Chapter 5: Risk and Return P1 = 0.2 r1 = 12% P2 = 0.35 r2 = 18% P3 = 0.3 r3 = -10% P4 = 0.15 r4 = 10% Expected rate of return r^ = 0.2x12% + 0.35x18% + 0.3x(-10%) + 0.15x10% = 0.072 = 7.2% Standard deviation σ= = 12 Year 2007 2008 2009 2010 2011 Large co stock return T-bill return –14.69% 7.29% –26.47 7.99 37.23 5.87 23.93 5.07 –7.16 5.45 2012 6.57 7.64 Average return Large co = ((-14.69)+(-26.47)+37.23+23.93+(-7.16)+6.57)/6 = 3.235% T-bill = (7.29+7.99+5.87+5.07+5.45+7.64)/6 = 6.55% Standard deviation Large co = T-bill = Portfolio’s beta = 1.42+0.75 = 2.17 PART 1: 1.Expected return is the weighted average of probability distribution of investment process 2.Coefficient of variation of A = 5%/10% = 0.5 Coefficient of variation of B = 9%/15% = 0.6 3.Coefficient of variation is useful in comparison times of risk per unit of return between companies (with large standard deviation) 4.Stock B is riskier than stock A 5.Because of higher coefficient of variation 6.Risk aversion 7.Combining stocks into portfolios because risk-averse investor would be better off holding the portfolio rather than just one of the individual stocks 8 Risk aversion PART 2: 1.Market risk RPM = 12%-5% = 7% 3.Stock A: r^ = 5% + (7%+0.7) = 9.9% Stock B: r^ = 5% + (7%+1.4) = 14.8% 4.No 5.Yes, stock in portfolio with low beta coefficients Weight of stock: Stock A = 1,000/5,000 = 0.2 Stock B = 1,500/5,000 = 0.3 Stock C = 2,500/5,000 = 0.5 Portfolio’s beta = (0.2x0.7) + (0.3x1.4) + (0.5x2) = 1.56 r^= 5% + (12%-5%)x1.56 = 15.92% Chapter 9: Stocks and their valuation 9-1 After drawing timeline, we have: D5 = $2.525 10-2 D0 = D1/(1+g) = 0.8/(1+0.05) = $0.762 10-3 P0 = 30 = ((1.5x(1+0.07)/(rs-0.07) rs = 12.35% P1 = D2/(rs-g) = (D0x(1+g)ˆ2)/(rs-g) = $32.1 9-4 The terminal, or horizon, date is the date when the growth rate becomes constant This occurs at the end of Year After drawing timeline, we have: D0 = 1.25 D1 = 1.5 D2 = 1.8 D3 = 1.89 P2 = 1.89/(0.1-0.05) = $37.8 CF2 = 39.6 P0 = 2.71 9-5 FCF1=$150mil Market value of company PV = $129.87mil Stock’s value per share = 129.87/50 = $2.6 9-6 r = dividend/price = 5/60 = 8.33% 9-7 $120x0.06 = $7.2 rp = Dp/Vp (a)7.2/70 = 10.3% (b)7.2/90 = 8% (c)7.2/110 = 6.5% (d)7.2/130 = 5.5% 9-8 a.Annual dividend is 120x5% = $6 Stock’s value = 6/0.1 = $60 b.Stock’s value = 6/0.14 = $42.86 9-9 dividend = 3x4 = $12 current price =$90 r = 12/90 = 13.33% EFF = (1+0.1333/4)ˆ4 – = 14% 9-10 P0^= D0x(1+g)/(rs-g) = 5x(1+(-0.05)) / (0.15+(-0.05)) = $23.75