FEEDBACK TUTORIAL LETTER 2 nd SEMESTER 2017 ASSIGNMENT 1 MANAGERIAL FINANCE 4B MAF412S 1
Assignment 1 QUESTION 1 COMPANY A & B a) Co. A Co. B Net Operating Income 5,000,000 5,000,000 Less: interest -1,500,000 Available to shareholders 3,500,000 5,000,000 Taxation 28% -980,000-1,400,000 2,520,000 3,600,000 Value of Equity [NI/capitalisation rate] 25,200,000 36,000,000 Value of Debt 30,000,000 Value of company [Debs + shares] 55,200,000 36,000,000 or S = (EBIT - K d D) (l-t) K s A = (R5m - R1.5m) (.72) + D = R25.2m + R30m = R55.2m 0.10 B = (R5m - 0) (.72) + D = R36m + R0 m = R36m.10 b) V B = R5m(1 - t) = R3.6m = R36 million.10.10 V A = R5m(1 - t) + Dt.10 = R3.6m + (R30m x 0.28) = R44.4m.10 Or Co. A Co. B Net Operating Income 5,000,000 5,000,000 Available to shareholders 5,000,000 5,000,000 Taxation 28% -1,400,000-1,400,000 3,600,000 3,600,000 Value of Firm = Value of Unlevered Firm + Debt tax shield Value of Equity [capitalisation rate 10%] 36,000,000 36,000,000 Value of Debt shield [Debt x tax rate] 8,400,000 - Value of company [Debs + shares] 44,400,000 36,000,000 2
or V A = V B + Dt = R36m + (R30m x 0.28) = R36m + R8.4m = R44.4m c) For co A k d = 5% (1 - t) = 5%(.72) = 3.6% k s = Income available for shareholders Market value of equity Co. A Net Operating Income 5,000,000 Available to shareholders 5,000,000 Taxation 28% -1,400,000 3,600,000 Value of Equity [capitalisation rate 10%] 36,000,000 Value of Debt shield [Debt x tax rate] 8,400,000 Value of company [Debs + shares] 44,400,000 Value of the Assets (V A ) 44,400,000 100% Value of Debt -30,000,000 68% Value of Equity 14,400,000 32% k s = 2.520m = 17.5% 14.4m ka = 17.5% (14.4m) + 3.6% (30.0m) = 17.5% (0.32) + 3.6% (0.68) (44.4m) (44.2m) = 8.05% for co A For co B, k a = 10%. Neither company has an optimal capital structure; under the MM assumptions, the optimal capital structure would call for 100 percent debt, or as close to it as the company could get. 3
d) The addition of debt increases the covariance of equity returns with the market. The increased covariance implies higher risk and therefore the cost of equity increases. The increase in the cost of equity is more than offset by the tax subsidy effect of debt so that the WACC declines. e) What is 1% of the Equity? 1% 25,200,000 252,000 Income 1% 2,520,000 25,200 You sell your holdings in A for its market value 252,000 Lever yourself with debt equal to 1% 30,000,000 300,000 Total Funds 552,000 Purchase 1% of B's shares 1% 36,000,000 360,000 Income from new investment 1% 3,600,000 36,000 Less: After-tax Interest 4% 300,000-10,800 25,200 The new investment offers the same income, R25200 but we have saved R192 000 in capital (552000-360000). Note: The cost of equity did not change as we increased the financial leverage. In practice, we would expect the cost of equity to increase as the firm s level of debt is increased. Question 2 (a) EPS (c) DPS (c) Payout ratio (%) Retention rate % 2017 2016 2015 2014 2013 140 136 131 127 122 82 81 79 78 77 58.6 59.6 60.3 61.4 63.1 41.4 40.4 39.7 38.6 36.9 100% 100% 100% 100% 100% Growth in EPS (%) 2.9 3.8 3.1 4.1 We use the dividend discount model (DDM) also called Gordon s Growth Model which you learnt last semester to find the value of the share: DDM: Po=D1/(ke g) 4
We determine the compound growth rate from the FV formula: FV = PV (1+r) n Which is substituted as: 140 = 122(1+r) 4 Therefore annual compound growth rate, r= (140/122) (1/4) -1 = 3.5% I accepted the use of the average annual growth: (2.9+3.8+3.1+4.1)/4 = 3.5% Coincidentally the rate is the same as the compound growth rate. Now, we determine the cost of equity, ke using the CAPM which you did last semester. ke=rf + (rm rf)β = 6% + 1.5 x 4 = 12% The expected dividend is 0.82, the required return is 12% and constant growth rate is 3.5%. therefore applying the DDM, the value of equity is: Po= 0.82/(0.12-0.035) Po=N$9.65 Alternative solution: If the company is able to achieve an investment return of 15%, then the growth rate will be higher. The company should achieve a growth in dividend equal to the growth in EPS. Applying the sustainable growth formula we can determine the future growth in earnings and dividends: Growth rate in earnings and dividends= Return x Investment rate = 15% x 41.4% = 6.214%p.a Therefore, Po = 0.82/(0.12-0.06214) = N$14.17 (b) If future retentions are expected to be 50%, then our growth rate is higher than the 6.214% at 41% retention: Growth rate = 50% x 15% = 7.5% p.a. The next dividend will therefore be: 50% x 140 =70c Therefore Po= 70/(12%-7.5%) = N$15.56 D1 / (Ke-g) 5
i.e. (82c x 1.035) / (0.12 -.035) = R9.99 1.2: In practice, share prices are determined by the interplay of supply and demand for the shares, liquidity and market sentiment. In turn, these are fuelled by individual judgements (based on facts, and sentiment) as to the likely future dividends and prices and may not always be driven by the directors calculations of earnings and net present value. However, we would expect the share price in the long-term to reflect its intrinsic value which will be driven by the investment rate, the growth rate and the cost of equity. 6
Question 3 a) Degree of operating leverage DOL at N$1 mil sales level = Degree of financial leverage Q(p vc) Q(p vc) FC = 50 000(20 8) 50 000(20 8) 200 000 = 1.5 DFL at N$400 000 level of EBIT = EBIT EBIT I = N$400 000 N$400 000 125 000 = N$400 000 N$275 000 = 1.45 Combine leverage effect b) Earnings per share DTL = DOL x DFL = 1.5 x 1.45 = 2.18 Stock financing Debt financing Sales 1 000 000 1 000 000 Variable costs (200 000) (200 000) Fixed operating costs(400 000) (400 000) EBIT 400 000 400 000 Less interest (125 000) (195 000) Profit before tax 275 000 205 000 Income tax at 40% (110 000) (82 000) Net income 165 000) 123 000 No. of shares 120 000 100 000 EPS N$1.38 N$1.23 Combined leverage effect 7
Stock financing DTL = Q(p vc) Q(p vc) FC I = 50 000 (20 4) 50 000(20 4) 400 000 125 000 = N$800 000 N$275 000 = 2.9 Debt financing DTL = 50 000 (20 4) 50 000(20 4) 400 000 195 000 = N$800 000 N$205 000 = 3.90 c) The debt financing will have the greatest impact because it has a higher degree of total leverage than equity financing. Any example may be given, but the point is to show the percentage changes in EPS, not absolute EPS only. 8