# Group 06 ïƒ Habiba Mustafa ïƒ Sumaiya Nishan ïƒ Muhammad Kashif ïƒ Hafiz Aamir Sohail ïƒ Altaf Hussain

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BOND VALUATION

Group 06Habiba MustafaSumaiya NishanMuhammad KashifHafiz Aamir SohailAltaf Hussain

BOND VALUATION

BOND: long term debtA security that pays a stated amount of interest to the investor, period after period until its maturity. Face valueCouponmaturityBOND VALUEPV(bond)=PV(coupon payments)+PV(final payment)PV= PMT(1-1/(1+i)^n)/i + MV/(1+i)^n

Factors affecting Bond pricesCredit QualityInterest RateYieldTax Status

Interest rate

yieldYield is a figure that shows the return you get on a bond.

Simplest versionYield= coupon amount/priceYIELD (Linking price and yield)Most important thing to remember!!!!**When prevailing interest rates rise, prices of outstanding bonds fall to bring the yield of older bonds into line with higher-interest new issues **When prevailing prices fall, prices of outstanding bonds rise, until the yield of older bonds is low enough to match the lower interest rate on new issues.

BOND VOLATILITYVolatility refers to the amount of uncertainty or risk about the size of changes in securitys value.

Volatility=Duration/1+yield

BOND DURATIONDuration is aweightedmeasure of the length of time the bond willpay out.Unlikematurity, durationtakesintoaccountinterestpaymentsthat occur throughout the course of holding the bond.Contd

Term structure/Yield Curve

A "term structure of interest rates, also known as yield curve is a graph that plots the yield/spot rates of bondsagainst their maturities, ranging from shortest to longest.Forms of yield curve

Contd

EXPECTATION THEORYThe expectation theory says that:Bonds are priced so that an investor who holds a succession of short bonds can expect the same return as another investor who holds a long bond.

INTRODUCING RISK In expectation theory risk factor must be considered. If predicted future level of interest rates, select strategy offering highest return.

Inflation and Term structureSuppose u are saving for your retirement. which of the following strategies is the more risky?Invest in one-year or invest in 20-year bond?Inflation and nominal interest ratesHow does inflation affect the nominal rate of interest?

FISHERS THEORY A change in the expected inflation rate will cause the same proportionate change in the nominal interest rate; no effect on the required real interest rate. 1+rnominal=(1+rreal)(1+i)REAL & NOMINAL INTEREST RATE In Real interest rate no inflation factor while in Nominal interest rate inflation factor exists.Inflation rate higher real return will be lower.NOMINAL INTEREST RATEReal cash flowt=nominal cash flowt/1+inflation rate)t

FOR EXAMPLE:If u were to invest \$1,000 in a 20-year bond with a 10% coupon, final payment would be \$1,100. if inflation rate=6% then real value would be =1,100/1.0620=\$342.99INDEXED BONDS Bonds promised you a fixed nominal rate of interest.Valuation of common stock

How Common Stocks are TradedPrimary MarketTrading through bank and OTCSecondary MarketTrading through Stock ExchangeHow Common Stocks are valuedPV(stock) = PV(expected future dividends)Todays PriceThe cash payoff to the owners of common stocks comes in two formsCash dividendsCapital gains or lossesContidExpected return = r = Divi1 + p1-p0/p0Example Suppose Fledgling Electronics stock is selling for \$100 a share (p0=100). Investors expect a \$5 cash dividend over the next year (Div1=5). They also expect stock to sell for \$110 a year (p1=110)ContidExpected return = r = 5+(110-100)/100 r = 0.15 or 15%On the other hand, if you are given investors forecasts of dividend and price and the expected return is same then you can predict todays price.Price = po = Div1+p1/(1+r)ConitdIf DIV1=5 and p1=110 and r=15%, then today's price should be 100:P0 = 5+110/1.15 =\$100But what determines the Next Years Price P1 = DIV2 + P2/(1+r)

That is, a year from now investor will be looking out at dividends in year 2 and price at the end of year 2. thus we can forecast p1 by forecasting DIV2 and p2 and we can express po in terms of DIV1, DIV2, and p2:ConitdPo=1/1+r(DIV1+p1)=1/1+r(DIV1+DIV2+p2/1+r)=DIV1/(1+r) + DIV2+p2/(1+r)*2ExampleSuppose they are looking today for dividends of \$5.5 in year 2 and subsequent price of \$121. that implies a price at the end of the year 1 ofP1 = 5.50+121/1.15 = \$110ContidFrom our expended formulaP0 = 5/1.15 + 5.50+121/(1.15)*2 = \$100Estimating the Cost of Equity CapitalPo = DIV1/ (r-g)

r = (DIV 1/p0) + gDanger lurk in Constant-Growth formulaDividend growth rate = plowback ratio*ROEThe link between stock price and Earning per shareGrowth stockIncome stockExpected return =dividend yield=earning-p ratioIf dividend is \$10 a share and stock price is \$100 then:Expected return=DIV1/P0 = 10/100 = .10Conti..dThe price equalsP0= DIV1/r = EPS1/r = 10/.10 =100

Po =EPS1/r+PVGOSo,EPS/Po= r ( 1- PVGO/Po)It will underestimate r if PVGO is +ve and overestimate it if PVGO is -ve Calculating PV of Growth OpportunitiesPo= DIV1/r-gPayout ratio = DIV1/EPS1Growth rate= g = plowback ratio*ROEPresent value of level stream of earnings= EPS/rPVGO = NPV1/r-gShare price = EPS1/r +PVGO

Valuing a Business by Discounting Cash FlowIn this you forecast dividend per share or total free cash flow of a business. Value today always equals future cash flow discounted at the opportunity cost of capitalValuing the Concatenator BusinessPV= FCF/1+r + FCF2/(1+r)^2 +.+FCF/(1+r)^H + PV/(1+r)^HEstimating Horizon ValueForecasting reasonable horizon is particularly difficult. The usual assumption is moderate long rum growth after the horizon, which allow us to growing-perpatuity DCF formula.It can also be calculated normal price-earnings or market-book ratios at the horizon date

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