Solution manual financial management 10e by keown chapter 12

CHAPTER 12 Cost of Capital CHAPTER ORIENTATION In Chapters and we considered the valuation of debt and equity instruments The concepts advanced there serve as a foundation for determining the required rate of return for the firm and for specific investment projects The objective in this chapter is to determine the required rate of return to be used in evaluating investment projects CHAPTER OUTLINE I The concept of the cost of capital A B C II Defining the cost of capital: The rate that must be earned in order to satisfy the required rate of return The rate of return on investments at which the price of a firm's common stock will remain unchanged Investor’s required rate of return is not the same as the firm’s cost of capital due to Taxes: Interest payments on debt are tax deductible to the firm Flotation costs:  Firms incur expenses when issuing securities that  reduce the proceeds to the firm.  Financial Policy Each type of capital used by the firm (debt, preferred stock, and common stock) should be incorporated into the cost of capital, with the relative importance of a particular source being based on the percentage of the financing provided by each source of capital Using the cost of a single source of capital as the hurdle rate is tempting to management, particularly when an investment is financed entirely by debt However, doing so is a mistake in logic and can cause problems Computing the weighted cost of capital A firm's weighted cost of capital is a function of (l) the individual costs of capital, (2) the capital structure mix, and (3) the level of financing necessary to make the investment A Determining individual costs of capital 50 The before-tax cost of debt is found by trial-and-error by solving for kd in NPd where $I t n  = (1  k d ) t 1 NPd t + $M (1  k d ) n = the market price of the debt, less flotation costs, $It = the dollar interest paid to the investor each period, $M = the maturity value of the debt kd = before-tax cost of the debt (before-tax required rate of return on debt) n = the number of periods to maturity The after-tax cost of debt equals: kd (1 - T) where T = corporate tax rate Cost of preferred stock (required rate of return on preferred stock), kps, equals the dividend yield based upon the net price (market price less flotation costs), or dividend kps = = net price D NPps Cost of Common Stock There are two measurement techniques to obtain the required rate of return on common stock a dividend-growth model b capital asset pricing model Dividend growth model a Cost of internally generated common equity, kcs kcs = dividend in year1  annual growth  +   market price  in dividends  kcs = D1 + g Pcs 51 b Cost of new common stock, kncs kncs = D1 + g NPcs where NPcs = the market price of the common stock less flotation costs incurred in issuing new shares Capital asset pricing model = krf + (km - krf) = the cost of common stock krf = the risk-free rate  = beta, measure of the stock's systematic risk km = the expected rate of return on the market kc where kc B III It is important to notice that the major difference between the equations presented here and the equations from Chapters and is that the firm must recognize the flotation costs incurred in issuing the security Selection of weights The individual costs of capital will be different for each source of capital in the firm's capital structure To use the cost of capital in investment analyses, we must compute a weighted, or overall, cost of capital It will be assumed that the company's current financial mix resulting from the financing of previous investments is relatively stable and that these weights will closely approximate future financing patterns In computing weights, we could use either the current market values of the firm's securities or the book values as shown in the balance sheet Since we will be issuing new securities at their current market value, and not at book (historical) values, we should use the market value of the securities in calculating our weights PepsiCo approach to weighted average cost of capital A PepsiCo calculates the divisional cost of capital for its snack, beverage and restaurant organizations by first finding peer-group firms for each division and using their average betas, after adjusting for differences in financial leverage, to compute the division's cost of equity They also use accounting betas in estimating the cost of equity They then compute the cost of debt for each division Finally, they calculate a weighted cost of capital for each division 52 B PepsiCo's WACC basic computation E   D  kwacc = kcs   + kd[1-T]   DE DE where: C kwacc = the weighted average cost of capital kcs = the cost of equity capital kd = the before-tax cost of debt capital T = the marginal tax rate E/(D+E)= percentage of financing from equity D/(D+E)= percentage of financing from debt Calculating the Cost of Equity Based on capital asset pricing model: kcs = krf + (km - krf) kcs = the cost of common stock krf = the risk-free rate  = beta, measure of the stock's systematic risk km = the expected rate of return on the market where: Betas for each division are estimated by calculating an average unlevered beta from a group of divisional peers The average beta for each division's peer group is unlevered and then relevered using that division's target debt-to-equity ratio D Calculating the Cost of Debt The after-tax cost of debt is equal to: kd (1 - T) where: kd = before-tax cost of debt T = marginal tax rate 53 IV Required rate of return for individual projects A Using the weighted cost of capital Investments with an internal rate of return exceeding the weighted cost of capital should be accepted Doing so, we must assume that the project has similar business risk as existing assets Otherwise, the weighted cost of capital does not apply B The weighted cost of capital, k wacc does not allow for varying levels of project risk We need to specify the appropriate required rates of return for investments having different amounts of risk C Risk also results from the decisions made within the company This risk is generally divided into two classes: Business risk is the variability in returns on assets and is affected by the company’s investment decisions Financial risk is the increased variability in returns to the common stockholder as a result of using debt and preferred stock ANSWERS TO END-OF-CHAPTER QUESTIONS 12-1 The cost of capital is the rate that must be earned on investments in order to satisfy the required rate of return of the firm's investors This rate is a function of the investors' required rate of return, the corporation's tax rate, and the flotation costs incurred in issuing new securities Therefore, the cost of capital determines the rate of return that must be achieved on the company's investments, so as to earn the target return of the firm's investors Stated differently, the cost of capital is the rate of return that will leave the price of the common stock unchanged 12-2 Two objectives may be given for determining a company's weighted average cost of capital: (1) The weighted average cost of capital is used as the minimum acceptable rate of return for capital investments The value of the firm should be maximized by accepting all projects where the net present value is positive when discounted at the firm's weighted average cost of capital (2) The weighted average cost of capital is also used in evaluating a firm’s historical performance That is, to create shareholder value a firm must not only earn a profit in the traditional accounting sense, but it must earn a return on its invested capital that is acceptable to the investors who provide the firm’s financing This “acceptable return” is the firm’s weighted average cost of capital 12-3 All types of capital, including debt, preferred stock, and common stock, should be incorporated into the cost of capital computation, with the relative importance of a particular source being based upon the percentage of financing to be provided 12-4 The effect of taxes on the firm's cost of capital is observed in computing the cost of debt Since interest is a tax deductible expense, the use of debt indirectly decreases 54 the firm's taxes Therefore, since we have computed the internal rate of return on an after-tax basis, we also compute the cost of debt on an after-tax basis In completing a security offering, investment bankers and other involved individuals receive a commission for their services As a result, the amount of capital net of these flotation costs is less than the funds invested by the individual purchasing the security Consequently, the firm must earn more than the investors' required rate of return to compensate for this leakage of capital 12-5 a Equity capital can be raised by either retaining profits within the firm or by issuing new common stock Either route represents funds invested by the common stockholder The first avenue simply indicates that the common stockholder permits management to retain capital that could be remitted to these investors b Even though a new stock issue does not result from retaining internal common equity, these funds should not be reinvested unless management can reasonably expect to satisfy the investors' required rate of return In essence, even though no explicit out-of-pocket cost results from retaining the capital, the cost in measuring a firm's cost of capital is actually the opportunity cost associated with these funds for the investor c The two popular methods for computing the cost of equity capital include (1) the dividend-growth model, and (2) the capital asset pricing model The first approach finds the rate of return that equates the present value of future dividends, assuming a constant growth rate, with the current market price of the security The CAPM finds the appropriate required rate of return, given the firm's systematic risk 12-6 In general, the relative costs of various sources of capital reflect the riskness of the source to the investor For example, for a given firm, we would expect debt securities to be less risky than preferred stock which is less risky than common stock Consequently, debt would demand a lower required return than the firm’s preferred stock, which is lower than the required rate of return for common stock 55 SOLUTIONS TO END-OF-CHAPTER PROBLEMS The following notations are used in this group of problems: kps = the cost of preferred stock kcs = the cost of internally generated common funds kncs = the cost of new common stock g = the growth rate kd = the before-tax cost of debt T = the marginal tax rate Dt = dollar dividend per share, where Do is the most recently paid dividend and D1 is the forthcoming dividend P = the value (present value) of a security NP = the value of a security less any flotation costs incurred in issuing the security a Net price after flotation costs 12-1A 10 $1068.75 =  t 1 kd b c kncs kcs = = $1,125 (1 - 05) = $1068.75 $1,000 $110 + t (1  k d ) (1  k d )10 9.89% = kd(1-T) = 6.53% = D1 + g NPcs = $1.80(1  07) + 07 $27.50(1  05) = 1437 = 14.37% = D1 + g Pcs 56 d e kps = $3.50 + 07 $43 = 1514 = 15.14% = D 09 x$150 = NPps $175(1  12) = $13.50 $154 = 0877 = 8.77% After tax cost of debt = kd (1 - T) = 12% (1 - 34) = 7.92% 12-2A a b c After tax cost of debt = kd(1 - T) = 8%(1 - 0.34) = 5.28% kncs = D1 + g NPcs kncs = $1.05(1  0.05) + 0.05 $25(1  0.09) $1,150(.90) = $1,035 $1,035 = 20  t 1 Rate = = net price after flotation costs $1,000 $120 + t (1  k d ) 20 (1  kd) Value 57 9.85% Value For: 11% $1,079.56 kd% 1,035.00 $1,079.56 12% 1,000.00 $ 44.56 kd d e 12-3A = $  $44.56  0.11 +    0.01  $79.56  = After tax cost of debt = kd (1 - T) After tax cost of debt = 11.56% (1 - 0.34) kps = D NPps kps = $7 $85 kcs = D1 + g Pcs kcs = $3 + 0.04 $38 kncs = D1 + g NPcs kncs = $1.45(1  0.06) + 0.06 $27(1  0.06) = 79.56 1156 = = 11.56% 7.63% 8.24% = 58 11.90% = 1206 = 12.06% 12-4A $958 (1 - 0.11) costs) = $852.62 = For: kd = $852.62 = the net price (value less flotation  (1  k d ) t 1 t + $1,000 (1  k d )15 Rate Value Value 8% $914.20 $914.13 kd% 852.62 9% 839.27 $61.58 $74.86  $61.58  0.08 +    0.01 =  $74.86  = 12-5A kps = D NPps 12-6A NPd =  $945 = $70 15 = 8.82% 8.82% (1 - 0.18) = 7.23% $2.50 $32.50 = n $I t t 1 (1  k d ) t 15 $120 t 1 (1  k d ) t  0882 + + = 7.69% $M (1  k d ) n $1,000 (1  k d )15 Since the net price on the bonds, $945, is less than the $1,000 par value, the beforetax cost of the debt must be greater than the 12 percent coupon interest rate ($120 ÷ $1,000) kd Rate Value Value 12% $1,000.00 $1,000.00 kd% 945.00 13% _ 935.44 $ 55.00 $ 64.56 = After tax cost of debt  $55.00  12 +    01 = 1285 = 12.85%  $64.56  = kd(1 - T) = 12.85%(1 - 34) = 8.48% 59 NPd $1,063.80 (1 - 0.105) = $952.10 Number of Bonds = $500,000 $952.10 = 525.15 ≈ 526 Bonds Cost of debt: $952.10 For: b = = 10 $100 t 1 (1  k d ) t  Rate Value 10% kd% 11% $1,000.00 952.10 $ 47.90 + $1,000 (1  k d )10 Value $1,000.00 940.90 $ 59.10 kd =  $47.90  0.10 +    (0.01) = 1081 = 10.81%  $59.10  After tax cost of debt = 10.81%(1 - 0.34) = 7.13% There is a very slight decrease in the cost of debt because the flotation costs associated with the higher coupon bond are higher ($138.65 in flotation costs for the 14 percent coupon bond versus $111.70 for the 10 percent coupon bond) 12-12A Source Common Stock Preferred Stock Debt Capital Structure 40% 10% 50% After-tax cost of capital 18% 10% 8% x (1-.35) kwacc = 62 Weighted cost 7.2% 1.0% 2.6% 10.8% 12-13A Net price after flotation costs = $975 - $15 = $960.00 Cost of debt: $1,000 $60 + t (1  k d ) (1  k d )15 15 $960.00  = t 1 For: kd Rate Value 6% kd% 7% $1,000.00 960.00 $ 40.00 $1,000.00 908.48 $ 91.52  $40.00  0.06 +    (0.01) = 064 = 6.4%  $91.52  = After tax cost of debt Value = 6.4%(1 - 0.30) = 4.48% Cost of common stock, kncs kncs = = = Source  D1    + g NP cs   $2.25 + 05 $30(1  0.05) 129 = 12.9% Capital Structure After-tax cost of capital Weighted cost Debt 60% 4.48% 2.69% Common Stock 40% 12.9% 5.16% kwacc = 63 7.85% 12-14A Net price after flotation costs = $1,050 (1-.04) = $1,008.00 Cost of debt: $1,000 $70 t + (1  k d ) (1  k d )10 10 $1,008.00  = t 1 For: Rate Value 6% kd% 7% $1,096.84 1,008.00 $ 88.84 Value $1,096.84 1,000.00 $ 96.84 kd =  $88.84  0.06 +    (0.01) = 069 = 6.9%  $96.84  After tax cost of debt = 6.9 %(1 - 0.30) = 4.8% Cost of preferred stock (kps) D Dividend = NPps Net Price kps = = $2.00 $2 = $25  $3 $22 = 091 = 9.1% Cost of common stock, kncs kncs = = =  D1    + g  NPcs  $3(1  10) + 10 $55  $5 166 = 16.6% Source Market Value Weight After-tax cost of capital Weighted Cost Bonds $4,000,000 33 4.8% 1.6% Preferred Stock 2,000,000 17 9.1% 1.5% Common Stock 6,000,000 50 16.6% 8.3% 12,000,000 1.00 kwacc = 11.4% 64 65 SOLUTION TO INTEGRATIVE PROBLEM Nealon, Inc - Weighted Cost of Capital Cost of Debt: $1,035 (1 - 15) = $879.75 = $879.75 For: $80 16  t 1 Rate = NPd (1  k d ) t + 9% kd% 10% = After tax cost of debt (1  k d )16 Value Value $917.04 879.75 $917.04 843.92 $ 73.12 $ 37.29 kd $1,000  $37.29  0.09 +   x (0.01) = 0951 = 9.51%  $73.12  = 9.51%(1 - 34) = 6.28% Cost of Preferred Stock: kps = D NPps $1.50 ($19  $2.01) = = 8.83% Cost of Internal Common Equity: kcs = D1 + g Pcs = $2.50(1  0.06) + 0.06 $35 = 1357 = 13.57% Weighted Cost of Capital (k wacc) is calculated as follows: Bonds Preferred Stock Common Stock Weights 38 15 47 1.00 Costs 6.28% 8.83% 13.57% 66 Weighted Costs 2.39% 1.32% 6.38% kwacc = 10.09% Solutions for Problem Set B The following notations are used in this group of problems: kps = the cost of preferred stock kcs = the cost of internally generated common funds kncs = the cost of new common stock g = the growth rate kd = the before-tax cost of debt T = the marginal tax rate Dt = dollar dividend per share, where Do is the most recently paid dividend and D1 is the forthcoming dividend P = the value (present value) of a security NP = the value of a security less any flotation costs incurred in issuing the security a Net price after flotation costs = 12-1B $1,125 (1 - 06) = $1,057.50 = 10 $120 t 1 (1  k d ) t  Rate For: + Value 11% kd% 12% $1,058.68 1,057.50 $ kd $1,057.50 = 1.18 $1,000 (1  k d )10 Value $1,058.68 1,000.00 $ 58.68  $1.18  11 +    01 = 1102 = 11.02%  $58.68  After tax cost of debt = kd(1 - T) After tax cost of debt = 11.02%(1 - 34) = 7.27% 67 b c d e kncs kcs kps = D1 + g NPcs = $1.75(1  08) + 08 $28.00(1  05) = 1511 = 15.11% = D1 + g Pcs = $3.25 + 07 $43.50 = 1447 = 14.47% = D 10 ($125) = NPps $150(1  12) = $12.5 $132 = 0947 = 9.47% After tax cost of debt = kd (1 - T) = 13% (1 - 34) = 8.58% After tax cost of debt = kd(1 - T) After tax cost of debt = 9%(1 - 0.34) After tax cost of debt = 5.94% 12-2B a 68 b c kncs = D1 + g NPcs kncs = $1.25(1  0.06) + 0.06 = 10.85% $30(1  0.09) $1,125(.90) = $1,012.50 = net price after flotation costs 20 $1,012.50  = t 1 Rate 12% kd% 13% For: $1,000 $130 20 + (1  k d ) (1  k d ) t Value $1,074.97 1,012.50 Value $1,074.97 1,000.00 $ 74.97 $ 62.47 =  $62.47   0.01 0.12 +   $74.97  After tax cost of debt = kd (1 - T) After tax cost of debt = 12.83% (1 - 0.34) kd d e kps = D NPps kps = $8.75 = 9.72% $90 kcs = D1 + g Pcs kcs = + 0.05 = 15.52% 69 = = 8.47% 1283 = 12.83% 12-3B 12-4B kncs = D1 NPcs kncs = $1.30(1  0.07) + 0.07 = 1229 = 12.29% $28(1  0.06) $950 (1 - 0.11) costs) $845.50 + g = $845.50 = the net price (value less flotation $80 15  = Rate 10% kd% 11% For: (1  k d ) t 1 t + Value $847.48 845.50 $1,000 (1  k d )15 Value $847.48 784.28 $63.20 $1.98 kd  $1.98  0.10 +    0.01 = 1004 = 10.04%  $63.20  = After tax cost of debt = 10.04% (1 - 0.19) = 8.13% 12-5B kps = D $2.75 = = 8.46% NPps $32.50 12-6B NPd =  $950 = n t 1 $I t (1  k d ) t 15 $130 t 1 (1  k d ) t  + + $M (1  k d ) n $1,000 (1  k d )15 Since the net price on the bonds, $950, is less than the $1,000 par value, the beforetax cost of the debt must be greater than the 13 percent coupon interest rate ($130 ÷ $1,000) Rate 13% kd% 14% Value $1,000.00 950.00 $ kd = 50.00 Value $1,000.00 938.46 $ 61.54  $50.00  13 +    01 = 1381 = 13.81%  $61.54  70 After tax cost of debt 12-7B = kd(1 - T) = 13.81%(1 - 34) = 9.11% Cost of preferred stock (kps) 12-8B kcs = D Dividend = NPps Net Price = 13% x$100 $13 = $97 $97 = 13.40% = D1 + g Pcs = $0.80(1  0.16) + 0.16 $22.50 = 2012 = 20.12% 12-9B If the firm pays out 50 percent of its earnings in dividends, its recent earnings must have been $9 ($4.50 dividend divided by 5) Thus, earnings increased from $5 to $9 in five years Using Appendix C and looking for a table value of 556 ($5/$9), the annual growth rate is approximately twelve percent a Cost of internal common stock (kcs): kcs b =  D1    + g P cs   = $4.50(1  12) + 12 $60 = $5.04 + 12 $60 = 204 = 20.4% Cost of external common (new common) stock, kncs kncs =  D1    + g  NPcs  = $5.04 + 12 $60(1  0.09) 71 = $5.04 + 12 $54.60 = 2123 = 21.23% 12-10B a b c d Price (Pd) 10  = NPd t 1 $150 (1  0.10) t + $1,000 (1  0.10)10 = $150(6.145) + $1000(.386) = $1,307.75 = $1,307.75(1 - 0.115) = $1,157.36 Number of Bonds = $600,000 $1,157.36 = 518.4 ≈ 519 bonds Cost of debt: $1,157.36 10 $150 $1,000  + t t 1 (1  k d ) (1  k d )10 = Rate For Value Value 12% $1,169.50 kd% 1,157.36 13% 1,108.90 $ 12.14 kd = After tax cost of debt $1,169.50 $ 60.60  $12.14  0.12 +    (0.01) = 12.20%  $60.60  = 12.20%(1 - 0.34) = 8.05% 12-11B 10 a Price (Pd) =  t $100 (1  0.10) t + $1,000 (1  0.10)10 = $100 (6.145) + $1,000 (.386) = $1,000.00 72 NPd = $1,000.00 (1 - 0.115) = $885.00 Number of Bonds = $600,000 $885.00 = 678 Bonds Cost of debt: $885.00 For: = 10 $100 t 1 (1  k d ) t  + Value $887.00 885.00 12% kd% 13% = After tax cost of debt (1  k d )10 Value $887.00 837.60 $49.40 $2.00 kd $1,000  $2.00  0.12 +    (0.01) = 1204 = 12.04%  $49.40  = 12.04%(1 - 0.34) = 7.95% b,There is a very slight decrease in the cost of debt because the flotation costs associated with the higher coupon bond are higher (flotation costs are $150.39 for the 15 percent coupon bond versus $115 for the 10 percent coupon bond) 12-12B Bias Corporation - Weighted Cost of Capital Bonds Preferred Stock Common Stock Capital Structure $1,100 250 3,700 $5,050 Weights 0.2178 0.0495 0.7327 1.0000 Individual Costs 6.0% 13.5% 19.0% Weighted Costs 1.31% 0.67% 13.92% 15.90% 12-13B Source Common Stock Preferred Stock Debt Capital Structure 50% 15% 35% 73 After-tax cost of capital 20% 12% 10% (1-.34) Weighted cost 10.0% 1.8% 2.3% 100% kwacc = 74 14.1% 12-14B Net price after flotation costs = $1,100- $20 = $1,080.00 Cost of debt: $1,000 $40 + t (1  k d ) (1  k d ) 40 40 $1,080.00  = t 1 Semi-annual Rate For: Value Value 3% $1,231.60 $1,231.60 kd% 1,080.00 4% 1,000.00 $ 151.60 $ 231.60 semi-annual kd =  $151.6  0.03 +    (0.01) = 0365 = 3.65%  $231.60  annual kd = 3.65% x = 7.3% = 7.3%(1 - 0.34) = 4.8% After tax cost of debt Cost of common stock, kncs kncs =  D1    + g  NPcs  = $2.00 + 08 $80(1  0.10) = 108 = 10.8% Source Capital St ru ct ur e After-tax cost of capital Weighted cost Common Stock 60% 10.8% 6.48% Debt 40% 4.8% 1.92% kwacc = 75 8.4% 12-15B Net price after flotation costs = $950 (1-.06) = $893.00 Cost of debt: $1,000 $80 t + (1  k d ) (1  k d ) 20 20 $893.00  = t 1 Rate 9% kd% 10% For: kd = Value $908.32 893.00 $ 15.32 Value $908.32 830.12 $ 78.20  $15.32  0.09 +    (0.01) = 092 = 9.2%  $78.20  After tax cost of debt = 10.4 % x (1 - 0.34) = 6.07% Cost of preferred stock (kps) D Dividend = NPps Net Price kps = = $2.50 $2.50 = $35  $5 $30 = 083 = 8.3% Cost of common stock, kncs kncs = = = Source Bonds  D1    + g NP  cs  $2(1  08) + 08 $50(1  10) 128 = 12.8% Market Value $500,000 Weight 50 Preferred Stock 100,000 10 8.3% 83% Common Stock 400,000 40 12.8% 5.12% $1,000,000 1.00 kwacc = 8.99% 76 After-tax cost of capital Weighted Cost 6.07% 3.04% ... Value Value 12% $1,169.50 kd% 1,157.36 13% 1,108.90 $ 12. 14 kd = After tax cost of debt $1,169.50 $ 60.60  $12. 14  0 .12 +    (0.01) = 12. 20%  $60.60  = 12. 20%(1 - 0.34) = 8.05% 12- 11B 10... $4.50(1  12) + 12 $60 = $5.04 + 12 $60 = 204 = 20.4% Cost of external common (new common) stock, kncs kncs =  D1    + g  NPcs  = $5.04 + 12 $60(1  0.09) 71 = $5.04 + 12 $54.60 = 2123 =... $90 kcs = D1 + g Pcs kcs = + 0.05 = 15.52% 69 = = 8.47% 128 3 = 12. 83% 12- 3B 12- 4B kncs = D1 NPcs kncs = $1.30(1  0.07) + 0.07 = 122 9 = 12. 29% $28(1  0.06) $950 (1 - 0.11) costs) $845.50 + g