 coupon bonds with a par "alue of 41!555. 2ecause current mar$et interest rates are greater than >8! the firm must sell the bonds at 4>?5. /lotation costs are 28 or 425. -he net proceeds to the firm for each bond is therefore 4>(5 )4>?5 425,. 2012 Pearson Prentice Hall. All rights reserved. 9-))Cost of Long-%er& 'e(t (cont.) -he beforetax cost of debt! rd! is simply the rate of return the firm must pay on new borrowing. -he beforetax cost of debt can be calculated in any one of three ways11. Using mar$et 'uotations1 obser"e the yield to maturity )@-0, on the firms existing bonds or bonds of similar ris$ issued by other companies2. &alculating the cost1 find the beforetax cost of debt by calculating the @-0 generated by the bond cash flows3. +pproximating the cost 2012 Pearson Prentice Hall. All rights reserved. 9-)2Cost of Long-%er& 'e(t (cont.)+pproximating the costwhereI 3 annual interest in dollarsNd3 net proceeds from the sale of debt )bond,n 3 number of years to the bonds maturity 2012 Pearson Prentice Hall. All rights reserved. 9-)3Cost of Long-%er& 'e(t (cont.)+pproximating the cost 2012 Pearson Prentice Hall. All rights reserved. 9-)4Cost of Long-%er& 'e(t" +fter-%a, Cost of 'e(t-he interest payments paid to bondholders are tax deductable for the firm! so the interest expense on debt reduces the firms taxable income and! therefore! the firms tax liability. -he aftertax cost of debt! ri! can be found by multiplying the beforetax cost! rd! by 1 minus the tax rate! T! as stated in the following e'uation1ri 3 rd )1 T, 2012 Pearson Prentice Hall. All rights reserved. 9-)5Cost of Long-%er& 'e(t" +fter-%a, Cost of 'e(t (cont.)Duchess &orporation has a #58 tax rate. Using the >.#%28 beforetax debt cost calculated abo"e! we find an aftertax cost of debt of %.(8 A>.#8 )1 5.#5,B. -ypically! the cost of longterm debt for a gi"en firm is less than the cost of preferred or common stoc$! partly because of the tax deductibility of interest. 2012 Pearson Prentice Hall. All rights reserved. 9-)6-ersonal .inance /,a&pleCait and Casim Dulli"an! a married couple in the 2?8 federal incometax brac$et! wish to borrow 4(5!555 for a new car. -hey can either borrow the 4(5!555 through the auto dealer at an annual interest rate of (.58! or they can ta$e a 4(5!555 second mortgage on their home at an annual interest rate of 7.28. 9f they borrow from the auto dealer! the interest on this consumer loan! will not be deductible for federal tax purposes. Eowe"er! the interest on the second mortgage would be taxdeductible because the tax law allows indi"iduals to deduct interest paid on a home mortgage. 2ecause interest on the auto loan is not taxdeductible! its aftertax cost e'uals its stated cost of (.58. 2ecause interest on the second mortgage is taxdeductible! its aftertax cost e'uals its stated cost of 7.28 )1 5.2?, 3 %.28. 2012 Pearson Prentice Hall. All rights reserved. 9-)Cost of -referre0 #toc1Freferred stoc$ gi"es preferred stoc$holders the right to recei"e their stated di"idends before the firm can distribute any earnings to common stoc$holders. 0ost preferred stoc$ di"idends are stated as a dollar amount.Dometimes preferred stoc$ di"idends are stated as an annual percentage rate! which represents the percentage of the stoc$s par! or face! "alue that e'uals the annual di"idend. -he cost of preferred stock, rp, is the ratio of the preferred stoc$ di"idend to the firms net proceeds from the sale of preferred stoc$. 2012 Pearson Prentice Hall. All rights reserved. 9-)!Cost of -referre0 #toc1 (cont.)Duchess &orporation is contemplating the issuance of a 158 preferred stoc$ that is expected to sell for its 4?7per share "alue. -he cost of issuing and selling the stoc$ is expected to be 4% per share. -he di"idend is 4?.75 )158 4?7,. -he net proceeds price )Gp, is 4?2 )4?7 4%,.rP 3 DPHNp 3 4?.75H4?2 3 15.(8 2012 Pearson Prentice Hall. All rights reserved. 9-)9Cost of Co&&on #toc1-he cost of common stoc$ is the return re'uired on the stoc$ by in"estors in the mar$etplace. -here are two forms of common stoc$ financing1 1. retained earnings 2. new issues of common stoc$ -he cost of common stock equity, rs, is the rate at which in"estors discount the expected di"idends of the firm to determine its share "alue. 2012 Pearson Prentice Hall. All rights reserved. 9-2*Cost of Co&&on #toc1 (cont.)-he constant-growth valuation (Gordon) model assumes that the "alue of a share of stoc$ e'uals the present "alue of all future di"idends )assumed to grow at a constant rate, that it is expected to pro"ide o"er an infinite time horiIon.whereP53 "alue of common stoc$D13 pershare di"idend expected at the end of year 1rs3 re'uired return on common stoc$g 3 constant rate of growth in di"idends 2012 Pearson Prentice Hall. All rights reserved. 9-2)Cost of Co&&on #toc1 (cont.)Dol"ing for rs results in the following expression for the cost of common stoc$ e'uity1-he e'uation indicates that the cost of common stoc$ e'uity can be found by di"iding the di"idend expected at the end of year 1 by the current mar$et price of the stoc$ )the di"idend yield!, and adding the expected growth rate )the capital gains yield!,. 2012 Pearson Prentice Hall. All rights reserved. 9-22Cost of Co&&on #toc1 (cont.)Duchess &orporation wishes to determine its cost of common stoc$ e'uity! rs. -he mar$et price! P5! of its common stoc$ is 4%5 per share. -he firm expects to pay a di"idend! D1! of 4# at the end of the coming year! 2513. -he di"idends paid on the outstanding stoc$ o"er the past ( years )25572512, were as follows1 2012 Pearson Prentice Hall. All rights reserved. 9-23Cost of Co&&on #toc1 (cont.)*e can calculate the annual rate at which di"idends ha"e grown! g, from 2557 to 2512. 9t turns out to be approximately %8 )more precisely! it is %.5%8,. Dubstituting D1 3 4#! P5 3 4%5! and g 3 %8 into the pre"ious e'uation yields the cost of common stoc$ e'uity1rs 3 )4#H4%5, ; 5.5% 3 5.5? ; 5.5% 3 5.135! or 13.58 2012 Pearson Prentice Hall. All rights reserved. 9-24Cost of Co&&on #toc1 (cont.)-he capital asset pricing model (!"#) describes the relationship between the re'uired return! rs! and the nondi"ersifiable ris$ of the firm as measured by the beta coefficient! b.rs 3 RF ; Ab )rm RF,BwhereRF 3 ris$free rate of return rm 3 mar$et returnJ return on the mar$et portfolio of assets 2012 Pearson Prentice Hall. All rights reserved. 9-25Cost of Co&&on #toc1 (cont.)Duchess &orporation now wishes to calculate its cost of common stoc$ e'uity! rs! by using the capital asset pricing model. -he firms in"estment ad"isors and its own analysts indicate that the ris$free rate! RF! e'uals 78J the firms beta! b, e'uals 1.%J and the mar$et return! rm! e'uals 118. Dubstituting these "alues into the &+F0! the company estimates the cost of common stoc$ e'uity! rs! to be1rs 3 7.58 ; A1.% )11.58 7.58,B 3 7.58 ; (.58 3 13.58 2012 Pearson Prentice Hall. All rights reserved. 9-26Cost of Co&&on #toc1 (cont.)-he &+F0 techni'ue differs from the constantgrowth "aluation model in that it directly considers the firms ris$! as reflected by beta! in determining the required return or cost of common stoc$ e'uity. -he constantgrowth model does not loo$ at ris$J it uses the mar$et price! P5! as a reflection of the expected ris$return preference of in"estors in the mar$etplace. -he constantgrowth "aluation and &+F0 techni'ues for finding rs are theoretically e'ui"alent! though in practice estimates from the two methods do not always agree. 2012 Pearson Prentice Hall. All rights reserved. 9-2Cost of Co&&on #toc1 (cont.)+nother difference is that when the constantgrowth "aluation model is used to find the cost of common stoc$ e'uity! it can easily be ad.usted for flotation costs to find the cost of new common stoc$J the &+F0 does not pro"ide a simple ad.ustment mechanism. -he difficulty in ad.usting the cost of common stoc$ e'uity calculated by using &+F0 occurs because in its common form the model does not include the mar$et price! P5! a "ariable needed to ma$e such an ad.ustment. 2012 Pearson Prentice Hall. All rights reserved. 9-2!Cost of Co&&on #toc1"Cost of 2etaine0 /arnings-he cost of retained earnings, rr, is the same as the cost of an e'ui"alent fully subscribed issue of additional common stoc$! which is e'ual to the cost of common stoc$ e'uity! rs.rr 3 rs-he cost of retained earnings for Duchess &orporation was actually calculated in the preceding examples1 9t is e'ual to the cost of common stoc$ e'uity. -hus rr e'uals 13.58. 2012 Pearson Prentice Hall. All rights reserved. 9-293atter of .act6etained Earnings "s. 6ein"esting Earnings-echnically! if a stoc$holder recei"ed di"idends and wished to in"est them in additional shares of the firms stoc$! he or she would first ha"e to pay personal taxes on the di"idends and then pay bro$erage fees before ac'uiring additional shares. 2y using pt as the a"erage stoc$holders personal tax rate and bf as the a"erage bro$erage fees stated as a percentage! we can specify the cost of retained earnings! rr! as rr 3 rs )1 pt, )1 bf,. 2012 Pearson Prentice Hall. All rights reserved. 9-3*Cost of Co&&on #toc1" Cost of 4ew 5ss$es of Co&&on #toc1 -he cost of a new issue of common stock, rn, is the cost of common stoc$! net of underpricing and associated flotation costs.Gew shares are underpriced if the stoc$ is sold at a price below its current mar$et price! P5. 2012 Pearson Prentice Hall. All rights reserved. 9-3)Cost of Co&&on #toc1" Cost of 4ew 5ss$es of Co&&on #toc1 (cont.)*e can use the constantgrowth "aluation model expression for the cost of existing common stoc$! rs! as a starting point. 9f we let Nn represent the net proceeds from the sale of new common stoc$ after subtracting underpricing and flotation costs! the cost of the new issue! rn! can be expressed as follows1 2012 Pearson Prentice Hall. All rights reserved. 9-32Cost of Co&&on #toc1" Cost of 4ew 5ss$es of Co&&on #toc1 (cont.) -he net proceeds from sale of new common stoc$! Nn! will be less than the current mar$et price! P5. -herefore! the cost of new issues! rn! will always be greater than the cost of existing issues! rs! which is e'ual to the cost of retained earnings! rr. -he cost of new common stoc$ is normally greater than any other longterm financing cost. 2012 Pearson Prentice Hall. All rights reserved. 9-33Cost of Co&&on #toc1" Cost of 4ew 5ss$es of Co&&on #toc1 (cont.)-o determine its cost of new common stoc$! rn! Duchess &orporation has estimated that on a"erage! new shares can be sold for 4#7. -he 43pershare underpricing is due to the competiti"e nature of the mar$et. + second cost associated with a new issue is flotation costs of 42.%5 per share that would be paid to issue and sell the new shares. -he total underpricing and flotation costs per share are therefore 4%.%5.rn 3 )4#.55H4##.%5, ; 5.5% 3 5.5> ; 5.5% 3 5.1#5! or 1#.58 2012 Pearson Prentice Hall. All rights reserved. 9-346eighte0 +verage Cost of Capital-he weighted average cost of capital ($!), ra, reflects the expected a"erage future cost of capital o"er the long runJ found by weighting the cost of each specific type of capital by its proportion in the firms capital structure.ra 3 )wi ri, ; )wp rp, ; )ws rr or n,wherewi3 proportion of longterm debt in capital structurewp3 proportion of preferred stoc$ in capital structurews3 proportion of common stoc$ e'uity in capital structurewi ; wp ; ws3 1.5 2012 Pearson Prentice Hall. All rights reserved. 9-356eighte0 +verage Cost of Capital (cont.)-hree important points should be noted in the e'uation for ra11. /or computational con"enience! it is best to con"ert the weights into decimal form and lea"e the indi"idual costs in percentage terms.2. -he weights must be nonnegati"e and sum to 1.5. Dimply stated! *+&& must account for all financing costs within the firms capital structure.3. -he firms common stoc$ e'uity weight! ws! is multiplied by either the cost of retained earnings! rr! or the cost of new common stoc$! rn. *hich cost is used depends on whether the firms common stoc$ e'uity will be financed using retained earnings! rr! or new common stoc$! rn. 2012 Pearson Prentice Hall. All rights reserved. 9-366eighte0 +verage Cost of Capital (cont.)9n earlier examples! we found the costs of the "arious types of capital for Duchess &orporation to be as follows1 &ost of debt! ri 3 %.(8 &ost of preferred stoc$! rp 3 15.(8 &ost of retained earnings! rr 3 13.58 &ost of new common stoc$! rn 3 1#.58-he company uses the following weights in calculating its weighted a"erage cost of capital1Longterm debt 3 #58Freferred stoc$ 3 158&ommon stoc$ e'uity 3 %58 2012 Pearson Prentice Hall. All rights reserved. 9-3%a(le 9.) Calc$lation of the 6eighte0 +verage Cost of Capital for '$tchess Corporation 2012 Pearson Prentice Hall. All rights reserved. 9-3!6eighte0 +verage Cost of Capital" 6eighting #che&es2oo$ Kalue "ersus 0ar$et Kalue1%ook value weights are weights that use accounting "alues to measure the proportion of each type of capital in the firms financial structure.#arket value weights are weights that use mar$et "alues to measure the proportion of each type of capital in the firms financial structure.Eistorical "ersus -arget1&istorical weights are either boo$ or mar$et "alue weights based on actual capital structure proportions.'arget weights are either boo$ or mar$et "alue weights based on desired capital structure proportions./rom a strictly theoretical point of "iew! the preferred weighting scheme is target mar$et "alue proportions. 2012 Pearson Prentice Hall. All rights reserved. 9-39-ersonal .inance /,a&ple&huc$ Dolis currently has three loans outstanding! all of which mature in exactly ( years and can be repaid without penalty any time prior to maturity. -he outstanding balances and annual interest rates on these loans are noted below. 2012 Pearson Prentice Hall. All rights reserved. 9-4*-ersonal .inance /,a&ple (cont.)&huc$ found a lender who would loan him 4?5!555 for ( years at an annual interest rate >.28 on the condition that the loan proceeds be used to fully repay the three outstanding loans! which combined ha"e an outstanding balance of 4?5!555 )42(!555 ; 4>!555 ; 4#%!555,.&huc$ wishes to choose the least costly alternati"e1 )1, do nothing or )2, borrow the 4?5!555 and pay off all three loans. 2012 Pearson Prentice Hall. All rights reserved. 9-4)-ersonal .inance /,a&ple (cont.)&huc$ calculates the weighted a"erage cost of his current debt by weighting each debts annual interest cost by the proportion of the 4?5!555 total it represents and then summing the three weighted "alues as follows1*eighted a"erage cost of current debt 3A)42(!555H4?5!555, >.(8B ; A)4>!555H4?5!555, 15.(8B ; A)4#%!555H4?5!555, 7.#8B3).32%5 >.(8, ; ).112% 15.(8, ; ).%(2% 7.#8,3 3.128 ; 1.1>8 ; #.1(8 3 ?.#78 L ?.%8