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Group 06

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- Habiba Mustafa
- Sumaiya Nishan
- Muhammad Kashif
- Hafiz Aamir Sohail
- Altaf Hussain

BOND VALUATION

- A security that pays a stated amount of interest to the investor, period after period until its maturity.
- Face value
- Coupon
- maturity

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

- Credit Quality
- Interest Rate
- Yield
- Tax Status

- Yield is a figure that shows the return you get on a bond.
Simplest version

Yield= coupon amount/price

- 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.

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

- 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.

- 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.

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.”

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

- 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?

- How does inflation affect the nominal rate of interest?

“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)

In Real interest rate no inflation factor while in Nominal interest rate inflation factor exists.

Inflation rate higher real return will be lower.

Real 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=$342.99

Bonds promised you a fixed nominal rate of interest.

Valuation of common stock

- Primary Market
Trading through bank and OTC

- Secondary Market
Trading through Stock Exchange

- 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

- 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)

Expected 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 today’s price.

Price = po= Div1+p1/(1+r)

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

- 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:

- 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 = 5.50+121/1.15

= $110

- From our expended formula
P0 = 5/1.15 + 5.50+121/(1.15)*2

= $100

- Po = DIV1/ (r-g)
- r = (DIV 1/p0) + g

- Dividend growth rate = plowback ratio*ROE

- 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

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

- 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

- 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

- PV= FCF/1+r + FCF2/(1+r)^2 +….+FCF/(1+r)^H + PV/(1+r)^H

- Forecasting reasonable horizon is particularly difficult. The usual assumption is moderate long rum growth after the horizon, which allow us to growing-perpatuityDCF formula.
- It can also be calculated normal price-earnings or market-book ratios at the horizon date