September 2015 Professional Examination Paper 2.1: Question & Solutions

Transcription

1 September 2015 Professional Examination Paper 2.1: Question & Solutions Financial Accounting and Financial Statement Analysis Economics and Financial Markets Quantitative Analysis and Statistics Level 2 Page 1 of 14

2 SECTION B: Question 2 - Financial Accounting and Financial Statement Analysis Explain how each of the items below would affect the statutory published earnings per share figure for a manufacturing company: 2a) The impairment of an intangible asset. 2b) Recognition of significant contingent liabilities in the financial statement. 2c) A profit on the sale of a property. Solution to Question 2 2a) The impairment of an intangible asset. Impairment of intangible asset results in an immediate write off (impairment charge). This in turn results in a reduction in net income and subsequently a reduction in the published Earnings Per Share (EPS). 2b) Recognition of significant contingent liabilities in the financial statement. This depends on the situation. i. If the contingent liability is both probable and the amount can be estimated, then the contingent liability and the related contingent loss are recorded in the books of account. This will result in a reduction in net income and published earnings per share. ii. If the contingent liability is only possible (not probable), or if the amount cannot be estimated, only a disclosure is required. This will not impact the published earnings per share. 2c) A profit on the sale of a property. Profit on the sale of property is recognized in the income statement. This increases net income as well as earnings per share. Question 3 - Economics and Financial Markets You are told that the market price of milk has increased and less milk is being purchased in the market. What change in supply for milk will result for the market to clear? Solution to Question 3 There must have been a decrease in the supply of milk for there to be market-clearing in the milk market, as shown in the following diagram Price D S 1 P 2 P 1 O E 2 E 1 S Quantity S D q2 q1 Quantity Page 2 of 14

3 Question 4 - Quantitative Analysis and Statistics Find the values of x and y for the matrix A = x + y x y 0 1 to be the identity matrix of order 2 (4 marks) Solution to Question 4: The identity matrix is I = Thus if x + y = 1 and x y = 0 then A will be the identity matrix x + y = 1 x = 1 y x y = 0 x = y x = y = ½ (4 marks) SECTION C: Question 5 - Financial Accounting and Financial Statement Analysis You are given below the condensed balance sheet and statement of income according to IFRS of Road Master Ltd, a sports car manufacturer, as at December 31, 2014 (figures in N 000). Balance sheet of RoadMaster as of December 31, 2014 Cash and cash equivalents 10,000 Current liabilities 159,000 Other current assets 120,000 Noncurrent liabilities 220,000 Noncurrent assets 325,000 Shareholders' Equity 76,000 Total 455,000 Total 455,000 Statement of income of RoadMaster for year 2014 EBIT 13,000 Financial expense -5,000 Income before taxes 8,000 Income taxes -2,400 Net income 5,600 5(a) Compute the current ratio, total gearing ratio and ROCE of RoadMaster Ltd. Given the industry average ratios below, briefly comment on your result and the performance of the company. Ratio Industry Average Current 1.1 Gearing (D/D+E) 50% ROCE 11% (5 marks) Page 3 of 14

4 5b) Assume RoadMaster Ltd issues a bonus of one additional share for every existing share to all its shareholders. What impact (if any) will this have on each of the ratios computed above? On December 31, 2014 RoadMaster Ltd acquired a 60 per cent interest in Runners Ltd for N35,000,000 in cash. The acquisition enabled RoadMaster to govern the financial and operating policies of Runners Ltd. Condensed balance sheets and statements of income according to IFRS of Runners Ltd before the business combination is shown below (figures in N 000). Balance sheet of Runners Ltd as at December 31, 2014 Cash and cash equivalents 3,000 Current liabilities 44,500 Other current assets 42,000 Noncurrent liabilities 78,000 Noncurrent assets 109,000 Shareholders' Equity 31,500 Total 154,000 Total 154,000 Statement of income of Runners Ltd for year 2014 EBIT 2,800 Financial expense -800 Income before taxes 2,000 Income taxes -600 Net income 1,400 5(c) Calculate the amount of goodwill that RoadMaster Ltd paid as part of its acquisition of 60% of Runners Ltd. To answer this question, use the following assumption: The assets of Runners Ltd as of December 31, 2014 include hidden reserves of N20,000,000. (Ignore Taxation) 5(d) Explain briefly the two methods that are available for the evaluation of non-controlling interests according to IFRS 3 Business Combinations (these methods are sometimes called the "full goodwill" method and the "partial goodwill" method). 5(e) Calculate the consolidated net income for the fiscal year 2014, assuming that the net income of RoadMaster and Runners Ltd does not include any profit or loss from intragroup transactions (provide a brief explanation in support of your calculations). 5(f) Prepare the consolidated balance sheet of the RoadMaster group as at December 31, State any assumption you make. (4marks) Solution to Question 5 5(a) Compute the current ratio, total gearing ratio and ROCE of RoadMaster Ltd. Given the industry average ratios below, briefly comment on your result and the performance of the company. Ratio Industry Average Current 1.1 Gearing (D/D+E) 50% ROCE 11% i. Current ratio = CA/CL = 130,000/159,000 = 0.82: 1 Page 4 of 14

5 ii. Gearing ratio = 220,000/(220,000+76,000) = 74.31% iii. ROCE = 13,000/296,000 = 4.39% Note: Return is defined as EBIT while Capital Employed is defined as Total asset less current Liability (5 marks) COMMENTS The liquidity position of RoadMaster Ltd is below par when compared with industry Average. With a ration of 0.82;1, the company is appears to be at risk of potentially not beign able to meet its obligations to creditoe as and when due even though the liquidity requirement of the industry as a whole appears fairly low at 1.1:1 As regards gearing, the company employs a higher level of debt financing in its capital structure than an average company in the industry. This means a higher level of financial risk. However, this could be of advantage in times of rising income and profitability as RoadMaster will likely record higher levels of earning per share as a result of benefits of the tax effects of debt financing. As measured by ROCE, RoadMaster Ltd s profitability performance is below industry average at 4.39% compared to 11%. Further assessment using Dupont analysis needs to be used to identify the factor responsible for this, which could be profit margin, leverage factor or asset turnover. 5b) A bonus issue of 1:1 will not impact on any of the ratios since bonus issuance is simply capitalization of existing reserves. Explanations i. For current ratio, a bonus does not affect current asset and current liabilities ii. For gearing ratio and ROCE, there is equally no impact as the shareholders fund remain the same after a bonus issue 5c) The Goodwill acquired by RoadMaster amounts to N4,100,000. Calculation: N Purchase price 35,000,000 - Proportionate book value of shareholders equity (60% of N31,500,000) -18,900,000 - Proportionate hidden reserves (60% of N20,000,000) -12,000,000 = Acquired goodwill N4,100,000 5d) According to the revised IFRS 3, the acquisition method for the accounting of business combinations gives entities the option to either measure non-controlling interests at the fair value of their proportion of identifiable assets and liabilities or at full fair value. Using the first method (partial goodwill method), goodwill is measured as the difference between the consideration paid and the purchaser s share of identifiable net assets acquired. Page 5 of 14

6 The second method (full goodwill method) means that goodwill is recognised for the controlling interest as well as for the non-controlling interests. 5e) The consolidated net income for the year 2014 amounts to 5,600 (That is the net income of RoadMaster only). The net income of Runners Ltd for the fiscal year 2014 has been generated before the combination and therefore cannot be consolidated. 5f) RoadMaster Group Consolidated Balance Sheet N N Cash and Cash equivalent Current liabilities (10,000+3,000) 13,000 (159, ,500) 203,500 Other current assets Non current liabilities (120, ,000-35,000) 127,000 (220, ,000) 298,000 Non current Assets (325, ,000+ Shareholders equity 76,000 20,000) 454,000 Goodwill (wk 1) 4,100 Minority interest (wk 2) 20,600 Workings 1) Computation of Goodwill ( 000) 598, ,100 35,000 60% (31, ,000) = N 4,100 2) Minority Interest ( 000) 40% (31, ,000) = N20,600 Question 6 - Economics and Financial Markets Since the Great Depression, most economists believe that economic policy can smooth out the volatile fluctuations of the business cycle 6(a1) Provide a profile of a business cycle to show its characteristic features. (8 marks) 6(a2) Identify and explain what kind of economic policy would be necessary to moderate or eliminate the fluctuations associated with the business cycle. (6 marks) 6(b) Suppose the consumption, investment and government expenditure functions of an economy is given as follows: C = (Y T) I = 50 G = 200 T = 50 Calculate the equilibrium national income (4 marks) Page 6 of 14

7 Solution to Question 6(a1) (i) The business cycle depicts the fluctuations in the level of economic activity (i.e., Gross National Product), alternating between the periods of depression and boom conditions. Level of economic activity depression recovery boom recession Potential GNP actual GNP Business cycle, fluctuations in the level of economic (2marks) (ii) (ii.) As shown in the figure, the business cycle is characterized by four phases: depression, recovery, boom and recession. (2marks) (iii) Depression is a period of rapidly falling aggregate demand accompanied by very low levels of output and heavy unemployment, which eventually reaches the bottom of the trough. (2marks) (iv) Recovery, a period of upturn in aggregate demand accompanied by rising output and a reduction in unemployment. (2marks) (v) Boom: a period of aggregate demand reaching and then exceeding sustainable output levels as the peak of the cycle is reached. Full employment is reached and the emergence of excess demand causes the general price level to increase (inflation) (2marks) (vi) Recession: this follows the period of boom in the business cycle. It is a period characterized by falling aggregate demand, bringing with it modest falls in output and employment. As demand continues to contract, it eliminates in the onset of depression. (2marks) 2 marks each for any 4 points = 8 marks Solution to Question 6(a2) (i) (ii) (iii) (iv) (v) The Volatile fluctuations in the business cycle usually call for countercyclical policy, a demand management or stabilisation policy. The demand management policy involves the control of the level of aggregate demand in an economy, using fiscal policy and monetary policy to moderate or eliminate fluctuation in the level of economic activity associated with the business cycle. The general objective of demand management is to fine-tune aggregate demand so that it is neither deficient relative to potential gross national product (thereby avoiding a loss of output and unemployment) nor overfull (thereby avoiding inflation). Ideally, the government would wish to manage aggregate demand so that it grows exactly in line with the underlying growth of potential gross national product, offsetting the amplitude of troughs and peaks of the business cycle. If the authorities can get the timing and magnitudes correct, then they should be able to counterbalance the effects of recession/ depression and follow the path of potential gross national product. Reducing the intensity of the recession in this way requires authorities to forecast accurately the onset of recession some time ahead, perhaps while the economy is still buoyant (i.e. boom). 2 marks each for any 3 points = 6 marks Page 7 of 14

8 Solution to Question 6(b) Y = C + I + G Y = [ (Y T)] Y = Y 0.75(50) Y = Y Y = Y Y 0.75Y = Y = Y = 2850 The equilibrium national income is 2,850 (4 marks) Question 7 - Quantitative Analysis and Statistics The statistics department of a manufacturing company came up with the daily cost and revenue functions for two of their flagship products as shown below: Product A: Product B: TC A =4Q A TC B = 13Q B Q A = 10-P A Q B = 15- P B where TC = Total Cost, Q = Quality and P = Price Currently, 5 units of product A and 3 units of product B are produced daily. Required: 7(a) How many units of products A and B should be produced in order to maximize profit? (4 marks) 7(b) How much should the company sell each unit of products A and B? 7(c) 7(d) What is the maximum profit achievable from the production of both commodities? The production manager is also concerned about a perceived high cost of production especially for product A. What is the estimated cost savings from your recommendation for product A? Solution to Question 7(a) Units of products A and B to be produced in order to maximize profit Product A: TC A =4Q A Q A = 10-P A P A =10-Q A TR A =P*Q=10Q A -Q A 2 MR A =DTR/DQ=10-2Q A MC A =DTC A/ DQ A =4 Page 8 of 14

9 To maximize profit, set MC A =MR A (or equate the derivative of the profit function to zero(0)) (½ mark) 10-2Q A =4 2Q A =10-4 2Q A =6 Q A =6/2=3 (½ mark) Product B Each unit of products A and B: TC B = 13Q B Q B = 15- P B P B =15-Q B 2 TR B =P*Q=15Q B -Q B MR B =DTR/DQ=15-2Q B MC B =DTC B/ DQ B =13 (1 mark) To maximize profit, set MC B =MR B (or equate the derivative of the profit function to zero(0)) (½ mark) 15-2Q B =13 2Q B =2 Q B =1. Solution to Question 7(b) Each units of Product A and B Solve for P A P A =10-Q A P A =10-3 P A =7 (½ mark) (1 mark) Solve for P B P B =15-Q B P B =15-1 P B =14 Product A should be sold at N7 while product B should be sold at N14. (1 mark) Solution to Question 7(c) 7(c) The maximum profit achievable from the production of both commodities Solution: Total revenue from A TR A =P*Q=10Q A -Q A 2 Q A =3 TR A =P*Q=10(3)-3 2 TR A =21 Total cost from A TC A =4Q A =4(3)=12 Profit from product A = TR A -TC A =21-12=9. (1½ mark) Page 9 of 14

10 Total Revenue from B TR B =P*Q=15Q B -Q B 2 Q B =3 TR B =P*Q=15(1)-1 2 TR B =14 Total cost from B TC B = 13Q B TC B = 13(1) TC B = 13 Profit from B TR B - TC B =14-13=1 (1½ mark) Maximum profit achievable from both products = N(9+1) = N10 Solution to Question 7(d) 7(d) The production manager is also concerned about a perceived high cost of production especially for product A. What is the estimated cost savings from the recommendation for product A. Solution: Current cost of Product A = 4Q A = 4Q(5) = N20 Cost at maximum profit of production for Product A = 4Q A = 4(3)= N12 Recommended estimated cost saving for Product A = = N8 Page 10 of 14

11 FORMULAE Regression Analysis: Y = a+bx b= n xy- x y n x 2 -( x) 2 a= y _ b x n n Page 11 of 14

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15 September 2015 Professional Examination Paper 2.2: Questions & Solutions Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis Level 2 Page 1 of 12

16 SECTION B: Question 2 Corporate Finance The appraisal of a new project needed for the expansion of production capacity has just been completed and the NPV is negative, with the implication that the project should be rejected. Then the operations manager argued that the discount rate used to calculate NPV was too high. He claimed The entire investment for the project should be funded with bond issues, and when calculating NPV we should use the cost of debt as the discount rate. Do you agree with the operations manager? Provide two reasons supporting your point of view. Solution to question 2 (i) (ii) Generally for an investment project to be adopted it must generate greater returns than the rate of return (cost of capital) demanded by the providers of funds (shareholders and creditors) from investment opportunities with equivalent risk. This project would increase production capacity, so its risk profile should be similar to the average risk profile of the company as a whole. It is therefore more reasonable to apply the company-wide WACC as the discount rate because it reflects the capital structure for the company as a whole. (1½ marks) The method by which investment funds are raised for a project has no direct bearing on the project's discount rate. The project itself does not bring the company any increase in debt capacity. In addition, it does not have any impact on the target debt ratio. (1½ marks) Question 3 Equity Valuation and Analysis Under what circumstances might a company be tempted to pay dividends which are in excess of earnings, and what are the dangers associated with such an approach? Ignore taxation. Solution to Question 3 Payment of dividends from reserves If a company pays dividends in excess of earnings, then this payment must be made out of reserves. The effect of this will be reduce the asset value of the business. Reasons for payment from reserves i) The company believes that it must continue to pay a high level of dividends in order to support the share price. If profits for the year are too low to support the previous level of dividends, the directors may decide that it should make a payment out of reserves rather than reduce the level of dividends ii) If a company has a high level of reserves for which it cannot find an attractive investment opportunity, it may decide that appropriate to repay part of those reserves to investors by means of dividend payment. (1 mar k) Problems with payment from reserves i) The fall in asset value of the business may make it more vulnerable to takeover bid. ii) The market may see the payment out of reserves as a desperate measure on the part of the directors, and this may trigger a significant drop in the price. iii) Payment of dividends that are in excess of earning could lead to a shortage of cash for the business. Page 2 of 12

17 Question 4 Fixed Income Valuation and Analysis 4a) When using duration to approximate the price change of a bond due to interest rates change, certain assumptions are made. List four of these assumptions. 4b) You want to immunise a liability occurring in 8 years with two bonds: A and B. Bond A has a maturity of 2.5 years and a duration of 2 years; Bond B has a maturity of 12.5 years and a duration of 10 years. Calculate the weight of the portfolio invested in bond A and bond B. Solution to Question 4 4a) The key assumptions are: i) The yield curve is flat. ii) A parallel change in yield iii) A small change in yield. iv) An instantaneous change in yield. ( 1/2 marks per valid point) 4b) Let w= weight of bond A and. 1 w = weight of bond B To be immunised, duration of asset must equal duration of liability: 2w+10(1-w) = 8 2w+10-10w = 8-8w=-2 w=-2-8 = 0.25 Bond A 25% Bond B 75% 4 marks Page 3 of 12

18 SECTION C: Question 5 Corporate Finance You are a financial consultant to Iwelabi Plc, a company listed on the stock exchange. Iwelabi is involved in publishing books mainly for primary, secondary and university students. The company is currently considering a project to manufacture ink which is a key raw material needed in its publishing business. A major concern at this stage is the determination of the appropriate cost of capital for the company. The company has compiled the following data: Debt capital The company s debt capital exclusively consists of two bonds: Bond Maturity Annual coupon Repayment Current market price Outstanding amount A 1year 5% 100% 102% N20m B 5years 0% 100% 84% N40m Equity capital and market Current value per share 16 Number of shares 5,000,000 Forecast dividend for next year 1 Growth rate in dividend 5% Equity beta 0.8 Risk-free rate 3% Equity market risk premium 10% Tax rate 25% 5(a) Compute the average cost of debt capital, taking into account tax effect. 5(b) Calculate the cost of equity capital using: (5 marks) 5b1) Dividend valuation model 5b2) Cost of equity using CAPM 5(c) In general, do the dividend valuation model and the CAPM lead to the same result? Explain your answer. (1 mark) 5(d) Determine the WACC, assuming cost of equity of 10%. 5(e) The CEO informs you that funding of the new project will not be a problem since shareholders have agreed to an appropriate right issue of shares. He suggests that the financial appraisal of the project should proceed, using the WACC determined in (d) above. Do you agree with the CEO on the use of the WACC calculated in (d) above? Justify your answer. (4 marks) Page 4 of 12

19 Solution to Question 5 Corporate Finance 5(a) First, we need to compute the YTM of each bond Bond A: YTM = Bond B (zero coupon bond): = = 2.94% (1 mark) YTM = = = 3.55% (1 mark) Next, we determine the weighted average cost of the two bonds Bond Market value (Nm) Cost Hash Total (Nm) A B Average cost, before tax = = 3.29% (½ mark) After tax cost of debt = 3.29% (1 0.25) = 2.47% (½ mark) (5 marks) 5(b) Calculate the cost of equity capital using: 5b1) Dividend valuation model Cost of equity using dividend model: K E = D 1 + g = = 11.25% (1½) V E 16 (1½ marks) 5b2) Cost of equity using CAPM K E = R F + β(r m R F ) = (10) = 11% (1½ marks) Page 5 of 12

20 (5c) The results may differ due to the fact that models are based on different assumptions. The assumptions may not apply to all models or they may not be fulfilled for both models (1mark) 5(d) Total market value of equity: 5m N16 = N80m (½ mark) The WACC is computed as follows: Capital Market value (Nm) Cost (%) Hash Total (Nm) Debt Equity (e) WACC = / 134 = 6.97% (2½ marks) The WACC computed above cannot be used to appraise the new project because its use will violate the following assumptions WACC: Constant business risk The use of WACC assumes that the business risk of the new project is the same as the average business risk of the company. This will probably be the case if the new project represents an expansion of existing activities in the existing industry. In the scenario here however, the new project is a diversification into a new industry (ink production vs publishing). The project is likely to belong to a radically different business risk class and if so the use of the existing WACC will be invalid. Constant financial risk It is assumed that the financing of the new project will not significantly alter the company s financial leverage and hence financial risk. It is being proposed however, to finance the project wholly with equity (rights issue). This will alter the company s financial leverage and its financial risk. The use of the existing WACC will not be appropriate in such situations. (1½ marks) What is required is that the company should determine the appropriate project specific discount risk that considers the project s business risk (its asset beta) and the company s method of financing. (½ mark) (4 marks) Page 6 of 12

21 Question 6 Equity Valuation and Analysis Glasy Plc is the world s premier manufacturer of glass. The global industry is estimated to be growing at an annual rate of 8%. Currently the company has a market share of 6% in the global glass industry. In the last 5 years, the company has average ROA (return on asset) of 16% and a payout ratio of 30%. The average interest rate on its debt capital has been 6%. The company has maintained a constant debt/equity ratio of 40% in the period. In the year just ended the company reported EPS of N20. The current stock price is N162. 6(a) Calculate the sustainable growth rate of dividends for the stock assuming that the firm will maintain the ROA of 16% and the payout ratio of 30% 6(b) Using the constant growth model, calculate the cost of equity of the company based on a current EPS of 20. Assume the long term sustainable growth rate equals the industry growth of 8%. 6(c) You feel that input prices (raw materials and labour) will drop significantly (as a result of world-wide crash in oil prices) in the medium term i.e. the next four years. Consequently, you expect there will be a margin expansion resulting in the EPS growing at 25% for four years and then settling down to an 8% growth rate. Calculate the value of the stock with these assumptions using the dividend discount model. Assume cost of capital 13.5% and current EPS as N20. Is the stock currently overvalued or undervalued? 6(d) What is the current P/E ratio of the company? Indicate how the P/E ratio will be affected by each of the following independent events? Indicate whether the ratio will increase, stay the same or reduce by each of the events. Justify your response. (4 marks) 6d1) An increase in investors risk aversion. 6d2) An investment in an advanced production technology that cuts unit variable production cost but increases fixed operating costs. 6d3) A reduction in the payout ratio. 6d4) A right issue of shares with the proceeds used to pay off part of long-term debt. Solution to Question 6 Equity Valuation and Analysis 6(a) Growth rate (g) is given by: g = (ROE)(b), where b = retention rate. ROE = ROA + (ROA i) D/E Where i = average interest rate on debt. ROE = 16 + (16 6)% (0.40) = 20% g = (20) (1 0.30) = 14% Page 7 of 12

22 6(b) P o = 162 g = 8% EPS 1 = 20(1.08) = ( 1/2 mark) DPS 1 = 21.60(0.30) = 6.48 ( 1/2 mark) P o = D 1 r g 162 = 6.48 r (r 0.08) = 6.48 r 0.08 = 0.04 r = 12% (1 mark) (1 mark) 6(c) E o = 20 D o = = 6 D 1 = = 7.5 D 2 = 6 (1.25) 2 = D 3 = 6 (1.25) 3 = D 4 = 6 (1.25) 4 = D 5 = 6 (1.25) 4 (1.08) = = (1.08) = The current stock price is the present value of future dividends 1 Year = = = = 8.85 Year 5 infinity: = Page 8 of 12

23 Alternative method The PV of dividends for the first 4 years can also be calculated using growing annuity: PV = D 1 r g 1 1+g 1+r n 7.5 = = = = Add PV of dividends from year 5 infinity as above = At 162, the stock seems to be clearly undervalued according to our expectations. 6(d) Current P/E = P o / E o = 162/20 = 8% To assess the impact of the various events, we know that P/E ratio = P 0 = 1 b (1 + g) (Trailing P/E ratio) E o 1 g Or P 0 = 1 b. E 1 1 g (Leading P/E ratio) 6d1) An increase in investors risk aversion will make the investors to demand a higher risk premium. This increases r in the formula and reduces P/E ratio. (1 mark) 6d2) This transaction increases the operating leverage, the asset beta and r in the formula. P/E ratio will drop. (1 mark) 6d3) A reduction in payout ratio increases retention rate and that leads to higher g in the formula. P/E ratio should increase. (1 mark) 6d4) A right issue of shares with the proceeds used to pay off part of long-term debt. This transaction reduces financial leverage and hence financial risk. The value of r should drop and P/E ratio should increase. (1 mark) (4 marks) Question 7 Fixed Income Valuation and Analysis 7(a) Table 1 shows the characteristics of two annual pay bonds from the same issuer with the same priority in the event of default, and Table 2 displays spot interest rates. Neither bond s price is consistent with the rates. Table 1: Bond Characteristics Bond A Bond B Coupons Annual Annual Maturity 3 years 3 years Coupon rate 10% 6% Yield to maturity 10.65% 10.75% Price Page 9 of 12

24 Table 2: Spot Interest Rates Term Spot Rates (zero coupon ) 1 year 5% 2 year 8% 3 year 11% Using the information in Table 1 and Table 2 recommend either Bond A or Bond B for purchase. Justify your choice. (6 marks) 7(b) A bond for the Kudi Plc has the following characteristics Coupon payment Semi-annual Maturity 12 years Yield to maturity 9.50% Macaulay duration 5.8 years Convexity 58 Noncallable 7b1) Calculate the approximate price change for this bond (using only its duration) assuming its yield to maturity increased by 150 basis points. Discuss the impact of the calculations, including the convexity effect. 7b2) Calculate the approximate price change for this bond (using only its duration) if its yield to maturity declined by 300 basis points. Discuss (without calculation) what would happen to your estimate of the price change if this was a callable bond. (3½ marks) 7(c) Explain how each of the following two ratios should be used to evaluate a firm s financial risk c1) Total debt to total capital 7c2) Pretax interest coverage (2½ marks) (6 marks) Solution to Question 7 Fixed Income Valuation and Analysis 7(a) The essence of the answer is to price each bond's cash flows using the spot curve (Table 2). The non-arbitrage price of bond A is = (21/2 marks) The market price 0 f Bond A is 98.40, which is 13 kobo (13.2 basis points of market price) less than the non-arbitrage price. The non-arbitrage price of Bond B is = (21/2 marks) The market price of Bond B is 88.34, only 2 kobo (2.3 basis points of market price) less than the non-arbitrage price. Page 10 of 12

25 Conclusion: Despite having the lower yield to maturity (10.65 percent versus percent), Bond A is the better value because the excess of its non-arbitrage price over market price is greater than for Bond B. (1 mark) 6 marks 7(b) 7b1) Assuming semiannual interest payments Modified duration = = years Percentage change in price = D mod i = (5.54) (+ 150/100) = 8.31 percent (11/2 marks) 7b2) A misestimate of the price change will arise because the modified-duration line is a linear estimate of a curvilinear function. That is, convexity measures the rate of change in modified duration as yields change. The effect of convexity on price should be added to the effect of duration on price in order to obtain an improved approximation of the change in price given a change in yield. (1/2 mark) Percentage change in price = % = % (½ mark) 7c2) 7c1) The 3% decline in rates may not elevate the bond price by 16.33% if the bond's call price is violated and protection against a call has elapsed. (½ mark) 3 marks The total debt to total capital ratio measures the degree of leverage of the firm. Leverage is the relationship of debt owed to the company's total resources as valued on the balance sheet. An analyst would evaluate the absolute leverage and the change in the use of leverage for a firm and compare the level of leverage to that of other companies in the same industry. A firm with a high total debt-total capital ratio will be perceived as having a higher level of credit risk. By comparing this ratio to its competitors' ratio, an analyst can judge the prudence of such leverage for a company in the particular industry. A firm increases its financial leverage when it takes on more debt in proportion to its total capitalization (resources). The change in financial leverage may indicate a change in the company's attitude towards risk taking. The firm will lose some financial flexibility financing alternatives and ability to access funds -and will generally pay a higher price to acquire funds than a lower-leveraged company. Higher financial leverage may also reduce the firm's choices for financing future growth and paying dividends. Covenants may restrict the company's ability to use its financial resources as it sees fit when this ratio becomes too high. (11/2 marks) The pretax interest coverage ratio measures the annual interest burden (the amount the firm must pay its creditors) placed on a firm relative to its earning capacity. This coverage ratio is important because it looks at the firm's ability to pay its annual interest expense from pretax earnings (EBIT). A high coverage ratio is considered positive; a low coverage ratio may indicate more risk, which is a financial constraint. The ratio also suggests the protection afforded creditors to continue to receive interest income, despite a business downturn or an increase in leverage by the firm. Although this ratio indicates the ability of the company to pay cash to its creditors, the numerator includes noncash earnings and is reduced by noncash expenses. Finally, the comfort level of coverage should be based on the expected consistency of earnings (an industry issue) and with consideration given to the firm's access to cash. (11/2 marks) 3 marks Page 11 of 12

26 FORMULAE Levered/unlevered beta: Annuities: Yield to maturity of a bond: Valuation of perpetual bonds: Price change approximated with duration: Portfolio duration: Macaulay duration: Page 12 of 12

27 September 2015 Professional Examination Paper 2.3: Questions & Solutions Derivatives Valuation Analysis Portfolio Management Commodity Trading and Futures Level 2 Page 1 of 13

28 SECTION B: Question 2 Derivative Valuation and Analysis Over the next three months, you expect a significant drop in the price of a particular stock. Call and put options are traded on the stock. You plan to profit from your expectation by shortselling the stock. Your compliance department has however reminded you that short-selling of stock is not allowed in the stock market (short-selling of other securities are however allowed). Explain, using put-call parity, how you can profit from your expectation without violating market regulation. Solution to Question 2 I will need to create a synthetic short stock. From put-call parity: C + Ee r.t = P + S S = C + Ee r.t P The right-hand side is a long synthetic stock. If we multiply both sides 1, we have: S = P C Ee r.t 1½ marks The right-hand side is now the synthetic short stock, which means: long the put 1½ marks short the call short (i.e. borrow) the riskless bond The net pay-off from this will be the same as that of a short stock. Question 3 Portfolio Management An investor owns the following portfolio today. Stock Market Value (N) Expected Annual Return R 2,000 17% S 3,200 8% T 2,800 13% Calculate the expected market value of the portfolio after three years and the total expected return over the same period. (4 marks) Solution to Question 3 Portfolio total value = 2, , ,800 = 8,000 ( 1/2 mark) Portfolio weights: R = 2,000 / 8,000 = 0.25 S = 3,200 / 8,000 = 0.40 T = 2,800 / 8,000 = 0.35 ( 1/2 mark) Page 2 of 13

29 Portfolio expected annual return ( ) + (0.40 8) + ( ) = 12% (1 mark) Expected portfolio value after 3 years is: 8,000(1.12) 3 = N11, (1 mark) Expected total return: 11, = 40.49% 8,000 Or (1.12) 3 1 = 40.49% (1 mark) 4 marks Question 4 Commodity Trading and Futures Briefly indicate the factors distinguishing a forward contract from a futures contract? What do forward and futures contracts have in common? What advantages does each have over the other? Solution to Question 4 While both forward and futures contracts are agreements to purchase a good at a future date, a futures contract provides liquidity by having a central marketplace and standardized contract terms. This allows holders of futures contracts to sell them in the market at any time prior to expiration. Futures trading is governed by the formal regulations of the futures exchange. Most important, the losses incurred by futures traders are guaranteed by the clearinghouse, which requires the daily settlement of gains and losses. That is, the holders of profitable contracts do not have to worry about whether their gains will be paid by the holders of losing contracts. Forward contracts, however, are subject to default risk. Forward contracts can be tailored to the unique needs of firms. For example, a firm may need to execute a hedge in which the expiration is a specific date. Futures contracts expire only on certain dates, which may not fit the needs of the firm. Page 3 of 13

30 SECTION C: Question 5 Derivative Valuation and Analysis Kola Iwelabi is a senior quantitative analyst in Eko Asset Management (EAM). Kola is going through market data concerning options on the stock of KB plc. Kola has the following information presented in Table 1. Table 1 : Stock and Options Data for KB plc and Risk-Free Interest Rate Current Call Price N2.30 Current Put Price N4.70 Exercise Price N Days to Expiration* 60 Current Stock Price N N(d 1 ) 0.64 Up Move on Stock 15% Down Move on Stock 10% Risk-Free Interest Rate 3% * Note: Assume a 365-day year. Assume continuous compounding. 5(a1) Using the information in Table 1, calculate the price of a synthetic 60-day call option with a N strike price. (5a2) A new trainee is interested in knowing why it is useful to construct and value synthetic calls and puts. One of your assistants responds, Deriving synthetic values enables us to determine whether it is possible to earn arbitrage profits. 5(b) Based on the information in Table 1 and using a one-period binomial model, calculate the value of 60-day KB plc call option with a strike of N What is the value of a corresponding put option? (5 marks) 5(c) Now assume you are currently short 104,000 units of KB s stock and long 50,000 call options on the stock. Calculate what position you need to take on the stock s put option for delta-hedging. 5(d) Using the Black-Schole option-pricing model, another assistant of Kola, Kevy, calculates the price of a 3-month call option and notices the option s calculated value is different from its market price. With reference to Kevy s use of the Black-Scholes option-pricing model: 5d1) Discuss why the calculated value of an out-of-the-money European option may differ from its market price. 5d2) Discuss why the calculated value of an American option may differ from its market value. (4 marks) Solution to Question 5 Derivative Valuation and Analysis 5(a1) To create synthetic call option, make C (i.e. call) the subject of the formula (in the put-call parity equation) Page 4 of 13

31 C = P + S Ee rt = e = /365 (5a2) The assistant is correct about the reason for calculating synthetic option values; it allows one to determine if it is possible to earn arbitrage profits. However, the assistant is incorrect about the set of transactions that can be used to earn an arbitrage profit if the current price of the call option is greater than the synthetic value. The correct strategy is to sell the call option and then take long positions in the put and the stock and a short position in the bond (purchase the synthetic call). He incorrectly states that a short position should be taken in the stock. 5(b) Stock and call prices S o = S u = = C u = Max(0, ) = S d = = C d = Max(0, ) = 0 (1 mark) (1 mark) Risk-neutral probability Let π = probability of up = π = e rt d = e 0.03 (60/365 ) 0.90 U d π = = (1 mark) π = e rt d = e (0.03 x 60/365) 0.90 U d Value of call (C o ) C o = (π C u + (1 π)c d )e rt [( x ) ( x 0)] x (e -0.03x60/360 ) = 7.45 (1 mark) The corresponding value of put can be calculated using put-call parity P = C + S o Ee rt /365 = e = (c) Let x = number of put needed Delta of total holding is Page 5 of 13

32 Security Qty Delta/unit Total Delta Stock 104, ,000 Call 50, ,000 Put x x Total portfolio delta = 72, x For delta hedging: 72, x = 0 x = 200,000 put options For delta-hedging, we need to sell 200,000 put options 5d1) 5d2) When European options are out of the money, investors are essentially saying that they are willing to pay a premium for the right, but not the obligation, to buy or sell the underlying asset. The out-of-the-money option has no intrinsic value, but, since options require little capital (just the premium paid) to obtain a relatively large potential payoff, investors are willing to pay that premium even if the option may expire worthless. The Black-Scholes model does not reflect investors' demand for any premium above the time value of the option. Hence, if investors are willing to pay a premium for an out-of-the-money option above its time value, the Black-Scholes model does not value that excess premium. With American options, investors have the right, but not the obligation, to exercise the option prior to expiration, even if they exercise for non-economic reasons. This increased flexibility associated with American options has some value but is not considered in the Black-Scholes model because the model only values options to their expiration date (European options) Question 6 Portfolio Management Tony John, FCS, manages the Big Bank plc s (BBP) pension fund. He recently presented his quarterly report to the fund s board of trustees and is recommending a change in the fund s asset allocation. Based on his market expectations, he recommends allocating 30% of assets to value stocks, 50% to growth stocks, and 20% to bonds. Tony s market expectations are shown in Table 1. Table 1: Tony s Market Expectations Value stock Portfolio Growth Stock Portfolio Bond Portfolio Expected annual return 12% 14% 8% Expected standard deviation of annual returns 16% 22% 8% Return correlations: Value stock portfolio Growth stock portfolio Bond portfolio Page 6 of 13

33 6(a) Using Tony s recommended asset allocation and market expectations from Table 1, calculate the expected standard deviation of annual returns for the pension fund s portfolio. 6(b) If Tony wants to achieve an expected annual return of 12.5% while maintaining the pension fund s current 20% allocation to bonds, calculate the proportion of the fund s assets that should be allocated to value stocks. (5 marks) 6(c) In describing the risk-return characteristics of his recommended portfolio, Tony states. I believe the recommended asset allocation will produce a portfolio that is the global minimum-variance portfolio. The global minimum-variance portfolio has the lowest level of risk compared with all other portfolios on the efficient frontier, and thus it also dominates all other portfolios on the efficient frontier. Is Tony Correct? Explain. 6(d) One of the board members, Ben Ema, suggests that Tony should consider broadening the diversification of the fund s portfolio into a fully diversified portfolio by adding real estate and international stocks. He states that these additions will improve the efficiency of the fund. Ben estimates the fully diversified portfolio would have an expected return of 13% and a standard deviation of 15%. He would then further expand the investment opportunity set by combining the proposed fully diversified portfolio with either risk-free borrowing or lending. He notes that the appropriate risk-free rate of return is 4%. 6d1) If Ben wants to construct an optimal portfolio that has an expected standard deviation of annual returns of 12%, what proportion of total assets should be invested in riskfree assets and what proportion in risky portfolio? (2½ marks) 6d2) If Ben uses his proposed fully diversified portfolio to construct an optimal portfolio that has an expected standard deviation of annual return of 12%, what will be expected annual return for the resulting portfolio? (1½ marks) 6(e) Another board member, Victor Dan, is not too sure he understands the concepts of growth investing and value investing. You are required to explain very briefly the two concepts to victor. (4 marks) Solution Question 6 Portfolio Management 6(a) 6(b) Standard deviation = ( % % % % 22% % 8% % 8% 0.2) 0.5 = 15.9%. Total portfolio weight = 100% % allocated to bond = 20 % allocated to stocks (value + Growth) = 80 (1 mark) Let w = % in growth stock 0.8 w = % in value stock (1 mark) The following equation holds: 12w + 14(0.8 w) + 8(0.20) = w w = w = 0.30 w = 0.15 or 15% Page 7 of 13

34 % in value stock = = 0.65 The final allocation is: Growth stock 15% Value stock 65% Bond 20% (1 mark) 100% (5 marks) 6(c) 6d1) Although he is correct that the global minimum-variance portfolio has the lowest level of risk compared with other portfolios on the efficient frontier, he is incorrect with regard to dominance. The global minimum-variance portfolio does not dominate portfolios on the efficient frontier. Let x = weight of the fully diversified portfolio 1 - x = weight of the risky asset. σ p = (x) (standard deviation of fully diversified portfolio) 12 =(x)(15 x = x = 0.20 Thus, 20% should be invested in the risk-free asset and 80% in the fully diversified portfolio. (2½ marks) 6d2) E(R) = R F + (E(R) R F ) x δ δ p = 4 + (13 4) 12 = 11.2% 15 Or: E(R) = (1 W p ) R F + W p R P = (1 0.8)(4) + (0.8 13) = 11.2% (1½ marks) 6(e) When you invest for growth, you are typically seeking capital appreciation over the long term. You will likely choose investments that you believe will exhibit a faster-than-average increase in share price over the coming years. Growth investors purchase stocks at relatively high price-to-earnings, price-to-book, and price-to-sales ratio, and low dividend yields. On the other hand, value investors seek out stocks that are undervalued relative to their fundamentals. They therefore look for stocks at relatively low prices, as indicated by low price-toearnings, price-to-book, and price-to-sales ratios, and high dividend yields (greater proportion of total return is from dividend income) In summary, value investing focuses on the present and letting the future sort itself out. Growth investing keeps the focus on the future. (4 marks) Question 7 Commodity Trading and Futures 7(a) Explain why futures and forward prices might differ. Assume that platinum prices are positively correlated with interest rates. What should be the relationship between platinum forward and futures prices? Explain. (4 marks) Page 8 of 13

35 7(b) Foodful Ltd is a large producer Golden Chocolate (GC) whose main ingredient is cocoa beans. The demand for GC is seasonal with the largest demand occurring mid-november through the end of December. Production schedules require acquisition of 25,000 bushels of cocoa seeds in late September to meet the holiday season demand. Foodful management is concerned about the possibility that a rise in price of cocoa seeds between now and September could hurt profitability. Cocoa seeds must be acquired at a price of N450 per bushel or less to ensure profitability. The September cocoa seeds futures contract (5,000 bushels quantity) is selling for N422 per bushel. What can Foodful do to ensure its profitability? 7b1) What risk does Foodful face in acquiring cocoa beans by taking delivery of the futures contract? How should Foodful acquire the cocoa beans it needs? (4 marks) 7b2) If the September spot price turns out to be N630 per bushel, show Foodful s transaction in the cocoa beans cash and futures markets and calculate its net wealth change. (6 marks) Solution to Question 7 Commodity Trading and Futures 7(a) Futures are subject to daily settlement cash flows, while forwards are not. If the price of the underlying good is not correlated with interest rates, futures and forward prices will be equal. If the price of the underlying good is positively correlated with interest rates, a long trader in futures will receive daily settlement cash inflows when interest rates are high and the trader can invest that cash flow at the higher rate from the time of receipt to the expiration of the futures. Because forwards have no daily settlement cash flows, they are unable to reap this benefit. Therefore, if a commodity's price is positively correlated with interest rates, there will be an advantage to a futures over a forward. Thus, for platinum in the question, the futures price of platinum should exceed the forward price. The opposite price relationship can occur if there is negative correlation. Generally, this price relationship is not sufficiently strong to be observed in the market. (4 marks) 7(b) Foodful can acquire cocoa beans today and store it until September or Foodful can acquire cocoa beans using the September cocoa beans futures contract, it would buy 5(25,000/5,000) September contracts at 422 per bushel. 7b1) 7b2) When September arrives, Foodful can acquire the cocoa beans in one of two ways. First, it can take delivery of the beans via the futures contract. Unfortunately, the short side of the contract chooses the delivery location. This location may or may not be convenient for Foodful. The second alternative for acquiring cocoa beans eliminates this risk. In this method, Foodful acquires cocoa beans in the spot market and enters a reversing trade in the futures market. If the futures price has moved since the initiation of the hedge, any gains (losses) on the futures contract offset any losses (gains) in the cash market so that the effective price Foodful pays for cocoa beans is N422. (4 marks) Cash Market Today: Foodfull anticipates need for 25,000 bushels of cocoa beans in September, wants to pay N422/ bushel or N10,550,000 total. September: Spot price of cocoa beans is N630. Foodful buys 25,000 bushels for N15,750,000 Loss over target = N10,550,000 15,750,000 = N5,200,00 Futures Market Today: Buy five 5,000 bushel September cocoa beans futures at 422/bushel. September: At maturity, the futures price equals the spot price. Sell 5 futures contracts at N630/bushel. Futures profit = 25,000 ( ) Page 9 of 13

36 = N5,200,000 Net wealth change: N Profit on futures 5,200,000 Loss in cash market (5,200,000) 0 (6 marks) Page 10 of 13

37 FORMULAE 1) Black and Scholes Options pricing model: ; ; 2) 2) General cost of carry relationship: 3) Continuous time cost of carry relationship: 4) Determinants of Options Price: 5) Correlation/Covariance: 6) Static portfolio insurance using put option: 7) Hedging with Stock Index Futures: 8) Risk adjusted performance measures: 9) Binomial Option Valuation Model: 10) Note: The variance of 3-asset portfolio is given by: 11) Page 11 of 13