Cost of capital

Cost of capital  Cost of capital to be minimized to maximize the value of a firm  Relevant from firm’s point of view in areas like capital budgeting, leasing, capital structure design etc.  Weighted average cost of capital relevant  Not the cost based on specific mode of financing  Cost of debt - interest rate minus tax savings,  i.e. kd (1-T)  kd being the interest rate and T being firm’s marginal tax rate  Interest rate 13%, tax rate 35%, cost of debt = ?  = 8.45%  Cost of debt as the discounting rate that equates  Net amount realized on debt issue with present value of after-tax periodic interest payment and the payment on redemption or maturity  P =  I(1-T)/(1+kd)t + F/(1+kd)n  kd = [ I x (1-T) + (F-P)/n] / (F+P)/2  6% coupon bond, semiannual payment $1000 par value, maturity 30 years, company selling price $515.16, company tax rate 40%  515.16 = 30 x 0.60/ (1+kd)t + 1000 / (1+kd) 60  [18 + 484.84 / 60 ] / 757.58 = 3.44%  After tax cost of debt =6.88%  Cost of equity capital  Difficult to estimate expectation of shareholders  3 different approaches followed  ks = D1/P0 + g - Dividend capitalization  E(Ri ) = Rf + b i x [E(Rm ) - Rf ] - CAPM approach  Bond yield plus risk premium approach  Cost of new equity higher than cost of retained earnings  Because of floatation expenses for new equity issue  Stock price $30, last dividend $2, growth7%, flotation cost 25%  Cost of retained earnings = ?  = (2.00*1.07)/ 30 + 0.07 = 14.13%  Cost of new equity = ?  = (2.00*1.07)/( 0.75*30) + 0.07 = 16.51%  Weighted average cost of capital  Weightings: Book value proportion or market value proportion for cost elements  Numerical No. 1  On 1st Jan, the firm’s total assets stand at $270 million  Financed 50% by long-term debt & the balance by equity  New bonds will have 10% coupon rate and saleable at par  New bonds will have 10% coupon rate and saleable at par  Common stock is currently selling at $60 per share  New issue can be sold net $54 a share  Stockholder’ required rate of return is estimated to be 12%  That includes a dividend yield of 4%  Retained earnings are estimated to be $13.5 million  Likely capital budget for the coming year = $135 million  Assume tax rate = 40%  Amount of capital budget to be financed by equity, assuming no change in capital structure  Capital budget of 135 million, to be financed by equity = 67.5 million $  Amount of equity to be generated internally and arranged externally  Retained earnings expected 13.5 million,  So external equity = 67.5 – 13.5 = 54 million $ needed  Cost of each of the equity components  Cost of equity  Cost of retained earnings = ?  = Dividend yield + growth  = 4 + 8 = 12%  Cost of new equity = ?  = D1/ P0 + g  = 2.40/ 54 + 0.08 = 12.4%  Weighted average cost of capital (WACC)  Variation in WACC  Break point = ?  Break in marginal cost of capital = estimated retained earnings/ 0.50 = 13.5/ 0.5 = 27 million $  Cost below break = 0.5* 6% + 0.5* 12% = 9%  Cost above break = 0.5* 6% + 0.5* 12.4% = 9.2%  Try out numerical 2  Capital structure of 45% long-term debt & 55% equity  Expected after-tax earnings in coming year = $2.5 million  Dividend policy of 60% payout  Current share price $22, last dividend $2.20, expected growth rate = 5%,  External equity can be sold at a flotation cost of 10%  Average tax rate 40%.  Comment on selection of investment opportunities Loan amount available ($) 0 to 500 000 500 001 to 900 000 900 001 and above Interest rate on increment of debt (%) Investment opportunities available Outlay ($) 9.00 1 675 000 11.00 2 900 000 3 375 000 13.00 4 562 500 5 750 000 Return (%) 16 15 14 12 11  Cost of internal equity = ?  = 2.20*1.05/ 22 + 0.05 = 15.5%  Cost of external equity = ?  = (2.20*1.05)/ (22*0.9) + 0.05 = 16.667% Equity 611 111 1000 000 Debt 500 000 818 182 Total capital (Break point) 1111 111 1818 182 1100 000 Range Less than 1.11 m 900 000 Debt (%) 5.4 6.6 6.6 7.8 2000 000 Equity (%) 15.5 15.5 16.667 16.667 WACC (%) 0.45* 5.4 + 0.55 *15.5 = 10.96 0.45* 6.6 + 0.55* 15.5 = 11.50 0.45* 6.6 + 0.55 *16.667 = 12.14 0.45* 7.8 + 0.55* 16.667 = 12.68 Above 1.11 but less than 1.82 Above 1.82 but less than 2.0 Above 2.0 m WACC & Return 1- 16% Investment opportunities 2-15% 12.68% 12.14% 11.50% Marginal cost 10.96% D 5.4% E 15.5% D 6.6% E 15.5% D 6.6% E 16.67% D 7.8% E 16.67% 0.675 1.11 1.575 1.82 2.0 Total capital