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1 FEEDBACK TUTORIAL LETTER 2 nd SEMESTER 2017 ASSIGNMENT 1 MANAGERIAL FINANCE 4B MAF412S 1

2 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 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

3 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, % 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

4 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 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 Total Funds 552,000 Purchase 1% of B's shares 1% 36,000, ,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 R in capital ( ). 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 % % 100% 100% 100% 100% Growth in EPS (%) 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

5 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: ( )/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% 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/( ) 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/( ) = 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

6 i.e. (82c x 1.035) / ( ) = R : 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

7 Question 3 a) Degree of operating leverage DOL at N$1 mil sales level = Degree of financial leverage Q(p vc) Q(p vc) FC = (20 8) (20 8) = 1.5 DFL at N$ level of EBIT = EBIT EBIT I = N$ N$ = N$ N$ = 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 Variable costs ( ) ( ) Fixed operating costs( ) ( ) EBIT Less interest ( ) ( ) Profit before tax Income tax at 40% ( ) (82 000) Net income ) No. of shares EPS N$1.38 N$1.23 Combined leverage effect 7

8 Stock financing DTL = Q(p vc) Q(p vc) FC I = (20 4) (20 4) = N$ N$ = 2.9 Debt financing DTL = (20 4) (20 4) = N$ N$ = 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

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