bao3403 ExamsolS2 20081.doc

Investment & Portfolio ManagementBAO 3403Question 41 Part A (i)Intrinsic value = PV(dividends) + PV(future price)V= (D1 * PVIF1) + (D2 * PVIF2).Yr 112%Yr 210%Yr 310%YearDividendPVIF 11%P.V0$3.50-1$3.920.9013.532$4.310.8123.503$4.740.7313.46PV of dividends$10.495% growth YR 4 and beyond.P3 = D4 = $4.74(1.05)=$4.98=$83k-g .11 - .05 0.06PV = $83 x PVIF 11%,3= $83 x 0.731 = $60.67Intrinsic Value = $10.49 + $60.67= $71.17Do not purchase the share at $75 (overvalued)Part (ii)g = 0 after Year 3P = D4=$4.74= $43.09K g0.11 0PV = $43.09 X PVIF 11%,3= $43.09 x 0.731= $31.50Value = $10.49 + $31.50 = $41.99 ($42)Question 41 Part B G = 0.15 x (1-0.4) = 0.09 (9%)P/E = 0.4/0.15-0.09 = 6.67 k = 6% + 1.5(12-6) = 15%EPS = 0.15 x $60 = $9Share Price = $9 x 6.67 = $60.Part C$2.00/$20 = 0.10 or 10% Part D(i) Decrease the P/E ratio(ii) Decrease the P/E ratio(iii) Increase the P/E ratio(iv) Increase the P/E ratioQuestion 42(i) BP = (I x PVIFA) + (FV x PVIF)= ($40 x PVIFA 3%,4) + ($1000 x PVIFA 3%,4)= $40 x 3.717 + $1000 x 0.888= $148.68 + $888 = $1036.68The market price and face value differ because the required yield is lower than the coupon rate (discount bond).(ii) Yield 6%/2 = 3%PeriodAnnual cash flowPVIF 3%Present ValueDiv Market ValueTime weighed cash flow0.540.97138.840.03750.0188140.94337.720.03640.03641.540.91536.600.03530.052921040.888923.520.89081.7816$1036.681.0001.8897Alternatively:(38.84x0.5)+ (37.72x1) + (36.60x1.5) + (923.52x2) / 1036.68(19.42 + 37.72 + 54.9 + 1847.04) / 1036.681959.08/1036.68 = 1.8897 yearsDuration in years = 1.89 years Modified Duration 1.89/(1 + 0.06/2)= 1.83 years(iii) Percentage change-1 x modified duration x change interest rates= -1.83 x 2.0= - 3.66% decrease in the bonds price(iv)YTM = $80 + (1000-940)/2/(1000+940)/2YTM = $80 + $30 / $970YTM = $110 / 970 = 0.113 or 11.3%(v)350 = $1000 / (1 + i)10 = $1000/350 = (1 + i)10 (2.857)0.1 = (1 + i) = 1.11 1 = 0.11 or 11%PV = 1000/(1+0.12)10 = 1000/3.11 = $321.54This bonds duration is 10 years. (iv) Term to maturity Longer maturities mean longer durations.Coupon rate Low coupon rates lead to longer durations.Yield to Maturity Low yields lead to longer durations.(vi)The Term structure of interest rates is the relationship between the interest rate or rate of return (yield) on a bond and its time to maturity. The theories are as follows:Expectations hypothesis theory that the shape of the yield curve reflects investor expectations of future interest rates.Liquidity preference theory theory that investors tend to prefer the greater liquidity of short-term securities, and therefore require a premium to invest in long-term securities.Market segmentation theory theory that the market for debt is segmented on the basis of maturity, that supply and demand within each segment determines the prevailing interest rate, and that the slope of the yield curve depends on the relationship between the prevailing rates in each segment.Preferred Habitat Theory theory that investors have preferred maturity sectors in which they seek to invest but are willing to shift to other maturity sectors if they can expect to be adequately compensated(vii) (1+r3) = (1+0.055)(1+0.06)(1+1.07)1/3r3 = 1.0616 -1 = 0.0616 or 6.16%Question 43(a)Futures positionSell Ten Treasury bond futures to set up the hedge. If bond market falls you will lose value from bond portfolio but will profit from your futures position.Sell to yield at 94.50 = 100 94.50 =5.5/200 = 0.0275V= 1/(1 + 0.0275) = 0.9732Vn = (0.9732)20 = 0.58081000 x ($3 x (1-0.5808)/0.0275 + $100 x 0.58081000 x ($45.73 + $58.08) 1000 x $103.81 = $103,810.90.Buy at 93.50 = 100-93.50 = 6.5/200 = 0.0325V = 1/(1 + 0.0325) = 0.96852Vn = (0.96852)20 = 0.527471000 x ($3 x (1-0.52747)/0.0325 + $100 x 0.527471000 x ($43.62+ $52.74)1000 x $96.36 = $96,360Profit on Futures position $103,810.90 - $96,360 = $7450.90$7450.90 x 10 contracts = $74,509. Part (b)Set up the hedge by Selling 1 SPI Futures contracts$20,000,000 x 100% x 1.2/ (6000 x $25) = $24,000,000/$150,000 = 160 contracts.Sell 100 SPI futures160 X $25 x 6000 = $24,000,000Buy 160 SPI futures160 x $25 x 5000 = $20,000,000Profit on Futures contracts($24,000,000 - $24,000,000) = $4,000,000Loss on share portfolio $20m -$16.5m = $3,500,000Net position on the Hedge$4,000,000 - $3,500,000 = (500,000)Part C$25 x 1 + (0.07 x 90/120) - $2 x 1 + (0.07 x (90-30)/120)$26.31 2.07 = $24.24Question 44Part (a)The value of options are determined by the following factors: Share price An increase in the share price will cause a call premium to rise and put premium to fall. Exercise Price An increase in the exercise price will cause the call premium to fall and the put premium to rise Time to Expiration An increase in the time to expiry will cause both the call and put premium to rise Volatility of Returns An increase in volatility will cause both the call and put premium to rise. Risk-free rate An increase in the RF rate will cause the call premium to rise and the put premium to fall.Part (b)(i)Total Profit, HPRShare price$15.00Market price of call$0.50Investment 40,000 x $15.00 = $600,000Share price rises to strike price $16.00 option is worth $0.Profit:Capital gain ($16 - $15 x 40,000)$40,000Dividend (0.50 x 40,000)$ 20,000Sale of call(40,000 x $0.50)$ 20,000Total profit$80,000HPR = Total ProfitInitial Investment=80,000 600,000=13.3%(ii) The above situation will remain the same. If the share price rises above $16 there will be losses on the written option which will exactly offset the increase in the value of the shares.Part (c)A Protective put option is a strategy involving the purchase of a put option as a supplement to a long position in an underlying asset. The put option acts as insurance against a decline in the underlying share, guaranteeing an investor a minimum price at which the share can be sold. Limits losses and allows for unlimited profit.Part (d)Loss from shares($9.00-$10.00) x 1000 -$1000Profit from put option ($13.00-$9.00) x 1000$4,000Cost of put Options ($500)Profit$2,500Without HedgeLoss from shares ($9.00-$10.00) x 1000 -$1000Advantages: Protects downside but allows unlimited upside.Disadvantage: cost of puts.Question 45(i)Beta ACovariance Stock A and Market = (0.7)(24)(21) = 352.8Market Variance = (21)2 = 441Beta = 352.8/441 = 0.80Beta BCovariance Stock B and Market = (0.9)(20)(21) = 378Beta = 378/441 = 0.86(ii)Required rate of return stock A = 8 + 0.8(12-8) = 11.2%Required rate of return stock B = 8 + 0.86(12-8) = 11.44%(iii)