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

BOND VALUATION

BOND: long term debt  A security that pays a stated amount of interest to the investor, period after period until its maturity.  Face value  Coupon  maturity

BOND VALUE  PV(bond)=PV(coupon payments)+PV(final payment) PV= PMT(1-1/(1+i)^n)/i + MV/(1+i)^n

Factors affecting Bond prices  Credit Quality  Interest Rate  Yield  Tax Status

Interest rate

yield  Yield is a figure that shows the return you get on a bond. Simplest version Yield= coupon amount/price

YIELD (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 VOLATILITY  Volatility refers to the amount of uncertainty or risk about the size of changes in security’s value. Volatility=Duration/1+yield

BOND DURATION Duration is a weighted measure of the length of time the bond will pay out. Unlike maturity, duration takes into account interest payments that occur throughout the course of holding the bond.

Cont’d…

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 bonds against their maturities, ranging from shortest to longest.

Forms of yield curve

Cont’d…

EXPECTATION THEORY The 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.” The 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 structure Suppose 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 rates How does inflation affect the nominal rate of interest?

FISHER’S 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+r nominal =(1+r real )(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 RATE Real cash flow t =nominal cash flow t /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/ =$342.99

INDEXED BONDS Bonds promised you a fixed nominal rate of interest.

Valuation of common stock

How Common Stocks are Traded Primary Market Trading through bank and OTC Secondary Market Trading through Stock Exchange

How Common Stocks are valued PV(stock) = PV(expected future dividends) Today’s Price The cash payoff to the owners of common stocks comes in two forms Cash dividends Capital gains or losses

Conti…d Expected return = r = Divi1 + p1-p0/p0 Example 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)

Conti’d Expected return = r = 5+( )/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 today’s price. Price = po = Div1+p1/(1+r)

Conit’d If DIV1=5 and p1=110 and r=15%, then today's price should be 100: P0 = 5+110/1.15 =$100

But what determines the Next Year’s 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:

Conit…’d Po=1/1+r(DIV1+p1)=1/1+r(DIV1+DIV2+p2/1+r) =DIV1/(1+r) + DIV2+p2/(1+r)*2 Example Suppose 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 of P1 = /1.15 = $110

Conti…d From our expended formula P0 = 5/ /(1.15)*2 = $100

Estimating the Cost of Equity Capital Po = DIV1/ (r-g) r = (DIV 1/p0) + g

Danger lurk in Constant-Growth formula Dividend growth rate = plowback ratio*ROE

The link between stock price and Earning per share Growth stock Income stock Expected return =dividend yield=earning-p ratio If dividend is $10 a share and stock price is $100 then: Expected return=DIV1/P0 = 10/100 =.10

Conti..d The price equals P0= DIV1/r = EPS1/r = 10/.10 =100 Po =EPS1/r+PVGO So, 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 Opportunities Po= DIV1/r-g Payout ratio = DIV1/EPS1 Growth rate= g = plowback ratio*ROE Present value of level stream of earnings= EPS/r PVGO = NPV1/r-g Share price = EPS1/r +PVGO

Valuing a Business by Discounting Cash Flow In 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 capital

Valuing the Concatenator Business PV= FCF/1+r + FCF2/(1+r)^2 +….+FCF/(1+r)^H + PV/(1+r)^H

Estimating Horizon Value Forecasting 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