# Chapter 8: Weighted Average Cost of Capital Chapter Review Solutions

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1 Chapter 8: Weighted Average Cost of Capital Chapter Review Solutions 1. ( a ) Next expected dividend: Year 1 = \$0.21 ( i ) Kr = d1 Po + g = ( ii ) Ke = do 0.20 = Po (1- f) 2.80 ( b ) Kps = dps 0.10 = Pps = 10.0% = 7.14% = 12.5% ( c ) Kd = n PV PMT FV COMP i Answer = x 0.70 = 8.67% ( d ) Market \$ Proportion Cost Weighted Cost Ordinary 500, % Preferred 100, % Debt 400, % 1,000, W.A.C.C. = 7.10% ( e ) ( i ) Shareholders Debt Retained earnings ( ii ) Date at which principal has to be repaid by the borrower with interest. ( iii ) Able to better manage changes in interest rates 2. Calculate the yield to maturity of the following \$100 debentures Present Interest Rate ( i ) % ( ii ) % ( iii ) % ( iv ) % Maturity Yield to Maturity After Tax Cost 3 ( a ) Ordinary Shares: Ke = d1 + g = Po = 10.50% 1.20 ( b ) Retained Earnings = 10.50% ( c ) Kps = dps 0.20 = Pps 2.50 = 8.00% ( d ) Cost of Debt (Kd) - Using Sharp EL 738 Enter: C.CE 2ndF C.CE n PV PMT FV COMP i Answer = 12.00% The cost will be = 12.00% x (1 - Rate of Tax) = 12.00% x 0.70 = 8.40% 62

2 0.16 (1.02) 4. ( a ) Cost of Equity = = 9.25% ( b ) Cost of Debt = 0.08 (1-0.30) = 5.60% ( c ) Market Proportion Cost W.A.C.C Equity 3, % Debt % 4, % 5. Cost of Ordinary Shares (Ke) = d1 Po + g = 0.08 (1.05) Cost of Debt (Kd) - Using Sharp EL 738 = 9.20% Answer = 4.63% After Tax ( x 0.70 ) = 3.24% Answer = 7.23% After Tax ( x 0.70 ) = 5.06% Market Proportion Cost W.A.C.C Ordinary Shares 800, % 6% Debentures 212, % 8% Unsecured 306, % Notes 1,318, % 63

3 6. ( a ) Cost of Debt (Kd) - Using Sharp EL Answer = 11.39% The cost will be = 11.39% x (1 - Rate of Tax) = 11.39% x 0.70 = 7.97% Preference Shares: = 7.27% Ordinary Shares: = 13.66% Retained Earnings: = 13.66% ( b ) Component Market Proportion Cost After W.A.C.C. Tax Ordinary 1,120, % Ret Earnings 280, % Preference 110, % Debentures 90, % 1,600, % \$ Proportion Ordinary Shares 800,000 80% 1,120,000 Retained 200,000 20% 280,000 Earnings 1,000, % 1,400,000 ( c ) Higher return; but also higher risk involved. 64

4 7. Cost of Ordinary Shares (ke) = d (1.05) + g = Po = 7.10% Cost of Debt (Kd) - Using Sharp EL Answer = 8.50% The cost will be = 8.50% x (1 - Rate of Tax) = 8.50% x 0.70 = 5.95% Answer = 10.00% The cost will be = 10.00% x (1 - Rate of Tax) = 10.00% x 0.70 = 7.00% Component Market Proportion Cost W.A.C.C. Ordinary 1,200, % 6% Debentures 270, % 8% Debentures 475, % 1,945, % 8. ( a ) Cost: Cost of Debt (Kd) - Using Sharp EL N PV PMT FV COMP i Answer = 8.50% Kd = 8.50 (1-0.30) = 5.95% Ke = Ordinary Preference Debentures d1 Po + g Kps = dps Kd = 8.50 pps = = = 8.50 x 0.70 = 10% = 4% = 5.95% Component Market Proportion Cost W.A.C.C. Ordinary 1,000, % 8% Preference 600, % 9% Debentures 411, % 2,011, % 65

5 9. Ordinary shares Ke = \$ = 11.00% \$5.00 Retained earnings Kre = = 11.00% 9% Preference shares Kp = \$0.09 = 4.50% \$ %Debentures Kd Yield to maturity = 8.00% x ( ) = 5.60% % Mortgage = 12.00% x ( ) = 8.40% Source of funds market value Source of Funds Market Proportion Cost W.A.C.C. Ordinary hares 3,333, Retained Earnings 1,666, % Preference Shares 200, % Debentures 533, % Mortgage 266, ,000, Balance Sheet Market Ordinary Shares 1,000,000 3,333,333 Retained Earnings 500,000 1,666,667 Total 1,500,000 5,000,000 66

6 10. Source of Funds Market Weighting Cost W.A.C.C. Ordinary Shares 1,215, Retained Earnings 135, % Preference Shares 250, % Mortgage 400, ,000, Balance Sheet Market Ordinary Shares 900,000 1,215,000 Retained Earnings 100, ,000 Total 1,000,000 1,350, ( a ) Investors purchasing ordinary shares acquire a proportion of shareholders funds. As retained earnings form part of the shareholders funds and could be paid as dividends, they rank equally with ordinary shares in terms of cost to the company. ( b ) Companies use the W.A.C.C as the discount factor when calculating present value of cash flows. It is also used as a benchmark, against which I.R.R are assessed. W.A.C.C. is the required rate of return on investment in assets. 12. Fudge-It Co. Cost of Ordinary Shares = = 10.83% Current Year x 1.05:0.10 x 1.05 = Cost of Retained Profits (same as ordinary) = 10.83% Cost of Preference: D/P = = 8.00% Cost of Debt (Kd) - Using Sharp EL 738 = 8.42% Answer = 12.02% x 0.70 Weighted Average Cost of Capital Component Market Proportion Cost WACC Ordinary Shares 1,125, Retained Profits 675, Preference Shares 500, Debentures 1,700, ,000, \$ Proportion Market Ordinary Shares 1,000, \$1,125,000 Retained Earnings 600, ,000 \$1,600, % \$1,800,000 67

7 13. Source of Funds Market Weighting Cost W.A.C.C. Ordinary Shares 1,600, Retained Earnings 400, % Preference Shares 200, % Mortgage 300, ,500, Balance Sheet Market Ordinary Shares 800,000 1,600,000 Retained Earnings 200, ,000 Total 1,000,000 2,000, ,000 x \$3.30 = \$2,310, ,000 1,000,000 x 2,310,000 = \$1,617, ,000 1,000,000 x 2,310,000 = 693,000 \$2,310,000 Sources of Funds Proportion Cost % WACC % Ordinary Shares 1,617, Retained Earnings 693, % Preference Shares 280, % Debentures 364, % Mortgage Loan 45, ,000,

8 15. As a fixed interest security the value of a debenture is determined by prevailing interest rates. Given the current interest rate, interest payment and maturity period it is possible to calculate the yield to maturity ,000 x \$2.70 = \$1,350, , , 000 x 1,350,000 = \$1,125,000 = Market valuation of Ordinary Shares 100, ,000 x 1,350,000 = 225,000 = Market valuation of General Reserve \$ 1,350,000 = Market valuation of Ordinary Equity Source of Funds Proportion Cost % WACC % Ordinary Shares \$1,125, General Reserve 225, % Preference Shares 132, % Debentures 285, % Mortgage loan 233, \$2,000,

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