13-LasherIM-Ch13

CHAPTER 13

THE COST OF CAPITAL

FOCUS The cost cost of capital was was introduced introduced in Chapter 10 as an underpinning for capital capital budgeting, budgeting, so the student is already familiar with the basic concept. concept. Here we focus on the practical intricacies of the calculation and the importance of using market values. PEDAGOGY The cost of capital capital is a "big" calculation. any students students have trouble trouble wrapping wrapping their arms around around it. !ts therefore important to develop an overview of the whole idea before getting lost in the calculations. !n other words, it#s a good idea to spend some time talking about the cost of capital as an $average rate% the company pays for the use of its long&term money, and why knowing the cost of capital is important. TEACHING OBJECTIVES 'fter studying studying this this chapter, chapter, the student should should appreciate appreciate the details details of the weighted average cost of capital concept, be able to calculate component capital costs, and develop the ('CC ('CC as well as an CC schedule. OUTLINE

!.

TH) *+*- *+*-) ) -/ -/ TH) TH) C-T C-T -/ -/ C'*!T C'*!T' ' The cost of capital as a benchmark for evaluating capital budgeting proects and as the firms re2uired rate of return.

!!. C-T C-T -/ C'*!T C'*!T' ' C-3C) C-3C)*T *T '. Capit Capital al Compon Component entss 4ebt, )2uity, and *referred tock. 5. Capi Capita tall tr truc uctu ture re tructure as a mi6 of components. The target structure structure and the proportions in which money is raised. C. eturns eturns on !nvestm !nvestments ents and and the Costs Costs of Capita Capitall Component Componentss The conceptual relationship between the return an investor receives and the cost of a component. 4. The (eighted (eighted 'verage Calculation Calculation & the ('CC ('CC ' preview of the weighted average idea and how it works. ). Capital Capital tructure tructure and Cost Cost & 5ook 7ersus 7ersus arket arket 7a 7alues The idea that structure and cost can be based on either book or market values and an e6planation of why market values values are preferred. !!!. C'C+'T C'C+'T!38 TH) ('CC '. 4eveloping arket&7alue&5as arket&7alue&5ased ed Capital tructures How to develop a structure based on the current prices of the underlying securities. 5. Calculati Calculating ng Compo Component nent Costs Costs of Capital Capital 'dusting returns for ta6es and flotation cost to arrive at component costs. C. *utting *utting the (eig (eights hts and and Costs Costs Tog Together ether !7. !7. TH) '8!3' C-T -/ C'*!T' C'*!T' 9CC: '. The 5reak 5reak in CC CC (hen (hen etained etained )arnin )arnings gs un un -ut 4efining the breakpoint and calculating its position. 5. The The CC CC ch ched edul ulee

B0F

The Cost of Capital

4efining the CC schedule and its use 7. TH) C-T -/ -/ C'*!T' C'*!T' & ' C-*) C-*)H)3 H)3!7) !7) );'*) );'*) ' detailed e6ample illustrating the calculation of the ('CC and CC. 7!. ' *-T)3T!' !T'. 9$#ge ?(4 1B. Harris !nc.#s preferred stock was issued five years ago to yield FL. !nvestors buying those shares on the secondary market today are getting a 1DL return. Harris generally pays flotation costs of 1AL on new securities issues. (hat is Harris#s cost of preferred financing@ SOLUTIONN The cost of preferred is the current investor#s return adusted for flotation costs. Cost of preferred P !nvestor#s return ? 91 − f: P 1DL ? 91 − .1A: P 1DL ? .JJ P 1G.F1L

1D.

/uller, !nc. issued K100, JL preferred stock five years ago. !t is currently selling for KJD.G0. 'ssuming /uller has to pay floatation costs of 10L, what is /uller#s cost of preferred stock@

BA0

The Cost of Capital

SOLUTION: Cost of *referred tock P KJ.00?9KJD.G0:91 & .1: P 10.GAL

1G. ' few years ago Hendersen Corp issued preferred stock paying JL of its par value of KG0. The issue is currently selling for KBJ. *referred stock flotation costs are 1GL of the proceeds of the sale. (hat is Hendersens cost of preferred stock@ SOLUTION: 4 p P KG0 × .0J P KD k  p P KD?KBJ P 10.GBL Cost of preferred P k  p?91−f: P 10.GBL ?.JG P 1A.BFL

1. 3ew buyers of immonds !nc. stock e6pect a return of about AAL. The firm pays flotation costs of FL when it issues new securities. (hat is immonds# cost of e2uity 9 Hint N This problem is very simple since we don#t have to estimate the investors# return.: a. /rom retained earnings@  b. /rom new stock@ SOLUTIONN a. 3ew e2uity from retained earnings is not subect to flotation costs nor is it ta6 deductible, so there are no adustments to the investors# returns to get cost. Hence the firm#s cost of retained earnings is AAL.

 b. 3ew stock is subect to flotation costs so the return must be grossed up to allow for their payment. Cost of new e2uity P !nvestor#s return ? 91 − f: P AAL ? 91 − .0F: P AAL ? .F1 P AD.1JL

C"t 2 Ret#i-e+ E#&-i-g"  C-"t#-t G&t 9G&+- =+e%: E8#$%e 13>( 9$#ge ?) 1I.  9$#ge ?1 A0. The onglife !nsurance Company of the preceding problem has several bonds outstanding that are currently selling to yield FL. (hat does this imply about the cost of the firms e2uity@ SOLUTION: The risk premium approach says the cost of e2uity should be B&GL higher than the return on the same companys debt. !n this case thats 1A&1DL which is consistent with the results of the  preceding problem.

A1. Hammell !ndustries has been using 10L as its cost of retained earnings for a number of years. anagement has decided to revisit this decision based on recent changes in financial markets. 'n average stock is currently earning JL, treasury bills yield B.GL, and shares of Hammell#s stock are selling for KAF.DD. The firm ust paid a dividend of K1.G0, and anticipates growing at GL for the foreseeable future. Hammell#s C/- recently asked an investment banker about issuing bonds and was told the market was demanding a .GL coupon rate on similar issues. Hammell stock has a beta of 1.D. ecommend a cost of retained earnings for Hammell. SOLUTION: )stimate the cost of retained earnings in three ways and reconcile the results. C'* k P k / S 9k  U k/:bH P B.GL S 9J.0L & B.GL: 6 1.D P F.JL isk *remium k P k d S rpe P .GL S DL P 10.GL 8ordon odel k P Q4091Sg:?*0R S g P QK1.G091.0G:?KAF.DDR S .0G P 10.BGL The three approaches give results that are fairly close to one another and average 10.AL, a figure that#s slightly higher than the one the firm has been using. ' change to 10.AL is appropriate but probably isn#t necessary.

BAA AA.

The Cost of Capital uppose Hammell of the previous problem needs to issue new stock to raise additional e2uity capital. (hat is its cost of new e2uity if and flotation costs are 1AL@

SOLUTION:

k P Q4091Sg:?*091&f:R S g P QK1.G091.0G:?KAF.DD91&.1A:R S .0G P 11.0JL

=CC: E8#$%e 13>< 9$#ge ?3 AB. (hitley otors !nc. has the following capital.  Debt N The firm issued F00, AG year bonds five years ago which were sold at a par value of K1,000. The  bonds carry a coupon rate of IL, but are currently selling to yield new buyers 10L.  Preferred Stock NB,G00 shares of JL preferred were sold 1A years ago at a par value of KG0. They#re now  priced to yield 11L.  EquityN The firm got started with the sale of 10,000 shares of common stock at K100 per share. ince that time earnings of KJ00,000 have been retained. The stock is now selling for KJF. (hitley#s business  plan for ne6t year proects net income of KB00,000, half of which will be retained.

The firm#s marginal ta6 rate is BJL including federal and state obligations. !t pays flotation costs of JL on all new stock issues. (hitely is e6pected to grow at a rate of B.GL indefinitely and recently paid an annual dividend of KD.00. 4evelop (hitley#s ('CC before and after the retained earnings break and indicate how much capital will have been raised when the break occurs.

SOLUTION: /irst develop the market based capital structure by valuing the capital components.

 Debt N +se a financial calculator to value (hitley#s bonds as followsN nPD0, !?=PG, *TPBG, /7P1000N *7 P KIDA.1 multiply by the number of bonds outstanding for the market value of debt KIDA.1 6 F00 P KJ,BDF  Preferred: )ach preferred share pays a dividend of KG0 6 .0J P KD.00 'nd is valued at KD.00 ? .11 P KB.B ultiply by the number of preferred shares outstanding for the market value of preferred stock  KB.B 6 B,G00 P K1AI,A0  Equity: imply multiply the number of shares outstanding by the stock#s market price for the market value of e2uity 10,000 6 KJF.00 P KJF0,000

BAB

Chapter 1B

The market value based capital structure is then 4ebt K J,BDF *referred 1AI,A0 )2uity JF0,000 K1,JG,0F

BF.IL I.GL GA.JL 100.0L

 3e6t develop the capital component costs.  Debt:

Cost of debt P k d91&T: P 1091&.BJ: P .AL

 Preferred:

Cost of preferred P k  p ? 91&f: P 11 ? 91&.0J: P 1A.0L

 Equity from RE:

k e P Q4091Sg: ? *0R S g P QD.0091.0BG: ? JFR S.0BG P .0DI S.0BG P J.AL  Equity from new stock:

k e P Q4091Sg: ? *091&f:R S g P QD.0091.0BG: ? JF91&.0J:R S.0BG P .0G1 S.0BG P J.L ('CC calculationsN 5efore the break 4ebt *referred )2uity

i6 .BFI .0IG .GAJ 1.000

Cost .A 1A.0 J.A

/actor   A.G .F D.B I.I

i6 .BFI .0IG .GAJ 1.000

Cost .A 1A.0 J.

/actor   A.G .F D.G I.F

'fter the break 4ebt *referred )2uity

Calculate the break point *lanned ) P KB00,000 6 .G P K1G0,000 K1G0,000 ? .GAJ P KAJD,0F1

AD. The ongenes Company uses a target capital structure when calculating the cost of capital. The target structure and current component costs based on market conditions follow. Component i6 CostO 4ebt AGL JL *referred tock 10L 1AL Common )2uity GL A0L O The costs of debt and preferred stock are already adusted for ta!es and"or flotation costs# The cost of equity is unadusted#

BAD

The Cost of Capital

The firm e6pects to earn KA0 million ne6t year, and plans to invest K1J million in new capital  proects. !t generally pays dividends e2ual to 0L of earnings. /lotation costs are 10L for common and preferred stock. a. (hat is ongenes# initial ('CC@  b. (here is the retained earnings breakpoint in the CC@ 9ound to the nearest K.1.:  c. (hat is the new ('CC after the break@ 9'dust the entire cost of retained earnings for flotation costs.:  d. ongenes can borrow up to KD million at a net cost of JL as shown. 'fter that the net cost of debt rises to 1AL. (hat is the new ('CC after the increase in the cost of debt@ e. (here is the second break in the CC@ That is, how much total capital has been raised when the second increase in ('CC occurs@  f. ketch ongenes# CC. SOLUTION: a. Component 4ebt *referred tock Common )2uity

i6 AGL 10L GL

Cost /actors J.0L A.0 1A.0L 1.A A0.0L 1B.0 ('CC P 1.AL  b. 'vailable retained earnings P KA0 × .D P KJ 5reakpoint P KJ ?.G P K1A.B c. Cost of new e2uity P k e?.F P A0L?.F P AA.AL Component 4ebt *referred tock Common )2uity

i6 AGL 10L GL

Cost /actors J.0L A.0 1A.0L 1.A AA.AL 1D.D ('CC P 1I.L

 

Component 4ebt *referred tock Common )2uity

i6 AGL 10L GL

Cost /actors 1A.0L B.0 1A.0L 1.A AA.AL 1D.D ('CC P 1J.L

e.

KD?.AG P K1

 

d.

f. 1J.L

('CC

1I.L

1.AL ??? K1A.B

K1.0

BAG

Chapter 1B

C"t 2 C#$it#% C$&ee-"i5e P&,%e #-+ IOS: E8#$%e 13>1) 9$#ge ?( #-+ C,i-i-g te =CC #-+ te IOS 9$#ge ?? AG. Taunton Construction !nc.s capital situation is described as followsN De,t: The firm issued 10,000 AG&year bonds10 years ago at their par value of K1,000. The bonds carry a coupon rate of 1DL and are now selling to yield 10L. P&e2e&&e+ Stc@: B0,000 shares of preferred stock were sold si6 years ago at a par value of KG0. The shares pay a dividend of K per year. imilar preferred issues are now yielding FL. E/'it0: Taunton was initially financed by selling A million shares of common stock at K1A. 'ccumulated retained earnings are now KG million. The stock is currently selling at K1B.AG. Tauntons Tar$et %apital Structure  is as followsN 4ebt *referred tock Common )2uity  

B0.0L G.0L G.0L 100.0L

Ote& i-2&#ti-: • Tauntons marginal ta6 rate 9state and federal: is D0L. /lotation costs average 1AL for common and preferred stock. • hort&term treasury bills currently yield I.GL. • • The market is returning 1A.GL. • Tauntons beta is 1.A. The firm is e6pected to grow at L indefinitely. • The last annual dividend paid was K1.00 per share. • • Taunton e6pects to earn KG million ne6t year. • The firm can borrow an additional KA million at rates similar to the market return on its old debt. 5eyond that lenders are e6pected to demand returns in the neighborhood of 1DL. • Taunton has the following capital budgeting proects under consideration in the coming year. These represent its investment opportunity schedule 9!-:.

*roect ' 5 C 4 )

! 1G.0L 1D.0L 1B.0L 1A.0L 11.0L

Capital e2uired KB KA KA KA KA

Cumulative Cap. e2. KB KG KI KF K11

a. Calculate the firms capital structure based on book and market values and compare with the target capital structure. !s the target structure a reasonable appro6imation of the market value based structure@ !s the book structure very far off@  b. Calculate the cost of debt based on the market return on the companys e6isting bonds. c. Calculate the cost of preferred stock based on the market return on the companys e6isting preferred stock. d. Calculate the cost of retained earnings using three approaches, C'*, dividend growth, and risk  premium. econcile the results into a single estimate. e. )stimate the cost of e2uity raised through the sale of new stock using the dividend growth approach.  f. Calculate the ('CC using e2uity from retained earnings based on your component cost estimates and the target capital structure. g. (here is the first breakpoint in the CC 9the point where retained earnings runs out:@ Calculate to the nearest K.1.

BA

The Cost of Capital

 h. Calculate the ('CC after the first breakpoint.  i. (here is the second breakpoint in the CC 9the point at which the cost of debt increases.: (hy does this second break e6ist@ Calculate to the nearest K.1.  . Calculate the ('CC after the second break.  k. *lot Tauntons CC.  l. *lot Tauntons !- on the same a6es as the CC. (hich proects should be accepted and which should be reected@ 4o any of those reected have !s above the initial ('CC@ !f so, e6plain in words why theyre being reected. m. (hat is the ('CC for the planning period@  n. uppose proect ) is self&funding in that it comes with a source of its own debt financing. ' loan is offered through an e2uipment manufacturer at FL. The cost of the loan is FL × 91−T: P G.DL. hould proect ) be accepted under such conditions@ SOLUTION: a. 4ebtN 5ook arket N *5

P 10,000 × K1,000 P K10,000,000 P *TQ*7/'G,B0R S /Q*7/G,B0R P KI091G.BIAG: S K1,0009.AB1D: P K1,B0I.DJ arket 7alue P 10,000 × K1,B0I.DJ P K1B,0ID,J00 *referred 5ook P KG0 × B0,000 P K1,G00,000 arket P 9K?.0F: × B0,000 P KA,000,000   )2uityN 5ook P A,000,000 × K1A S KG,000,000 P KAF,000,000 arket P A,000,000 × K1B.AG P KA,G00,000 5ook

4ebt *referred )2uity

arket

7alue (eights K10,000,000 AD.IL K 1,G00,000 B.IL KAF,000,000 I1.L KD0,G00,000 100.0L

7alue (eights K1B,0ID,J00 B1.DL K A,000,000 D.JL KA,G00,000 B.JL KD1,GID,J00 100.0L

Target (eights B0.0L G.0L G.0L 100.0L

The target structure is very close to the market structure. The book structure is off, but not by a great deal.  b. Cost of 4ebt P k d91−T: P 10L91−.D: P L c. Cost of *referred P k  p?91−f: P FL?91−.1A: P 10.AL d.

Cost of etained )arningsN C'*N k e P k /S9k −k /:b P I.G S 91A.G −I.G:1.A P 1B.GL

k e 4ividend 8rowthN isk *remiumN econciliationN

=

4 0 91 + g : *0

+

g=

K1.0091.0H: + .0J + .0H = 1DL K1B.AG + .0H

k e P k d S B&GL P 10L S B&GL P 1BL&1GL 1DL is a reasonable, round number.

BAI

e.

Chapter 1B

Cost of new e2uityN

k e

=

4 0 91 + g: *0 91 − f :

+

g=

K1.0091.0H: K1B.AG9.JJ:

+

.0F1 + .0H0 = 1G.1L

f. Component 4ebt *referred tock Common )2uity

Target (eights .B0 .0G .G 1.00

Cost /actors .0L 1.J0 10.AL 0.G1 1D.0L F.10 ('CC P 11.D1 +se ('CC P 11.DL

g. 3e6t years dividend and retained earningsN   4ividends CommonN K1.0?share × A,000,000 shares P KA,1A0,000 *referredN K?share × B0,000 shares P 1J0,000   KA,B00,000 ) P )arnings − 4ividends P KG.0 − KA.B P KA.I 5reakpoint P KA.I?.G P KD.A h.

 

Component 4ebt *referred tock Common )2uity

Target (eights .B0 .0G .G 1.00

Cost /actors .0L 1.J0 10.AL 0.G1 1G.1L F.JA ('CC P 1A.1B +se ('CC P 1A.1L

i. KA?.B0 P K.I. This break e6ists because the cost of debt, a capital component, has increased. That impacts the ('CC in the same way that the earlier rise in the cost of e2uity does.  .

 

Component 4ebt *referred tock Common )2uity

O1DL × . P J.DL

Target (eights .B0 .0G .G 1.00

Cost /actors J.DLO A.GA 10.AL 0.G1 1G.1L F.JA ('CC P 1A.JG +se ('CC P 1A.FL

BAJ

The Cost of Capital

k and l. kL

1GL

KB

A

KG

B

1DL IOS C 

KI

1BL   1A.FL 1A.1L

1AL

D

WACC

KF

  11.DL E

11L ???

K11

K KA

KD KD.A

K

KJ

K10

K.I

'ccept ', 5, and C eect 4, ) =es, proect 4 5y the time 4 is undertaken, the ('CC has risen higher than its !. m. n.

/or the planning period, ('CC P 1A.FL. 3o. ee the *otential istake discussion.

A.

3ewrock anufacturing !nc. has the following target capital structure 4ebt AGL,  preferred A0L e2uity GGL !nvestment bankers have advised the C/- that the company could raise up to KG million in new debt financing by issuing bonds at a .0L coupon rate, beyond that amount new debt would re2uire a IL coupon. 3ewrock#s J.GL preferred stock, issued at a par value of K100, currently sells for K11A.G0. There are B,000,000 shares of common stock outstanding on which the firm  paid an annual dividend of KA.00 recently. The stock currently trades at KB per share. 3e6t year#s net income is proected at K1D,000,000 and management e6pects L growth in the foreseeable future. /loatation costs are L on debt and 11L on common and preferred stock. The marginal ta6 rate is D0L. a. Calculate the ('CC using the target capital structure and the cost of retained earnings for the e2uity component.

BAF

Chapter 1B  b. *lot 3ewrock#s CC identifying the levels of funding at which the first two breaks occur, and calculate the ('CCs after each break. c. 3ewrock has identified the following capital proects for ne6t yearN *roect !nvestment !   ' K D.0 million 11.0L 5 K B. million 10.GL C K J. million 1B.AL 4 K A.0 million J.IL ) K G.G million F.GL / K G.0 million I.AL 8 K D.1 million 10.GL H K .D million J.0L *roects ' and 5 are mutually e6clusive, as are *roects C and H. *lot the !- and the CC and determine the ideal sie of ne6t year#s capital program.

SOLUTION: a. Cost of Capital Components Cost of debt P kd91&T:?91&f: 9flotation costs on debt are unusual: P Q.0L 6 91 & .D:R?91 & .0: P B.JBL

 b.

Cost of *referred

P 4p?*p91&f:  P KJ.G0?9K11A.G0:91 & .11:  P J.DFL

Cost of )2uity

P Q4 091Sg:?*091&f:R S g  P QKA91.0:?KBR S .0  P 11.JFL

('CC Calculation 4ebt B.JB 6 .AG P .FGI *referred J.DFL 6 .A0 P 1.FJ )2uity 11.JF 6 .GG P .GD0 ('CC F.1FGL use F.AL 5reakpoint for new e2uity P 93et !ncome U 4ividends:?L )2uity P QK1D million U B million 9KA.1A:R?.GG P K1B.JF million Cost of new )2uity P KA.1A?QKB.00 6 91 & .11:R S .0 P 1A.AL 5reakpoint for debt P KG million?.AG P KA0 million Cost of 3ew 4ebt P IL 6 91 & .D:?91 & .0: P D.DIL ('CC after the first break point 9new e2uity: 4ebt B.JBL 6 .AG P *referred J.DFL 6 .A0 P )2uity 1A.AL 6 .GG P ('CC

.FGI 1.FJ .FD1 F.GFL use F.L

('CC after the second break point 9debt: 4ebt D.DIL 6 .AG P *referred J.DFL 6 .A0 P )2uity 1A.AL 6 .GG P ('CC

1.11J 1.FJ .FD1 F.IGIL use F.JL

BB0

The Cost of Capital

c.

5etween *roects ' and 5, pick ' between C and H, pick C. Therefore of the remaining  proects the order should be C, ', 8, ), 4 and /.

15

IOS 14 13 12

C

11

 A

10 9

WACC

G

8

E D

7

F

6 5 4 3 2 1 0

$10

$20

*roects C, ', and 8 should be accepted which will result in a capital program totaling K1.I million. The ne6t eligible proect ) has an e6pected return of F.GL, but the marginal cost of capital is F.L at this point, so *roect ) should be reected.

$29