Chapter 12 - ererererere PDF

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CHAPTER1 2 COSTOFCAPI TAL Answers to Critical Thinking and Concepts Review Questions 1.

It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than this, value is created.

2.

Book values for debt are likely to be much closer to their market values than are book values for equity.

3.

No. The cost of capital depends on the risk of the project, not the source of the money.

4.

In a classical tax system interest expense is tax-deductible and there is no difference between pretax and aftertax equity costs. In an imputation system tax is tax deductible reducing its cost however for the shareholder the dividend does generate a franking credit if the company has paid tax in Australia or New Zealand and the shareholder is a resident. This has the effect of reducing the cost of equity for the firm for these shareholders.

5.

The primary advantage of the DCF model is its simplicity. The method is disadvantaged in that (1) the model is applicable only to firms that actually pay dividends; many do not; (2) even if a firm does pay dividends, the DCF model requires a constant dividend growth rate forever; (3) the estimated cost of equity from this method is very sensitive to changes in growth-g, which is a very uncertain parameter; and (4) the model does not explicitly consider risk, although risk is implicitly considered to the extent that the market has impounded the relevant risk of the share into its market price. While the share price and most recent dividend can be observed in the market, the dividend growth rate must be estimated. Two common methods of estimating g are to use analysts’ earnings and payout forecasts, or determine some appropriate average historical g from the firm’s available data.

6.

Two primary advantages of the SML approach are that the model explicitly incorporates the relevant risk of the share, and the method is more widely applicable than is the DCF model, since the SML doesn’t make any assumptions about the firm’s dividends. The primary disadvantages of the SML method are (1) estimating three parameters: the risk-free rate, the expected return on the market, and beta, and (2) the method essentially uses historical information to estimate these parameters. The risk-free rate is usually estimated to be the yield on very short maturity risk free debt and is hence observable; the market risk premium is usually estimated from historical risk premiums and hence is not observable. The share beta, which is unobservable, is usually estimated either by determining some average historical beta from the firm and the market’s return data, or using beta estimates provided by analysts and investment firms. In a dividend imputation system the additional value of the tax credits on dividends needs be accounted for and this will depend on the level of franking credits generated and the ability of the shareholders to use them.

7.

The appropriate aftertax cost of debt to the company is the interest rate it would have to pay if it were to issue new debt today. Hence, if the YTM on outstanding bonds of the company is observed, the company has an accurate estimate of its cost of debt. If the debt is privately placed, the firm could still estimate its cost of debt by (1) looking at the cost of debt for similar firms in similar risk classes, (2) looking at the average debt cost for firms with the same credit rating (assuming the firm’s private debt is rated), or (3) consulting analysts and investment bankers.

Even if the debt is publicly traded, an additional complication is when the firm has more than one issue outstanding; these issues rarely have the same yield because no two issues are ever completely homogeneous. 8.

a. b. c.

9.

This only considers the dividend yield component of the required return on equity. This is the current yield only, not the promised yield to maturity. In addition, it is based on the book value of the liability, and it ignores taxes. Equity is inherently riskier than debt (except, perhaps, in the unusual case where a firm’s assets have a negative beta). For this reason, the cost of equity exceeds the cost of debt. If taxes are considered in this case, it can be seen that at reasonable tax rates, the cost of equity does exceed the cost of debt.

ROutback = .12 + .75(.08) = .18 or 18% Both should proceed. The appropriate discount rate does not depend on which company is investing; it depends on the risk of the project. Since Outback is in the business, it is closer to a pure play. Therefore, its cost of capital should be used. With an 18% cost of capital, the project has an NPV of $1 million regardless of who takes it.

10. If the different operating divisions were in much different risk classes, then separate cost of capital figures should be used for the different divisions; the use of a single, overall cost of capital would be inappropriate. If the single hurdle rate were used, riskier divisions would tend to receive funds for investment projects, since their return would exceed the hurdle rate despite the fact that they may actually plot below the SML and hence be unprofitable projects on a riskadjusted basis. The typical problem encountered in estimating the cost of capital for a division is that it rarely has its own securities traded on the market, so it is difficult to observe the market’s valuation of the risk of the division. Two typical ways around this are to use a pure play proxy for the division, or to use subjective adjustments of the overall firm hurdle rate based on the perceived risk of the division. Solutions to Questions and Problems NOTE:Al le n do f c h apt e rpr obl e mswe r es ol v e dus i n gas pr e ads he e t .Manypr obl e msr e qui r emul t i pl e s t e ps .Du et os pac eandr e ada bi l i t yc o ns t r ai nt s ,whe nt he s ei nt e r me di at es t e psar ei nc l ude di nt hi s s ol ut i onsmanual ,r oundi ngmaya ppe a rt ohav eo c c ur r e d.Ho we v e r ,t hefinalans we rf ore ac h pr o bl e mi sf o undwi t houtr oundi ngdu r i n ga nys t e pi nt hepr obl e m. Ba s i c 1. Wi t ht hei nf o r ma t i ongi v e n,wec a nfindt hec os tofe qui t y ,us i n gt hedi vi de ndgr o wt hmode l . Us i n gt hi smode l ,t hec os to fe qui t yi s : RE=[ $2. 40( 1. 06) / $48]+. 06 RE=. 11 30or11. 3 0% 2. He r eweha v ei nf or ma t i ont oc a l c ul a t et hec os tofe q ui t y , us i ngt heCAPM. Th ec os tofe qui t yi s : RE=. 05+1. 30 ( . 13–. 05) RE=. 15 40or15. 4 0% 3. Weha v et hei nf or ma t i ona va i l a bl et oc a l c u l a t et hec o s tofe q ui t y ,us i n gt heCAPM a ndt he di vi de ndgr o wt hmode l .Us i n gt heCAPM, wefind: RE=. 04 5+0. 90( . 08 )=. 1170or11. 70%

Andus i n gt hedi v i de ndgr o wt hmode l , t hec os tofe qui t yi s RE=[ $2. 60( 1. 05) / $48]+. 05=. 1 069or1 0. 69% Both estimates of the cost of equity seem reasonable. If we remember the historical return on the all ordinaries index, the estimate from the CAPM model is about average, and the estimate from the dividend growth model is about two percent lower than the historical average, so we cannot definitively say one of the estimates is incorrect. Given this, we will use the average of the two, so: RE=( . 1170+. 1069 ) / 2=. 1119or11. 19% 4. Tous et h ed i v i de ndgr o wt hmod e l ,wefir s tne e dt ofindt hegr o wt hr a t ei ndi vi de nds .So,t h e i nc r e a s ei nd i v i de ndse a c hye a rwa s : g $1. 62–1. 47) / $1. 47 1=( g = . 1 0 2 0 o r 1 0 . 2 0 % 1 g $1. 67–1. 62) / $1. 62 2=( g 0309or3. 09% 2=. g $1. 78–1. 67) / $1. 67 3=( g 0659or6. 59% 3=. g $1. 89–1. 78) / $1. 78 4=( g = . 0 6 1 8 o r 6 . 1 8 % 4 So , t hea ve r a g ea r i t h me t i cgr o wt hr a t ei ndi v i de ndswa s : g=( . 1020+. 0309+. 065 9+. 06 18) / 4 g=. 065 1o r6. 51% Us i n gt hi sgr owt hr a t ei nt hedi vi de ndgr o wt hmode l ,wefindt hec os tofe qui t yi s : RE=[ $1. 89( 1. 0651 ) / $65. 00 ]+. 0651 RE=. 09 61or9. 61 % Ca l c u l a t i ngt hege ome t r i cg r owt hr a t ei ndi vi de nds , wefind: 4 $1 . 8 9=$1. 47( 1+g ) g=. 064 8o r6. 48%

Thec os tofe q ui t yus i n gt hege o me t r i cdi vi de ndgr o wt hr a t ei s : RE=[ $1. 89( 1. 0648 ) / $ 65. 00]+. 064 8 RE=. 09 58or9. 58 % 5. Thec os tofpr e f e r r e ds ha r ei st hedi vi de ndp a yme ntdi vi de db yt hepr i c e ,s o: RP =$ 6/ $ 94 RP =. 06 38or6. 38% 6. Thepr e t a xc os tofde b ti st heYTM oft hec ompa n y’ sbonds ,s o:

P 930=$2 8( PVI FAR%,14)+$1, 000( PVI FR%,14) 0=$ R=3 . 4 38% YTM =2×3 . 43 8% YTM =6 . 8 8% Andt hea f t e r t a xc os tofde bti s : RD=. 06 88( 1–. 30 ) RD=. 0 481or4. 81 % 7. a.Thepr e t a xc os tofde bti st heYTM oft hec o mpa n y’ sb onds ,s o: P0 = $1,080 = $40(PVIFA R%,46) + $1,000(PVIFR%,46) R = 3.639% YTM = 2 × 3.639% YTM = 7.28% b.

The aftertax cost of debt is: RD = .0728(1 – .30) RD = .05095 or 5.095%

c.

The after-tax rate is more relevant because that is the actual cost to the company.

8. Thebookva l u eofde bti st het ot a lpa rv a l ueofa l lout s t a ndi ngde bt , s o: BVD =$6 0, 0 00, 000+70, 000, 000 BVD =$1 30, 000, 000 Tofindt hema r ke tv a l ueofde bt ,wefindt hepr i c eoft hebon dsa ndmul t i pl yb yt henu mb e rof bo nds .Al t e r na t i ve l y ,wec a nmul t i pl yt h ep r i c equ ot eoft hebo ndt i me st hepa rva l ueoft he bo nds .Doi n gs o, wefin d: MVD =1. 08( $60, 00 0, 0 00)+. 265 ( $7 0, 0 00, 000) MVD =$83 , 3 50, 000 TheYTM oft hez e r oc ouponb ondsi s : P 265=$1 , 00 0( PVI FR%,20) Z =$ YTM =6 . 8 7% So , t hea f t e r t a xc os toft hez e r oc ouponbond si s : RZ=. 06 87( 1–. 30 ) RZ=. 04 806or4. 8 1% Thea f t e r t a xc os to fde btf ort hec omp a n yi st hewe i ght e da v e r a geoft hea f t e r t a xc os tofde b tf or a l lo ut s t a ndi n gbondi s s ue s .Wene e dt ou s et hema r ke tv a l uewe i ght soft hebo nds .Th et o t a l a f t e r t a xc os tofde btf ort hec ompa n yi s : RD=. 05 095[ ( 1. 08) ( $60 , 0 00, 000) / $ 83, 350, 000]+. 0481[ ( . 265) ( $ 70, 000, 000) / $83, 350 , 00 0] RD=. 05 03or5. 03 %

9.

a.

Using the equation to calculate the WACC, we find: WACCclassical tax = .70(.14) + .05(.06) + .25(.075)(1 – .30) WACCclassical tax = .1141 or 11.41% Assuming that the preference and ordinary shares carry 100% franking credits at the 30% tax rate WACCimputation tax = .70(.14)(1 – 0.30) + .05(.06)(1 – 0.30) + .25(.075)(1 – 0.30) WACCimputation tax = 0.0838 or 8.38%

b.

Since interest is tax deductible and dividends are not in a classical tax system, we must look at the after-tax cost of debt, which is: RD = .075(1 – .30) RD = .0525 or 5.25% Hence, on an after-tax basis, debt is cheaper than the preference shares in a classical tax system. However in an imputation system if the preference shares have a lower return and are fully franked dividends paid then they would be a cheaper form of financing.

10. Here, we need to use the debt-equity ratio to calculate the WACC. A debt-equity ratio of .8 implies a weight of debt of .8/1.8 and an equity weight of 1/1.8. Using this relationship, we find: WACC = .14(1/1.8) + .08(.8/1.8)(1 – .30) WACC = .1127 or 11.27% WACCimputation tax = 0.14(1/1.8)(1 – 0.30) +0 .08(0.8/1.8)(1 – 0.30) WACCimputation tax = 0.0793 or 7.93% 11.He r e ,weha v et heWACCa ndn e e dt ofindt hede bt e qui t yr a t i ooft hec ompa n y .Se t t i n gupt he WACCe q ua t i on,wefind: WACC=. 105=. 14( E/ V)+. 08( D/ V) ( 1–. 30) Re a r r a n gi ngt hee qua t i o n,wefind : . 105 ( V/ E)=. 14+. 08( . 70) ( D/ E) No wwemus tr e a l i z et ha tt heV/ Ei sj us tt h ee q ui t ymul t i p l i e r ,whi c hi se qua lt o: V/ E=1+D/ E . 105 ( D/ E+1 )=. 14+. 056( D/ E) No w,wec a ns ol v ef orD/ Ea s : . 049 ( D/ E)=. 0350 D/ E=. 7143 12. a.

The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so:

BVE = 10,000,000($1) = $10,000,000 BVD = $75,000,000 + 40,000,000 = $115,000,000 So, the total value of the company is: V = $10,000,000 + 115,000,000 = $125,000,000 And the book value weights of equity and debt are: E/V = $10,000,000/$125,000,000 = .08 D/V = 1 – E/V = .92 (A check using book values: 115,000,000/125,000,000 = 0.92) b.

The market value of equity is the share price times the number of shares, so: MVE = 10,000,000($53) = $530,000,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MVD = 0.97($75,000,000) + 0.96($40,000,000) = $111,150,000 This makes the total market value of the company: V = $530,000,000 + 111,500,000 = $641,150,000 And the market value weights of equity and debt are: E/V = $530,000,000/$641,150,000 = .8266 D/V = 1 – E/V = .1734

c.

The market value weights are more relevant because they represent a more current valuation of the debt and equity.

13.Fi r s t ,wewi l lfindt h ec os tofe qui t yf o rt hec ompa n y .Thei nf or ma t i onpr o v i de da l l owsust os ol v e f ort h ec o s tofe qu i t yu s i ngt hedi vi de ndgr o wt hmode l ,s o: RE=[ $2. 60( 1. 07) / $53 ]+. 07 RE=. 12 25or12. 2 5% Ne xt ,wene e dt ofin dt heYTM onbot hbondi s s ue s . Doi n gs o, wefind : P 970=$3 7. 50( PVI FAR%,40)+$ 1, 000( PVI FR%,40) 1=$ R=3 . 8 99% YTM =3 . 8 99% ×2 YTM =7 . 8 0% P 960=$3 5( PVI FAR%,24)+$1, 000( PVI FR%,24) 2=$ R=3 . 7 56% YTM =3 . 7 56% ×2 YTM =7 . 5 1%

Tofindt hewe i ght e da v e r a g ea f t e r t a xc os tofde bt ,wene e dt hewe i ghtofe a c hbo nda sa pe r c e nt a g eoft het o t a lde bt .Wefind: wD1=. 97( $75, 00 0, 000) / $1 11, 150, 000 wD1=. 654 5 wD2=. 96( $40, 00 0, 000) / $1 11, 150, 000 wD2=. 345 5 No w wec a nmul t i pl yt hewe i ght e da v e r a gec os tofde btt i me sonemi nust het a xr a t et ofindt h e we i ght e da v e r a g ea f t e r t a xc os tofde bt .Thi sgi v e sus : RD=( 1–. 30) [ ( . 6 545) ( . 0780 )+( . 3455 ) ( . 0751) ] RD=. 05 39or5. 39 % Us i n gt he s ec os t sweh a v ef ounda ndt h ewe i ghto fde btwec a l c u l a t e de a r l i e r ,t heWACCi s : WACC=. 8266( . 1225)+. 1734( . 0539) WACC=. 1106or11. 06% 14. a.

Using the equation to calculate WACC, we find: WACC = .105 = (1/1.55)(.14) + (.55/1.55)(1 – .30)RD RD = .0591 or 5.91%

b.

Using the equation to calculate WACC, we find: WACC = .105 = (1/1.55)RE + (.55/1.55)(.065) RE = .1270 or 12.70%

15.Wewi l lbe gi nbyfin di n gt hema r ke tv a l ueofe a c ht ypeoffina nc i n g. Wefin d: MVD =6, 500 ( $1, 00 0) ( 1. 04)=$6, 760 , 00 0 MVE =150 , 0 00( $ 78)=$1 1, 7 00, 000 MVP=10 , 00 0( $ 80)=$80 0, 000 Andt het ot a lma r ke tva l ueoft hefir mi s : V=$6, 760, 00 0+1 1, 700, 000+800, 000 V=$19, 260 , 0 00 No w,wec a nfindt hec os tofe qui t yus i n gt heCAPM.Thec os tofe qu i t yi s : RE=. 05 25+1. 15( . 08) RE=. 14 45or14. 4 5% Thec os tofde bti st heYTM oft hebo nds ,s o: P 1, 040=$4 2. 5 0( PVI F AR%,50)+$1, 000( PVI FR%,50) 0=$ R=4 . 0 62% YTM =4 . 0 62% ×2 YTM =8 . 1 2%

Andt hea f t e r t a xc os tofde bti s : RD=( 1–. 30) ( . 0812) RD=. 05 69or5. 69 % Thec os tofpr e f e r r e ds ha r ei s : RP=$6. 25/ $80 RP=. 0781or7. 81% No wweha v ea l loft hec ompone nt st oc a l c ul a t et h eWACC.Th eWACCi s : WACC=. 0569( $6, 760/ $19 , 2 60)+. 144 5( $ 11, 700/ $19, 260)+. 0781( $80 0/ $1 9, 260) WACC=. 1110or11. 10% Notice that we didn’t include the (1 – t C) term in the WACC equation. We used the aftertax cost of debt in the equation, so the term is not needed here. Now to recalculate WACC under a imputation system we have to adjust the equity components: WACC = . 0569( $6, 760/ $19, 260 )+. 1445(1-0.3)( $11 , 70 0/ $ 19, 260)+. 0781(1-0.3)( $800/ $19, 260 ) WACC = 0.0837 or 8.37%

16. a.

Wewi l lbe gi nbyfind i n gt hema r ke tv a l ueofe a c ht ypeoffina nc i n g. Wefind : MVD = 200,000($1,000)(1.08) = $216,000,000 MVE = 9,000,000($64) = $576,000,000 MVP = 500,000($83) = $41,500,000 And the total market value of the firm is: V = $216,000,000 + 576,000,000 + 41,500,000 V = $833,500,000 So, the market value weights of the company’s financing is: D/V = $216,000,000/$833,500,000 = .2591 P/V = $41,500,000/$833,500,000 = .0498 E/V = $576,000,000/$833,500,000 = .6911

b.

For projects equally as risky as the firm itself, the WACC should be used as the discount rate. Fi r s t , wec a nfindt h ec o s tofe qu i t yus i n gt heCAPM.Thec o s tofe qui t yi s : RE = .055 + 1.10(.08) RE = .1430 or 14.30% The cost of debt is the YTM of the bonds, so: P0 = $1,080 = $47(PVIFA R%,30) + $1,000(PVIFR%,30) R = 4.225% YTM = 4.225% × 2

YTM = 8.45% And the aftertax cost of debt is: RD = (1 – .30)(.0845) RD = .0591 or 5.91% The cost of preferred share is (it is assumed the face value of the preference shares is $100): RP = $6/$83 RP = .0723 or 7.23% Now, we can calculate the WACC as: WACC = .2591(.0591) + .0498(.0723) + .6911(.1430) WACC = .1177 or 11.77% 17. a. b.

Projects Y and Z. Using the CAPM to consider the projects, we need to calculate the expected return of the project, given its level of risk. This expected return should then be compared to the expected return of the project. If the return calculated using the CAPM is higher than the project's expected return, we should reject the project; if not, we accept the project. After considering risk via the CAPM: E[W] = .05 + .70(.13 – .05) = .1060 > .10, so reject W E[X] = .05 + .90(.13 – .05) = .1220 < .125, so accept X E[Y] = .05 + 1.20(.13 – .05) = .1460 > .14, so reject Y E[Z] = .05 + 1.80(.13 – .05) = .1940 < .21, so accept Z

c . If the firm’s overall cost of capital were used as a hurdle rate, then Project X would be incorrectly rejected; Project Y would be incorrectly accepted. 18.Wewi l lbe gi nbyfin di n gt hema r ke tv a l ueofe a c ht ypeoffina nc i n g. Wefin d: MVD =7, 000 ( $1 , 00 0) ( 1. 08)=$7, 560 , 0 00 MVE =180 , 0 00( $ 60)=$1 0, 8 00, 000 MVP=8, 000 ( $9 4)=$752 , 000 Andt het ot a lma r ke tva l ueoft hefir mi s : V=$7, 560, 00 0+1 0, 800, 000+756, 000 V=$19, 112 , 0 00 So, the market value weights of the company’s financing is: D/V = $7, 560, 000$1 9, 112, 000 = 0.3956 P/V = $752, 000/$19, 112 , 0 00 = 0.0393 E/V = $10, 800 , 00 0/$1 9, 112, 000 = 0.5651 No w,wec a nfindt hec os tofe qui t yus i n gt heCAPM.Thec os tofe qu i t yi s : RE1=. 05+. 90( . 12–. 05) RE1=. 113 0or11. 30 %

Wec a na l s ofindt hec os to fe qui t y ,us i ngt hedi v i de nddi s c oun tmode l .Thec os tofe q ui t ywi t h t hedi vi de nddi s c o untmode li s : RE2=( $2. 80/ $60 )+. 06 RE2=. 106 7or10. 67 % Bot he s t i ma t e sf ort hec o s tofe qui t ys e e mr e a s ona bl e ,s owewi l lus et hea v e r a g eo ft h et wo .The c os tofe q ui t ye s t i ma t ei s : RE=( . 1130+. 1 067) / 2 RE=. 10 98or10 . 98% Thec os tofd e b ti st heYTM oft hebonds ,s o : P 1, 080=$3 7. 2 5( PVI F AR%,40)+$1, 000( PVI FR%,40) 0=$ R=3 . 382% YTM =3 . 3 82% ×2 YTM =6 . 7 6% Andt hea f t e r t a xc os to fde bti s : RD=( 1–. 30) ( . 0676) RD=. 04 74or4 . 74% Thec os tofp r e f e r r e ds h a r ei s : RP=$5. 50/ $94 RP=. 0585or5. 85% No w,weha v ea l lo ft hec omp one nt st oc a l c u l a t et heWACC.TheWACCi s : WACC=. 0474( 0.3956)+. 0585 ( . 0393 )+. 1098 ( $0. 5651) WACC=. 0831or8 . 31 % The WACC under a imputation system is: WACC = . 0474( 0.3956)+. 0585( 10. 3) ( . 039 3) +. 109 8( 1 0. 3) ( $0 . 5 651) WACC = 0.0638 or 6.38% 19.Wewi l lbe g i nb yfindi n gt hema r k e tv a l u eo fe a c ht ypeoffina nc i n g .Wefind : MVD = $2,000,000)(.93) = $1,860,000 MVE = 80,000($45) = $3,600,000 MVP = 7,000($93) = $651,000 And the total market value of the firm is: V = $1,860,000 + 3,600,000 + 651,000 V = $6,111,000 So, the market value weights of the company’s financing is: D/V = $1,860,000/$6,111,000

= 0.3044

E/V = $3,600,000/$6,111,000 P/V = $651,000/$6,111,000

= 0.5891 = 0.1065

Now, we can find the cost of equity using the CAPM. The cost of equity is: RE1 = 0.04 + 1.20(.12 – .04) RE1 = 0.1360 or 13.60% We can also find th...