Essays on Finance Principles Assignment 2 Math Problem

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QUESTION ONEHISTORICAL RETURNS FOR STOCKThe historical price return for a stock is given by Ln (Pt/Pt-1)100Where Ln is the natural logarithmPt -price of stock for the month Pt-1-price of stock for the previous monthEXPECTED RETURNS FROM HISTORICAL RETURNSBHP= -2.521%QBE= -2.246%WES= 3.136%WOW= 3.278%Monthly volatilityRisk is the Standard deviation of the monthly returnsR= VolatilityBHP= 4.693%QBE= 8.145%WES= 4.571%WOW= 1.964%Risk-return diagramWOW is the best investment based on past performance. It has the expected return (3.278%) and the lowest risk (1.964%) for all available investment options. SEE EXCEL FILE ATTACHEDQUESTION TWOCompletely independentStock AAAExpected return, = 10%Volatility, σ = 25%Stock BBBExpected return, = 5%Volatility, σ = 3%Weight in AAA, W1=0.20Weight in BBB, W2=0.80E [Rp] = E [Ri]E [Rp] = E [RAAA] + E [RBBB]= 0.225% + 0.8 5%=9%σp2=∑∑WAWB σA, BWhere: σp2= variance of returns for the portfolioσA, B= covariance of the stock returns for AAA and BBBσA2 or σB2 = variance of AAA and BBB stocks returnsWA = proportion of funds invested in AAA stocksWB = proportion of funds invested in BBB stocksExpanding the formula, σp2 = WA σA2 + WB σB2 + 2 WAWB σA, B= WA σA2+ (1- WA) σB2 + 2WA (1- WA)ρA, BσB σAIf AAA and BBB are independent, ρA, B=0Hence the formula collapses toσp2= WA σA2+ (1- WA) σB2= 0.2 0.252+ 0.8 0.032= 0.0125 + 0.00072σp =0.01322σp= 11.5%Perfectly correlatedThe portfolio return is the same as in A above. There are two scenarios for perfect correlation, Perfect negative correlation, where ρ= -1σp2 = WA σA2+ (1- WA) σB2 + 2WA (1- WA)ρA, BσB σAThe correlation component is given as 2 0.2 0.8 -1 0.25 0.03=0.0024σp2= 0.01322-0.0024 =0.01082σp= 10.4%Perfect positive correlation, where ρ=1Therefore the correlation component is addedσp2= 0.01322+0.0024=0.01562σp= 12.5%Question threeCost of capital to the Bank of its ordinary sharesOutstanding shares2.2731 billionClosing price25.06Dividend1.80 (0.9 already paid)The dividend is not expected to grow, but remains constant, therefore, g=025.06=, but since g is 0,r= 7%Cost of capital to the Bank of NABHA floating rate notesNABHA, a perpetual floating rate note, interest paid quarterly, Pre tax cost of debt is given by Coupon rate is 5.04/4=1.126PV = = 68= YMT3months= 0.0185Effective rate (1+0.0185)4-1= 7.6%Post tax rate for NABHA floating rateEffective tax rate= 22.4%= 0.076203 (1-0.224) = 0.05913=5.913%WACCMarket value of equity = $25.06 per share  2.2731 billion shares outstanding = $56.963886 billionMarket value of floating rate notes (debt) = 100M  68 = 6.8 billionMarket value of assets = $56.963886 + 6.8 = 63.763886WACC = (0.076203 (1-0.224) + (0.07183)=0.06417+ 0.006306= 0.0705=7.05%Question fourexpected return on investmentJennifer, investment amount = $100,000Debt capital, 50,000 at I = 5%Investment rate= 12%The interest from portfolio investment before interest expenses is given asP (1+r)n- PWhere P is the initial investment n- Period in yearsr= rate of interest(150,000 1.12) – 150,000 = 18,000The interest gained from the loan is given by(50,000 1.05) – 50,000 = 2500 Interest after expenses, 18,000 – 25000 = 15,500Expected return= 15,500/150,000=10.33%Using CAPM equationE [ Rp ]= Rf + βp*( E[Rm ] - Rf)Where: E [ Rp ]- expected portfolio returnRf – the market free rate, given as 5%E[Rm ] – the expected market returnβp- the portfolio risk 10.33% = 5% + βp* (12% - 5%)10.33% = 5% + 7%* βpβp=0.0533/0.07= 0.7614Volatility of Jennifer’s portfolioβp = (σ Portfolio returns*ρ portfolio and Market returns) / σm

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