FEEDBACK TUTORIAL LETTER 2 nd SEMESTER 2017 ASSIGNMENT 1 AND 2 MANAGERIAL FINANCE 4B MAF412S 1
ASSIGNMENT 1 QUESTION 1 (i) Investment A at end of Year 3: Year 4 5 6 7 8 Cash flows 1 000 1 000 1 000 1 000 2 000 Present value = 1 000 x (1 1/(1 + 0.1)^4) 2000 + 0.1 (1 + 0.1)^4 Present value = 1 000 x 3.17 + 2000 1.6105 Present value = 3 170 + 1 241.85 Present value = N$4 412 (ii) Investment A at Year 0 Year 1 2 3 Cash flows 800 800 800 Future cash flow 4 412 800 800 5 212 Present value = 800 (1 + 0.1) + 800 (1 + 0.1)^2 + 5 212 (1 + 0.1)^3 Present value = 727.27 + 661.16 + 3 915.85 Present value = N$5 304 (iii) Investment B Year 1 2 3 4 5 to infinity Cash flows 3 000 400 to infinity Present value at Year 4 = 400/0.1 = N$4 000 Cash flow at Year 4 = 3 000+ 4 000
= 7 000 Present value at Year 0 =7 000/1.4641 =N$4 781 (iv) Investment C Year 1 2 3 4 Cash flows 3 000 +2% growth to infinite Value of investment growth as at Year 3 = 400 0.10 0.02 Present value = 1 000 (1 + 0.1)^2 + 500 (1 + 0.1)^3 + 5 000 (1 + 0.1)^3 = 826 + 376 + 3 756 = N$4 958 Question 2 (a) Determine whether Marine should acquire shark Marine Fisheries expected return State Return Expected mean 0.25 X 0.16 = 0.04 0.50 X 0.10 = 0.05 0.25 X 0.02 = 0.01 Mean 0.094 Standard deviation Marine Resources Return Expected mean Deviation Squared Deviations Prob Sq. Dv x Prob 0.16 0.094 0.07 0.004356 0.25 0.001089
0.10 0.094 0.01 0.0001 0.5 0.00005-0.02 0.094 0.07 0.005476 0.25 0.001369 Variance 0.002508 SD 0.05.(5%) Shark Bait expected return State Return Expected mean 0.25 X 0.19 = 0.05 0.50 X 0.12 = 0.06 0.25 X - = - Mean 0.094 Shark Bait S.D. Standard deviation Return Expected mean Deviation Squared Deviations Prob. Sq. Dev x Prob. 0.19 0.094 0.10 0.009216 0.25 0.002304 0.12 0.094 0.03 0.000676 0.5 0.000338 - - 0.094 0.09 0.008836 0.25 0.002209 Variance 0.004851 SD 0.0696 7% Covariance: Marine Fisheries & Shark Bait State Exp. Return (Marine) Exp. Ret. Shark Bait Marine Fisheries Dev. Marine Shark Bait Dev. Shark Covariance 0.25 0.0016 0.094-0.0924 0.002 0.094-0.092 0.002128 0.50 0.0010 0.094-0.0930 0.001 0.094-0.093 0.004315 0.25 0.0002 0.094-0.0938 0.000 0.094-0.094 0.002204 Covariance 0.0086471 Expected return of a portfolio of Marine & Shark Bait (40% x 9.4) + (60% x 9.4) = 9.4%
Risk of the portfolio: = (0.6 2 x 0.002508) + (0.4 2 x 0.004851) + (2 x 0.6 x 0.4 x 0.0086471) = 0.00090288 + 0.00077616 + 0.004151 Variance = 0.0058 or 0.58% Standard deviation = 0.0762 or 7.62% The CV of Marine Fisheries = 0.05/0.094 = 0.53 The CV of the new company = 0.0762/0.094 = 0.81 They should acquire Shark Bait. The returns of the company do increase while the risk increases after acquisition. (b) The required return for a portfolio with the same characteristics as Marine Fisheries: P (R m -R f )/ m Rf + (5.4/3.2) (R m R f) = 5 + (5.4/3.2) (9.2 5) = 12.0875% = Market returns = (0.30 x 14%) + (0.40 x 8%)+ (0.30 + 6%) = 9.2% (c) Calculate, in line with portfolio theory, how an investor can move along the capital market to a point that gives him a standard deviation equal to 6.4%. (Ignore Marine and Shark Ltd) Rf +( i / m) (R m R f ) = 5 + (6.4/3.2) (9.2 5) = 13.4% As the required risk is twice the market risk, an investor would have to borrow an amount equal to his/her investment in the market portfolio at the risk-free rate and invest the whole amount in the market. Borrow 1 Own capital 1 Invest in the market 2 Market return 9.2 x 2 18.4 Cost 5
Return 13.40% (d) Determine whether Marine Fisheries and Shark Bait are a good investment in the context of the capital asset pricing model. The required return for both companies is determined by: ke = R f + β(r m R f) Βeta for Marine Fisheries = 0.0024/0.032 2 = 2.34% Marine expected return: Required return = 5 + 2.34 (9.2 5) = 14.828% Expected return = 9.4% Βeta for Shark Bait = 0.0023/0.32 2 = 2.25 Shark Bait: Required return = 5 + 2.25 (9.2 5) = 14.45% Expected return = 10.8% Both companies offer a return well below their required return. This means that both returns are below the SML and are overpriced.
FEEDBACK TUTORIAL LETTER 2 nd SEMESTER 2017 ASSIGNMENT 2 MANAGERIAL FINANCE 4B MAF412S 1
ASSIGNMENT 2: MEMO Question 1 [16 Marks] (a) Value of equity YEAR 1 2 3 4 5 Earnings after tax 48.57 52.46 56.65 61.18 63.62 Dividends (70%) 34.00 36.72 39.66 42.83 44.53 Cost of equity: k e = R f + β(e (rm) R f) k e = 7% + 1.35 (12.8 7%) =14.83% P 4 = D 5/(ke g) P 4 = 44.53 /(14.83% 4%) 411 Discounting the future dividend and P 4 34/(1.1483 1 ) + (36.82/1.1483 2 ) + (39.66/1.1483 3 ) + (42.83/1.1483 4 ) + [(411 + 44.53)/1.1483 5 ] = 29.61 + 27.92 + 26.17 + 24.63 + 228.16 P o = 336.49 cents Total market value = N$3.36 x 100 000 = N$336 000 (b) Preference shares P p = N$10/0.09 V= N$111.11 Total value = N$111.11 x 8 100 =N$900 000 (c) Zero coupon Bonds Bo = N$100/(1.085) 10 = N$44.23 5 000 x N$44.23 = N$221 150 10% Bonds : Bo = (11.470 x 5) + (100/1.06 20 )
Bo = 57.35 + 31.18 Bo =N$88.53 Total value N$88.53 x 6 000 = N$531 180 (d) Calculating the weights Market Value Weight Cost Weighted cost Equity 336 000 16.90% 14.83 2.51 Preference shares 900 000 45.26% 9.00 4.07 Zero coupon bonds 221 150 11.12% 8.55 0.95 10% Bonds 531 180 26.71% 12.00 3.21 Total value 1 988 330 100.00% WACC 10.74% Question 2 2.1 ER(A) = Rf + β(erm Rf) 9% = Rf+ 0.4(11% - Rf) 9% = Rf+ 4.4 0.4Rf 9% - 4.4% = Rf - 0.4Rf 4.6 = 0.6Rf Rf= 7.67% 2.2 (a) βa= CovAM = 18.6 ƠM 9.3 ΒNictus= 2 ER = 6% + 2 (13% - 6%) = 20% (a) The return on the asset is incorrect. This asset is offering low returns (8%) given its risk. The asset therefore plots below the SML. Given the EMH (efficient market hypothesis) the asset s price will fall and its return will rise until it plots at the SML with a return of 20%. (b) The beta value measures systematic risk. The total risk of an asset comprises systematic and unsystematic risk. Unsystematic risk is diversifiable by holding different assets with negative correlation. However systematic risk cannot be diversified away. It is therefore the true risk of the firm hence the use of the beta coefficient in the CAPM and not the variance or Std deviation.
Question 3 Calculation of NPV. 3.1 Determining the NPV. Fixed Op. costs per year Residual value Operating cash flows Taxation 1 2 3 4 5 (81 250) (81 250) (81 250) (81 250) 250 000 (151 200) Cash flows Disc factors @12% Present values Cost Net present value 358 800 0.8929 320 373 (750 000) 645 531 358 800 0.7972 286 035 358 800 0.7118 255 394 358 800 0.6355 228 017 538 800 0.5674 305 715 The project is acceptable because it has a positive NPV. Workings: 1. Taxation 1 2 3 4 5 Operating cash flows Fixed costs Net income Recoupment Depreciation deduction 440 000 (150 000) 440 000 (150 000) 440 000 (150 000) 440 000 (150 000) 440 000 250 000 (150 000) 290 000 290 000 290 000 290 000 540 000 Taxation 81 200 81 200 81 200 81 200 151 200 2. Operating cash flows Revenue Variable costs 2 400 000 1 600 000 2 400 000 1 600 000 2 400 000 1 600 000 2 400 000 1 600 000 2 400 000 1 600 000 Operating cash flows 2.2 Ratios (a) From the Du-Pont system: Return on equity = Net Income/Sales x Sales/assets x Assets/equity = NP percentage x asset turnover x financial leverage multiplier
= ROA x FLM ROA = Net Income/Sales x Sales/assets = NP percentage x asset turnover = 3% x 1.7 = 5.1 (b) Return on Equiy = ROA x FLM FLM = 1 + D/E ratio. = 1+40% = 1.40 = 1.40 x 5.1 ROE= 7.14% (c) ROE = NP% x Asset turnover x equity multiplier = 10% x 2.5 x 1.67% = 41.67%