Question

QUESTION 1 (15 MARKS) Jeanne is attempting to evaluate two possible portfolios consisting of the same five assets but held in different proportions. She is particularly interested in using beta to compare the risk of the portfolio and, in this regard, has gathered the following data: Portfolio Weights (%) Asset Beta Portfolio Portfolio B 1.30 0.70 1.25 1.10 0.90 20 NO 10 10 40 Total 100 100 Required: a) Calculate the betas for portfolios A and B. marks) (CL01:PLO2:01) Compare the risk of each portfolio to the market as well as to each other. Which portfolio is more risky? b) (3 marks) (CL01:PLO2:04) c) If the risk-free rate is 2% and the market return is 12%, calculate the required return for each portfolio using the Capital Allocation Pricing Model (CAPM). marks) (CLO1:PLO2:01)

Answer 1

13 30/ 25/ 10 QUESTION 1 a. Calculation of portfolio Beta Asset Beta Portfolio A Weights Beta x Weights Portfolio B Weights Beta x Weights 1l 100 39 2 0.7 300 21 107 100 12.5 20 201 36 20 TOTAL 100 93.5 100 1111 Beta of Portfolio A= Sum of (Weights x Beta) Sum of Weights =93.5/100 0.935 Beta of Portfolio B= Sum of (Weights x Beta) Sum of Weights =111/100 1.11 c. Calculation of Return of Each Portfolio Return as per CAPM Method=Rf+Beta(Rm-Rf) where Rf= Risk free rate of Return Rm= Market Rate of Return Return of Portfolio A=2+0.935(12-2) 11.35 Return of Portfolio B= 2+1.11(12-2) 13.1

QUESTION 2 a. Calculation of Payback period Year Project A Cummulative Reture Project B Cummulative Return 0 -35000 35000 -40000 11 8000 -27000 10000 -30000 2 130001 - 14000 10000 -20000 15000 10001 8000 -12000 20000 21000 16000 4000 Payback Period Project A = 2+(14000/15000) 2.933333333 Payback Period Project B = 4+(12000/16000) 4.75 Project A should be accepeted as it has lower payback period as compared to Project B

QUESTION 2 b. Calculation of Discounted Payback period Year PVF @10% Project A Discounted Cummulative Project B Discounted Cummulative 01 1 ] -35000 -35000.0 -35000.01 -400001 - 40000.01 -40000.0 1 0.90909091 8000 7272.7 -27727.3 10000 9090.9 -30909.1 2 0.82644628 13000 10743.8 -16983.5| 10000 8264.5 -22644.6|| 3 0.7513148 15000 11269.71 -5713.7 8000 6010.5 -16634.1 4 0.68301346 20000 | 13660.3 7946.5 16000 10928.21 -5705.9 Payback Period Project A = 3+(5713.7/13660.3) 3.41827046 Project B Payback period is higher than 4 years. Project A should be accepeted as it has lower payback period as compared to Project B c.Calculation of Profitability Index Profitabilty Index of Project A = Present Value of Future Cash flows Initia Investment Required Profitabilty Index of Project B = Present Value of Future Cash flows Initia Investment Required d.Calculation of NPV Year PVF @10% Project A Discounted Project B Discounted 1 0.90909091 8000 7272. 7 1 0000 9090.9 2 0.82644628 13000 10743.8 10000 8 264.5 3 0.7513148 15000_ 11269.7| 80001 6010.5 4 0.68301346 20000_ 13660.3 16000 10928.2 TOTAL NPV 42946.5 L 34294.11 NPV of Project A = Present value of future Cash inflows-PV of Cash Outflows =42946.5-35000 7 946.5 NPV of Project B =34294.1-40000 -5705.9

QUESTION 4 a. Calculation of Value of Bond Value of Bond= Present Value of all the Future Cash Flows = Intrest Payable x PVAF(7.5%,40)+ Bond Value x PVF(7.5%,40) =100 x 8.5%/2 x 20.551 = (100 x 0.2293) 110.27175 b.Calculation of Yield to Maturity YTM Intrest (Face value-Price) = 8.5 (100-120) No.of Years 20 (Face value-Price) (100+120) 6.82 QUESTION 5 a.Calculation of Expected rate of Return expected Return =(Dividend Growth) Date Market Value 1.32+8% -.+8% 23.5 13.9574 b.Calculation of Expected rate of Return Year PVF @12% Dividend Discounted 0.8929 0.90 0.8000 0.7972 0.97 0.7714 0.71181 .05 0.7439 0.7118 28.35 20.1790 Intrinsic Value of Stock 22.50 Stock value at the End of Year 3=(Dividend-Growth) Expected return-Growthrate = 1.05-8% 12%-8% = 28.35

Question 1

b. Portfolio B is more riskier as compared to partfolio A because portfolio B has higher beta value compared to portfolio A which means portfolio B goes deviates along with market at higher rate compared to Portfolio A