Cost of Capital Practice Problems 1. Why is it that, for a given firm, that the required rate of return on equity is always greater than the required rate of return on its debt? 2. The Mountaineer Airline Company has consulted with its investment bankers and determined that they could issue new debt with a yield of 8%. If Mountaineer ' marginal tax rate is 39%, what is the after-tax cost of debt to Mountaineer? 3. The Blue Dog Company has common stock outstanding that has a current price of $20 per share and a $0.5 dividend. Blue Dog’s dividends are expected to grow at a rate of 3% per year, forever. The expected risk-free rate of interest is 2.5%, whereas the expected market premium is 5%. The beta on Blue Dog’s stock is 1.2. a. What is the cost of equity for Blue Dog using the dividend valuation model? b. What is the cost of equity for Blue Dog using the capital asset pricing model? 4. Gaggle Internet, Inc. is evaluating its cost of capital under alternative financing arrangements. In consultation with investment bankers, Gaggle expects to be able to issue new debt at par with a coupon rate of 8% and to issue new preferred stock with a $2.50 per share dividend at $25 a share. The common stock of Gaggle is currently selling for $20.00 a share. Gaggle expects to pay a dividend of $1.50 per share next year. Market analysts foresee a growth in dividends in Invest stock at a rate of 5% per year. Gaggle' marginal tax rate is 35%. a. If Gaggle raises capital using 45% debt, 5% preferred stock, and 50% common stock, what is Gaggle's cost of capital? b. If Gaggle raises capital using 30% debt, 5% preferred stock, and 65% common stock, what is Gaggle’s cost of capital? Prepared by Pamela Parrish Peterson Cost of Capital Practice Problems 1. Why is it that, for a given firm, that the required rate of return on equity is always greater than the required rate of return on its debt? The required rate of return on equity is higher for two reasons: • • The common stock of a company is riskier than the debt of the same company. The interest paid on debt is deductible for tax purposes, whereas dividends paid on common stock are not deductible. 2. The Mountaineer Airline Company has consulted with its investment bankers and determined that they could issue new debt with a yield of 8%. If Mountaineer ' marginal tax rate is 39%, what is the after-tax cost of debt to Mountaineer? rd* = 0.08 (1 – 0.39) = 0.0488 or 4.88% 3. The Blue Dog Company has common stock outstanding that has a current price of $20 per share and a $0.5 dividend. Blue Dog’s dividends are expected to grow at a rate of 3% per year, forever. The expected risk-free rate of interest is 2.5%, whereas the expected market premium is 5%. The beta on Blue Dog’s stock is 1.2. a. What is the cost of equity for Blue Dog using the dividend valuation model? re = {[$0.50(1 + 0.03)] /$20} + 0.03 = 0.05575 or 5.575% b. What is the cost of equity for Blue Dog using the capital asset pricing model? re = 0.025 + (0.05) 1.2 = 0.025 + 0.06 = 8.5% 4. Gaggle Internet, Inc. is evaluating its cost of capital under alternative financing arrangements. In consultation with investment bankers, Gaggle expects to be able to issue new debt at par with a coupon rate of 8% and to issue new preferred stock with a $2.50 per share dividend at $25 a share. The common stock of Gaggle is currently selling for $20.00 a share. Gaggle expects to pay a dividend of $1.50 per share next year. Market analysts foresee a growth in dividends in Invest stock at a rate of 5% per year. Gaggle' marginal tax rate is 35%. rd* = 0.08 (1 – 0.35) = 0.52 or 5.2% rp = $2.50 / $25 = 10% re = $1.50 / $20 + 5% = 7.5% + 5% = 12.5% a. If Gaggle raises capital using 45% debt, 5% preferred stock, and 50% common stock, what is Gaggle's cost of capital? WACC = [0.45 (0.052)] + [0.05 ( 0.10)] + [0.50 (0.125)] WACC = 0.0234 + 0.005 + 0.0625 = 0.0909 = 9.09% b. If Gaggle raises capital using 30% debt, 5% preferred stock, and 65% common stock, what is Gaggle’s cost of capital? WACC = [0.30 (0.052)] + [0.05 ( 0.10)] + [0.65 (0.125)] WACC = 0.0156 + 0.005 + 0.08125 = 0.10185 = 10.185% Prepared by Pamela Parrish Peterson Capital structure practice questions/problems 1. Consider the Albatross Company that has $1 million of assets, which are currently financed using 40 percent debt and 60 percent equity. Suppose Albatross were to acquire $0.5 million of additional assets, but can select between two financing alternatives: all debt, borrowing at 5%, or all equity, issuing 1 million new shares. What is the debt-equity ratio for each alternative financing arrangement? 2. Consider two firms, A and B: Discount rate for earnings stream Discount rate for risk-free debt earnings Earnings before additional interest Alternative 1 Debt Alternative 2 Debt Firm A 10% 5% $100 $0 $500 Firm B 12% 8% $200 $0 $1,000 Assume that the tax rate is 0%. Calculate the capitalization rate for earnings for each firm and for each alternative financing arrangement. In addition, calculate the value of equity and debt in each case. 3. Explain why interest deductibility would encourage companies to use debt financing. 4. Explain a. b. c. d. how each of the following affects the capital structure decision: Interest deductibility Likelihood of bankruptcy Limited liability Net operating loss carryovers 5. The ABC Company has a current capital structure consisting of $100,000 of 10% coupon debt and $300,000 of equity. ABC wants to raise $100,000 of capital by either selling additional shares of stock or issuing debt. There is currently 30,000 shares of stock outstanding and ABC expects to pay 10% interest per year. ABC expects operating earnings of $30,000 in the following year. a. What is ABC’s debt ratio under each of the two financing alternatives? b. If interest on debt is not deductible by ABC, what is the distribution of next year’s $30,000 among claimants? c. If interest on debt is deductible by ABC, and ABC has a tax rate of 30%, what is the distribution of next year’s $30,000 among claimants (including the government)? d. Suppose ABC’s probability distribution of next year’s earnings is as follows: Scenario Good Normal Bad Probability 25% 50% 25% Operating earnings $50,000 $30,000 $0 What is ABC’s expected earnings to owners and standard deviation of earnings to owners under the two alternatives? Assume that there are no taxes. Capital structure practice questions/problems 1 Solutions to capital structure practice questions/problems 1. Debt-equity for all debt = ($0.4+0.5) / $0.6 = 1.5 Debt-equity for all equity = $0.4 / ($0.6+0.5) = 0.3636 2. Discount rate for earnings stream Discount rate for risk-free debt earnings Earnings before additional interest Alternative 1 Debt/equity Earnings after interest Capitalization rate Value of debt Value of equity (EBT/discount rate) Value of the firm (debt + equity) Alternative 2 Debt/equity Earnings after interest Capitalization rate Value of debt Value of equity (EBT/discount rate) Value of the firm 1.0 $75 Firm A 10% 5% $100 0.0 $100 0.10 $0 1,000 $1,000 1.5 $120 Firm B 12% 8% $200 0.0 $100 0.12 $0 1,667 $1,667 0.10+[(0.10-0.05)(1)] = 0.15 0.12+[(0.12-0.08)0.04(1.5)] =0.18 $500 $500 $1,000 $1,000.00 666.67 $1,666.67 3. Interest deductibility lowers the cost of using debt vis-à-vis equity financing. Therefore, companies have an incentive to use debt because its cost is much lower than that of equity. 4. a. Interest deductibility: makes the use of debt more attractive by lowering the cost of debt to the company. b. Likelihood of bankruptcy: the greater the probability of bankruptcy, the less debt that a company would want to take on. c. Limited liability: The fact the owners bear only a fixed amount of the risk on the downside of investments creates an incentive to take on riskier projects. This limit on the owners’ liability encourages creditors to require a premium for bearing this risk. d. Net operating loss carryovers: If a company cannot use all of its tax benefits from interest, then the cost of debt is not as low as it could be if they could use these benefits; hence, the lack of profitability negates the benefits from interest deductibility. Therefore, companies that are not generating profits for tax purposes do not benefit from the tax deductibility of interest. Solutions to capital structure practice questions/problems, prepared by Pamela Peterson-Drake 1 5. a. b. Alternative 1 Income to claimants $30,000 Alternative 2 $30,000 Alternative 1 debt ratio = 0.25 Alternative 2 debt ratio = 0.67 Debt owners Equity owners $10,000 $20,000 $20,000 $10,000 c. Alternative 1 Income to claimants $14,000 Alternative 2 $7,000 Debt owners Equity owners Government $10,000 $14,000 $6,000 $20,000 $7,000 $3,000 Solutions to capital structure practice questions/problems, prepared by Pamela Peterson-Drake 2 d. ABC Company: Evaluating financing alternatives Without taxes Alternative 1 Operating Interest Net earnings on debt income Probability $50,000 $10,000 $40,000 25% $30,000 $10,000 $20,000 50% $0 $10,000 ($10,000) 25% E(x) = Scenario Good Normal Bad pn xn $10,000 $10,000 -$2,500 $17,500 x n -E(x) $22,500 $2,500 -$27,500 (x n -E(x)) 506,250,000 6,250,000 756,250,000 σ2 = σ= Coefficient of variation = 2 pn (x n -E(x)) $126,562,500 $3,125,000 $189,062,500 $318,750,000 $17,854 1.020 $126,562,500 $3,125,000 $189,062,500 $318,750,000 $17,854 2.380 2 Alternative 2 Good Normal Bad $50,000 $30,000 $0 $20,000 $30,000 $20,000 $10,000 $20,000 ($20,000) 25% 50% 25% E(x) = $7,500 $5,000 -$5,000 $7,500 $22,500 $2,500 -$27,500 506,250,000 6,250,000 756,250,000 σ2 = σ= Coefficient of variation = Solutions to capital structure practice questions/problems, prepared by Pamela Peterson-Drake 3 With taxes Alternative 1 Net income Operating Interest after earnings on debt taxes Probability $50,000 $10,000 $28,000 25% $30,000 $10,000 $14,000 50% $0 $10,000 ($7,000) 25% E(x) = Scenario Good Normal Bad pn xn $7,000 $7,000 -$1,750 $12,250 x n -E(x) $15,750 $1,750 -$19,250 (x n -E(x)) 248,062,500 3,062,500 370,562,500 σ2 = σ= Coefficient of variation = 2 pn (x n -E(x)) $62,015,625 $1,531,250 $92,640,625 $156,187,500 $12,497 1.020 $62,015,625 $1,531,250 $92,640,625 $156,187,500 $12,497 2.380 2 Alternative 2 Good Normal Bad $50,000 $30,000 $0 $20,000 $21,000 $20,000 $7,000 $20,000 ($14,000) 25% 50% 25% E(x) = $5,250 $3,500 -$3,500 $5,250 $15,750 $1,750 -$19,250 248,062,500 3,062,500 370,562,500 σ2 = σ= Coefficient of variation = Solutions to capital structure practice questions/problems, prepared by Pamela Peterson-Drake 4