f

Página 1

-Finance [cg1]

Financial claims

A claim to the payment of a sum of money at some future dates

Risk (uncertainty)

Liquidity

Real value

Term/time

Expected return

Currency denomination

Divisibility

E.g. of expected return

Let’s flip a coin, if heads up, you win 100 pounds, if tails up, you lose 50 pounds, obviously, there is a 50% chance of each occurring, so what is the expected return of this game for you.

E( R ) = 50%*100 + 50%*(-50) = 25

Although finally the actual return will be either 100 or -50, but the expected return is 25.

Basic principles

Risk requires compensation: return

Markets determine prices and allocate resources

Market based system (market driven by supply and demand) Uk and US

The dominant role of financial markets

Transition economies: BRICS countries

What Is Money?

Money as ‘currency’ – in international market

Money as ‘wealth’ – in capital market

Money as ‘income’ – in household/ accounting

Functions of Money

Medium of exchange

As a medium of exchange, money is what we use to buy goods and services (the transactions demand for money is assumed to be positively related to the level of national income)

Unit of Account

As a unit of account, money provides the terms in which prices are quoted and debits are recorded

Store of value

As a store of value, money is a way to transfer purchasing power from the present to the future (demand for money is negatively related to the real rate of interest)

Financial Centres

What is a financial centre?

A market (city) meets much of the demand for financial services of domestic/international market, and it is a key component of financial system

Most developed countries have a major financial centre

The role of financial centres

Retaining the domestic financial market

Competing for international business

Being a foreign exchange earner

Providing employment

Aiding the economy by channelling funds

Roles to play

Recycling funds from surplus agents to deficit ones as efficiently as possible

Facilitating the transfer of funds

Global concerns: foreign exchange, risk management, insurance, primary and secondary markets for bonds and equities, international banking etc.

How do finance systems work ?

Surplus agents

Households, public/private bodes and government

Risk averse, short term investment

Deficit agents

Households, public/private bodies and government

Risk lover/ less risk averse, medium/long term borrowing

Financial and intermediaries

Reconciling the needs between surplus and deficit agents

Financial markets to transfer funds

Money markets = short term ( less than1 years)

Capital markets = long term (more than 1 years)

Banking systems = loans

The growth of financial industry

Contribution to GDP (financial service industry is the top contributor to UK GDP, 2018)

Globalization of financial markets

Breakdown of Bretton woods system, 1970s

International portfolio diversification

Abolishing exchange controls

Asian financial crisis, 1997

Subprime crisis 2007

Brexit

The growth of financial industry

Technology

Computers, ATM, internet banking

Security issues

Financial innovation

Why? Loophole regulation, variety of needs

Financial derivative, securitization

Deregulation since 1980s

Emerging markets

BRICS

Brazil, Russia, china and south Africa

Big economy body but low per capital

Types of finance [cg2]

Direct finance

The transfer of funds from surplus units (lenders/ savers) to deficit units (borrowers) occurs via financial markets

Savers/ lendersßàfinancial markets ßàBorrowers

Indirect finance

The transfer of funds does not occur directly from lenders to borrowers – financial intermediaries interpose between lenders and borrowers

Savers/Lenders ßà Financial intermediaries ßà Borrowers

Why do financial markets and financial intermediaries?

Pricing function

Determining the fair and prices and allocating resources

Financial markets provide both buyers and sellers with “fair” evaluation of the asset they are buying/selling

Discipline function

Ensuring the prudent discipline on trading parties

Financial markets are regulated – regulation encourages issuers of securities (borrowers) not to engage in activities that the market deems detrimental to the value of their assets

Difficulty and expense of matching the complex needs of individual borrowers and lenders – cost reduction

Absolute incompatibility of the financial needs of borrowers and lenders

Needs for lenders and borrowers

Lenders requirements

Minimisation of risk

Minimisation of costs

Maximisation of returns

Liquidity (ease of converting a financial claim into cash without loss of capital value)

Borrowers requirements

Funds at a particular specified date, for a specific period of time (preferably long term) and at the lowest possible cost.

Direct and indirect finance (traditionally)

Direct and Indirect Finance, which one is better?

Financial intermediaries has advantage over direct finance, but also additional costs for borrowers and lenders (in terms of either fees or interest rate spreads)

To state intermediated finance is more advantageous than direct finance it is necessary that the benefits of such activity outweigh the costs associated intermediation

Financial claims and financial liabilities

Debt and equity are the most commonly known financial claims in financial markets

Debt claim holder as a predetermined cash via the rate interest

Equity claim holder entitle to cash a payment in the form of dividends once debt claim holders have been paid

Debt claim holders facing less risk than equity claims holders

Financial claims and financial liabilities

Each financial claim undertakes one of the following financial liabilities

Type 1: the amount of liability is known and the timing of the liability is known (bank deposit)

Type 2: the amount of liability is known and the timing of the liability is uncertain (life insurance)

Type 3: the amount of liability is uncertain and the timing of the liability is uncertain and the timing of the liability is known (bank deposit with variable interest rate)

Type 4: the amount of liability is uncertain and the timing of the liability is uncertain (non-life insurance, such as car insurance)

Financial Markets[cg3] : different Taxonomies

Financial markets can be classified according to several features they present:

Whether the assets traded are newly issued or already issued

Type of asset trade

Maturity of the asset traded

The means of settlement

The obligation to exchange

The organisational structure of the market

The method of sale/pricing

Primary and Secondary markets

Primary markets deal with the issue of new securities à securities must be Underwritten and distributed

à issuer receives funds from sale

Secondary markets deal financial securities that have been issued

-à issuer does not receive funds from sale (securities bought and sold in the market)

Primary Market

Corporations, government, local authorities might decide to issue securities to raise funds

The new securities are underwritten by financial institutions (investment and commercial banks), who dispute them to the public and other institutions

Underwriting process can occur via: bought deals, auctions, pre-emptive rights offerings, private placements

Secondary markets

Once a security has been allocated to the investors for the first time, it can be bought and sold on the stock market

Despite the fact that the issue does not get any proceeds from the issuance on the secondary markets, this market is very important for the issues, for two reasons:

Prices on secondary market are an estimate of a company’s value

The liquidity provided by secondary markets decreases the cost of capital of the issuers

Role of market: market makers provide liquidity to the market by quoting bid and ask prices continuously – if market makers did not exist trading would slow down and for certain securities stop altogether

Bond and equity markets

Financial markets mainly deal in two types of financial securities

Bonds: issues by corporations, banks or government

Equity (shares): issued by any kind of public company- but not by the government

Markets exist also for financial securities other than bonds and equities – e.g. hybrid instruments or future markets

Money markets and capital markets

Money markets are those where short term debt securities are traded (typically, maturity <1 year) – e.g. treasury bills

Capital markets are those where medium or long term securities are traded e.g. treasury or corporate bonds

Cash and future markets

In a cash market the settlement occurs immediately – the price is agreed on today and the settlement also take place today

Ina futures market, the settlement occurs at a future date with respect to when the transaction take place – the price is agreed on today but the settlement takes place some time in the future

Forward and options markets

In the spot/forward market, the buyer is obliged to buy the asset on the date and at the price agreed some time in the past

In the options market, the buyer has the right but no the obligation t buy the asset on the date and at the price agreed some time in the past

Regulated and OTC markets

In a regulated market, the trading is organised by the exchange

Clearing house: for each transaction, the buyer/seller enters a contract with the exchange itself – the risk that the counterparty does not fulfil the contract is covered

In an Over the Counter market, dealers simple trade between themselves

There is no clearing house – the parties are not protected from the risk that either of them does not fulfil the contract.

Market makers and dealers market; screen based and pit trading

In regulated markets, market makers provide liquidity to the market by quoting bid ask prices

In OTC markets, dealers negotiate prices between themselves

Screen based trade occurs via computers – no need for traders to be located in the same space

Pit trade occurs inside the exchange

The role of Financial Intermediaries

The main function of financial intermediaries

Size transformation

(bank) depositors usually have small sight/saving accounts in comparison with loans required by borrowers

If FI’s did not exist, depositors would have to pool their funds together to lend them to borrowers

Maturity transformation

Savers generally prefer investing their money in sage short term investment whereas borrowers prefer long term loans, to finance their projects

IF FI’s did not exist, either part (or both) should accept a non-optimal solution

Risk transformation

Depositors generally not willing to take great risks when investing their money; however borrowers often look for funds in order to finance risky projects

If FI’s did not exist, many risky (but profitable) projects would not be implemented. FI’s are willing to take the risks involved in the borrowers activities, if an adequate compensation for taking such risks provided

Liquidity provision

Surplus agents prefer that the assets they invest in be liquid, i.e easily convertible into cask; on the other hand borrowers prefer long term funding to carry out their projects

FI are able to provide liquidity by maintaining a sufficiently larger number of lenders and ensuring that potential withdrawals are covered by cash introduced by new accounts

If FI’s did not exist, surplus agents would not be willing to hold tightly liquid assets to finance borrowers

Costs reduction

FI’s are able to reduce transaction costs, ie the costs associated with the buying and selling of a financial instrument

Because of the reduction of transaction costs, FIs offer lower loan rates relative to direct financing

Why are FI’s able to reduce transaction costs ?

Economies of scale = cost saving arising from decreasing unit costs of production as output increases. By increasing the cost per unit of transaction decreases

Because FIs engage in numerous transaction, they are able to exploit the benefits of economies of scale

Economies of Scope = cost saving arising from joint reduction. Let us consider two outputs, Q1 and Q2 and their separate costs C(Q1) and C(Q2). If the join cost of producing the two outputs is expressed by C(Q1,Q2), then the economies of scope are said to exist if:

C(Q1,Q2)

Because FIs offer a range of financial services, they are able to exploit the benefits of economies of scope

Provision of a Payments system

In modern times, Fis (especially commercial banks) facilitate payments via a number of non- cash means: cheques, credit/debit cards, electronic transfers and so on

However, because of the importance of the payment system for an economy, appropriate regulation is needed regarding the activities that Fis are allowed to engage

Issues in a financial system without FIs

Asymmetric information

Not everyone has the same information

Everyone has less than perfect information

Some parties to a transaction have ‘inside’ information which is not made available to both sides of the transaction

Information asymmetric or the imperfect distribution of information among parties can generate adverse selection and moral hazard

Adverse selection

It occurs before the financial transaction has taken place

It consists in the worst potential borrowers most likely to produce adverse outcomes being the ones most likely to seek loans and be selected

This occurs if it is hard to determine the riskiness of each borrower -worst borrowers will be those that most actively look for funds at that price

Moral Hazard

It occurs after the financial transaction has taken place

The borrower has incentives to engage in undesirable activities making it more likely that will not pay loan back

FIs reduce adverse selection and moral hazard problems, enabling them to make profits

Principal agent problem ( also called agency problem)

It occurs whenever a person ( or group of people), called the agent; makes decisions on behalf of another person, called the principal

Problems arise because the agent often has superior information and expertise (which may be the reason the principal employs him/her)

The agent can choose his behaviour after the contract has been established, and because of this the agent is often able to conceal the outcome of a contract. Agency problems also arise because the agent cannot be efficiently or costlessly monitored

Possible moral hazard problem

Principal agent and the role of the banks

In order to reduce agency problem, lenders can insert clauses in debt contracts that limit the discretionary use of the funds by the borrowers – this is hard to achieve for individual lenders

FIs (in particular, banks) have more expertise than individual investors – they also have more contractual power which they used to decrease the information asymmetries between them and the borrowers

FIs can act delegated monitors with respect to possible moral hazard of the borrowers

Issues in a financial system – The remedy

Delegated Monitoring

Since monitoring borrowers is costly, it is efficient for depositors to delegate the rake of monitoring to specialised agents such as banks

Banks can act as delegated monitors as:

They can diversify among different investment

They can finance a large number of borrowers

Financial Institutions

Central banks

Implementation of monetary and exchange rate policy

Management of national debt

Supervision of banking sector

Capital adequacy

Liquidity

Risk profile

Lender of last resort

Banker to government and commercial banks

Deposit institutions

This type of financial institutions take deposits from units in surplus (savers: they have funds in excess with regard to their consumption needs) and lend the money gathered to units in deficit ( borrowers: they need funds to satisfy their need for investment/consumption)

Main types of deposit institutions

Commercial banks

Saving institutions

Banks Balance sheet = Bank Assets = Bank liabilities +Bank Capital

Assets

Liabilities

Cash

Liquid assets

Loans

Other investments

Fixed assets

Deposits

Equity

Bank capital

Assets – liabilities = Net Worth

This is bank capital

It is the vale of the bank to it owners

Bank capital is roughly 9% of assets

Ratio of Debt to equity is about 10:1

That substantial leverage

A typical Banks income statement

Net interest income

(interest income – interest expense)

Net fees and commissions income

Net trading income

Net investment income

Staff and other admin costs

Amortisation and depreciation

Income before tax

Tax

Profit after tax

Deposit institutions

Deposit institutions base their business on net interest income: come (difference) between interest income and interest expense

E.g. Savers à lend at 2% annual àDeposit institution àlend at 5% annualà Borrowers

Interest spread: 5%- 2% = 3%

If total deposits and loans = £1,000,000,000

Net interest income 3% x £1bn = £30,000,000

Performance measure

Return on assets (ROA)

ROA = Net profit after taxes / total bank assets

Return on Equity (ROE)

ROE = Net profit after taxes / Bank Capital

Deposit Institutions main risks

Default risk: risk that borrowers go bankrupt

Funding risk (interest rate risk): risk that adverse movements in interest rates reduce or wipe out completely net interest income

Regulatory risk: risk coming from new regulation e.g. constraints on quantity and/or riskiness of loans

Liquidity risk: because deposits are most likely in short term and are transformed into large amount of simultaneous withdrawals can cause bankruptcy of deposit institutions – bank run (northern rock)

Deposit institutions – role in the payments system

Banks are deposit taking institutions (DTIs) and are also known as monetary financial institutions (MFIs)

Monetary financial institutions play a major role in a country’s economy as their deposit liabilities form a major part of a country’s money supply and are therefore very relevant to Governments and Central Banks for the transmission of monetary policy

Bank deposits functions as money; as a consequence an expansion of bank deposits results in an increase in the stock of money circulating in an economy

All other things being equal the money supply, that is the total amount of money, will increase if interest rates drops.

Insurance companies

Insurance companies are nondeposit institutions, and as a result they do not participate in the payment system

Insurance companies carry out the intermediation function by gathering funds from policy holders and investing them in the capital markets

In exchange for the premiums paid, insurance companies provide policy holders with compensation should a particular event occur.

How to calculate the premiums?

Premium = f(L,P)

The premium paid by policy holders depends on the likelihood of the insured event occurring (L) and on the magnitude of the payment of the insurance company to the policy holder should the event occur (P)

The large L or P, the Larger the premium paid by the policy holders

The premiums are pooled by the insurance company and the money invested in capital markets – when payments are to be made, the money is withdrawn from the funds gathered through the premiums

Mutual funds or unit trusts

Mutual funds (US) or unit trusts (UK) are non – deposit financial institutions

Intermediation function is carried out by pooling funds from the public and investing them in the equity and bond markets

By exploiting professional expertise diversification benefits and economies of scale, mutual funds should be able to provide investors with better risk adjusted returns than if they were to invest their money individually

Total return deriving from investing in mutual funds has two components:

Share in capital appreciation of assets comprised in the fund (increase in price), capital gain/loss

Share in the flow of income generated by the assets in the fund, income.

Investment companies and investment trusts

Investment companies and investment trusts are public quoted companies invest in financial securities

Return for investors derives from appreciation of equity shares of investment company, not from assets comprised in a single mutual fund. More over, whereas fund are “open ended”, investment companies are “closed ended”

Pension Funds

A pension fund is an asset pool that accumulated over an employees working years and pays retirements benefits during the employees nonworking years

Funds are usually collected by employers on behalf of employees and hand over to the pension fund

The pension fund invests the money of the subscribers in the stock markets in an attempt to guarantee the value of the savings increases at a rate at least equal to the inflation rate

Why not simply relying on state pension

State pension system pay benefits to the pensioners using the money generated by taxes paid by currently active workers

Countries relying mainly on this system are at present facing enormous difficulties as ageing population, generous benefits for pensioners and PAYG system are putting the whole contribution on system under sever strain – taxes from currently active workers may not be enough to pay pension benefits to retired population

Private pension funds:

Generally, both employers and employees make contribution to the fund, which is managed by a board trustees

Pensions fund legally separated from that company manages the fund in case the latter becomes bankrupt the asset of the former cannot be claimed by the creditors of the company that manages the fund.

Other types of financial institutions

Venture capital companies (dragons den)

Hedge funds (using financial derivatives)

Finance Companies (financial leasing)

Factoring agencies (buy up invoice at discount )

Final Securities

Financial security also can be referred to a financial claim/financial instrument

It is a claim to the payment of a sum of money at some future dates

There are two distinct types of financial securities: Debt and equity

What is debt

Debt: an amount of money borrowed by one party from another

Government debt is borrowed via the issue of treasury bonds and bills

Corporate debt is borrowed from financial institutions or pubic via the issue of corporate bonds or commercial

What is equity

equity (share): a share representing an ownership stake in a company, the holder is entitled to periodic dividends and can sell the sharers to other parties at the market price

shares are issued in primary markets

underwriting and distribution

traded in secondary markets at he market price

Debt vs Equity

Both are sources of finance

A Firm can be finance by debt (bank loans, corporate bonds etc)

A firm can be finance by equity (issuing shares e.g. public limited companies )

A firm can be finance by both equity and debt

Leverage ratio = debt/equity

if you are an investor (risk preference)

if you are the firm (possibility of default)

Types of Debt

Money Market

Treasury bill (no coupon, sold at a discount)

London interbank offered (LIBOR)

Bankers acceptance

Commercial paper (unsecured)

Repurchase agreements (repo

Certificated of deposit (CD): negotiable/ non- negotiable

Capital market

Government bonds

Corporate bonds

Bonds

Bonds is type of financial claims (financial instruments )

A bond is a certificate showing that a borrower owes a specified sum

To repay the borrowing, the borrowers has agreed to make interest and principal payments on designated date.

Some terms of bonds

Coupon: the stated interest payment made on a bond

Face/ Par value: the principal amount of a bond that is repaid at the end of the term

Coupon rate: the annual coupon divided by the face value of a bond

Maturity: the specified date on which the principal amount of a bond is paid

Bond value and interest rate

If the cash flows from a bond keep constant, while the interest rate changes in the market, the value of the bond will fluctuate.

If interest rate rises, the present value (PV) of the bonds cash flows declines, then the bonds value declines and vice versa.

Bond value and interest rate

To determine the value of a bond at a particular point in time, we need to know the number of periods remaining until maturity, the face value, the coupon and the interest rate (discount rate)for bonds with similar features. The interest rate required in the market on a bond is called the bonds yield to maturity or the bonds yield.

If the cash flows from a bond keep constant while the interest rate changes in the market, the value of the bond will fluctuate

If the interest rate, the present value of the bonds cash flows declines, then the bonds value declines and vice versa

Bond issuers

Corporations, private firms, governments

Government bond market accounts for the largest share of the whole bond market

Governments use bond to manage the long term and short term cash flow and money supply

Example of a bond

Company A just issued bonds for 10,000 each where the bonds have coupon rate of 5 percent and a maturity for two years. Coupon on the bonds is to be paid yearly

Example illustration

1 billion (100,000 *10,000) has been borrowed by the company

The firm must pay coupon (interest) of 50 million (5% * 1 billion at the end of year 1

The firm must pay both 50 million of coupon (interest) and 1 billion of principal at the end of year 2

Bond price quotes

If you buy a bond between coupon payment dates, the price you pay is usually more then the price quoted. Standard convention in the UK bond market is to quote prices net of so called ‘accrued interest’ meaning that the accrued interest is deducted to arrive at the quoted price.

Bond price quote

Clean price

The price of a bond net of accrued interest. That is the price is typically quoted.

Example

The accrued interest on a bond is calculated by taking the fraction of the coupon that has passed in this case 2 month out of 6 months and multiplying this faction by the next coupon 60. So the accrued interest in this example is (2/6) * 60 = 20, therefore the bonds quoted price (clean price) would be 1080 – 20 = 1060

Dirty price

The price of a bond including interest, also known as the full or invoice price. That is the price the buyer actually pays.

Example

Assuming you buy a bond (1,000 face value) with a 12% annual coupon, payable semi-annually. You actually pay 1,080 for this bond, so 1080 is the dirty price. Further on the day you buy it, the next coupon (60) is due in 4 months so you are between coupon dates

Types of Bonds

Pure discount bonds

(zero coupon bonds): it is sold at discount e.g. sold at 90 and promises a single payment e.g. 100 at a fixed future date

Level coupon bonds

(plain vanilla): it offers cash payments not just at maturity, but also at regular times in between e.g. annual coupon, semi-annual coupon

Consols

It is the bond that never stops paying a coupon, has no final maturity date and therefore never matures, similar to a perpetuity.

Bond valuation

Pure discount bonds

PV=F1+RT

where PV is the present value (fair market) of the bond, F is the face value of the bond, R is the discount rate (normally, interest rate and T is the time of Maturity)

(level ) coupon bonds

Can also be written as

Where c is the coupon, A is the annuity factor and all other notations remain the same

Consols

PV = CR

All notations remain the same

Bond price

Obviously the bond price has a negative relationship with market interest rate

The bong price rises if interest rate falls

The bong price falls if interest rate rises

Equity

What is equity?

Equity (share)

A share representing an ownership stake in a company, the holder is entitled to periodic dividends and can sell the shares to other parties at the market price

A pizza and a slice (a firm and a share)

Traded in secondary markets at the market price

Equity (stock) Markets

major international stock markets

USA, JAPAN and UK and CHINA

Measurement of sotck markets

Stock market capitalization: the total value of the companies listed on the stock market

Why is stock market important?

A country’s relative importance is influenced by the current state of its stock market and performance of its currency

Large stock markets/ exchanges in the world

NYSE (new York stock exchange)

Biggest stock exchange in the world, capitalization accounts for ¼ of the world total

NASDAQ (USA)

Where high potential and high technology firms listed

Tokyo stock exchange (japan)

Post war economic growth

London stock exchange

Operated by a computer based trading system, highly efficient

Emerging countries ( China and India )

Classification of stock markets

Stock markets can be classified by following

Public or private

Cash or forward markets

Fixed or continuous quotation

Computerized or floor trading

Public or private

Self regulating (UK, US, Japan, Hongkong)

Government influenced (France, Spain, Italy)

Trading via commercial banks (Germany, Switzerland and Austria)

Cash or forward markets

Most of markets are cash (spot) markets. The stocks are delivered as quickly as the settlement procedures permit

Paris bourse is a forward market. All major stocks are delivered at the end of the month.

Fixed or continuous quotation

Most major markets have high degree of liquidity and therefore quote most stocks on a continuous basis

In some low liquid stock markets, quoted prices are for a day

Computerized or floor trading

Computerized trading is necessary for trading international stocks

Floor trading is still a popular features in the NYE. High degree of interaction and rapid exchange of information.

Investors (institutional and individual)

Pension funds

Mutual funds

Insurance funds

Brokers (on behalf of clients)

Market makers (providing information)

The Primary Stock Market

The primary market

Privatization: the sale of state owned enterprises to the private sectors, often through the sale of shares to the public and institutions

Allotment policy: the public of distributing shares from an initial public offering (IPO) to underwriters and investors

Listing requirements: the set of conditions and standards that a conditions and standards that a company must meet in order to gain and then maintain a stock exchange listing

Types of shares

Ordinary shares

Shares which represent partial ownership of a company, entitling the owner to vote. The holder may or not receive dividends depending on profits

Preference shares

Shares which entitle the holder to a given divided, holders have priority over ordinary shareholders. Holders entitled to a share of the asset if the firm goes into liquidation, but have lower priority than debt holders. \holders are not entitled to vote.

Preference Shares

Cumulative preference shares

Holders is entitled to any missed dividends if earning recover sufficiently before any dividends are made to ordinary shareholders

Convertible preference shares

Holders have the right to convert their shares into ordinary shares at predetermined conditions if a certain number of dividend payments are missed

Redeemable preference shares

The company can buy back the shares at their original price

Participating preference shares

Allow greater dividend in the event that profits above certain levels

A right issue

If the company wishes to raise further capital by method other than the issue of debt, it can choose to issue new equity in the form of rights issue

Rights issue: the issuance of new shares by company to raise new finance, the shares are offered to current shareholders first in proportion to the number of shares that they own. Shareholders can transfer their rights to a third party.

The new shares are usually offered at a discount to the existing price to encourage take up of the issue

Example

A ‘one for two’ issue, the existing stock holders are offered one new share for every two shares that they already hold. If the shares are currently valued at 100 pence each, then the new share maybe pence at 7 pence, the stock holder must decide whether to take up his rights or sell them to a third party.

If the stock holder takes up his rights then he retains the same proportion of ownership of the company as prior to the issue, but the price of his shares will fall after the rights issue

(100 +100+70)/3 = 90 pence

The stockholder also can sell his right a third party for up to 20 pence (90 pence – 70 pence)

Returns

Return on an investment comes in two forms:

A) income

i.e. dividends in the case of sharers or coupons in the case of bonds

b) capital gain/ loss based on change in price

Arithmetic Return (R)

This is for one period:

Share valuation

based on the dividend growth model, the current price of a share is present value of all future dividends

what is the dividends payments

have a zero growth rate

have a constant growth rate

have differential growth rate

define g is the dividends growth rate, R is the required rate of return of the stock, Po is the shares current market price

limitations of dividends growth model

R must be greater than g

No dividend firm

A lack of consideration of growth opportunity

Time value of Money

What is time value of money ?

Present value: the value of the asset now

Future value: the value of the asset on a specific date in the future

Time value of money: a pound to be received in the future is worth less than a pound received today. The present value of a sum of money depends on the date of it receipt.

The sample example

Assuming the interest rate is 10% per annum and you saved 100 in the bank today. How much are you going to have in your bank account in a year?

Balance in a year = 100 +100*10% = 110

Present value: 100

Future value: 110

Why does money have time value?

Opportunity cost: the sacrifice of the return available on the best for gone alternative

Time value of money is the compensation to the opportunity cost of investors

E.g. saving money in the bank we receive interest. The interest rate is the time value of money to against inflation, compensating your loss of liquidity and potential return from alternative investment (opportunity cost)

you will generously lend me 1,000 if I repay you the 1000 plus interest in 10 years time. The interest is the time value of this 1,000 to compensate your opportunity cost over this 10 years.

Discounted Cash Flow

What is discounted cash flow?

Future cash flows are converted into common denominator of time zero by adjusting for the time value of money.

Single cash flow in single period

FV = PV * (1+R)

Where R is the interest rate (required rate of return, discount rate..), PV is the present value of the cash flow and FV is the future value of the cash flow. Rearrange above equation, we have PV = FV/ (1 +R)

Example

Assuming a sum of 10 is deposited in a bank account that pays 12 per cent annum interest rate. How much will be in the account at the end of year 1? (what is the FV of 10 in a year)

FV = PV * (1+R)

= £10*(1+12%)

= £11.2

Example

Given the interest rate of 12 per cent per annum. If you anticipate the receipt 11.2 in the bank account in one year, how much do you need to deposit now? (what is the PV of 11.2 you are to receive in on year?)

PV = FV/(1+R)

= ₤11.2/(1+12%)

= ₤10

In this case, we say we discount the FV for one year

Single cash flow in multiple periods

FV = PV * (1+R)T

Where R is the interest rate (required rate of return, discount rate..), T is the number of period, PV is the present value of the cash flow and FV is the future value of the cash flow. Rearrange above equation, we have

PV = FV/(1+R)T

Example

Assuming a sum of 10 is deposited in a bank account that pays 10 per cent per annum interest rate. How much will be in the account at the end of year 2? (what is the FV of 10 in two years)

FV = PV * (1+R)T

= £10 *(1+10%)2

= £12.1

In this case we say the interest rate is compounding for 2 years

Example

Given the interest rate of 10 per cent per annum. If you anticipate the receipt of 12.1 in the bank account in two years, how much do you need to deposit now? (what is the PV you are to receive in two years)

PV = FV/(1+R)T

= ₤12.1/(1+10%)2

= ₤10

In this case, we discount the FV for 2 years.

the general formula for both single cash flow in single period and single cash flow in multiple periods are

FV = PV * (1+R)T

and

PV = FV/(1+R)T

Where R is the interest rate (required rate of return, discount rate..), T is the number of period, PV is the present value of the cash flow and FV is the future value of the cash flow.

Multiple cash flow in multiple periods

Annuities

Perpetuities

Annuities

What is an annuity?

An annuity is a financial instrument which offers the holder a series of identical payments over a period of years

What is the PV of annuity?

PV of an annuity is the sum of PVs of all future payments

PV and market price

Example

A five-year annuity offers the annual payment of ₤10 per year, the payment starts at the end of year one, and given the interest rate is 12% per annum, what is the PV of this annuity.

Illustration (breakdown to each year)

Year FV PV

1 10 10/(1+12%)

2 10 10/(1+12%)2

3 10 10/(1+12%)3

4 10 10/(1+12%)4

5 10 10/(1+12%)5

So the PV value of this annuity is:

PV = 10/(1+12%)+10/(1+12%)2+10/(1+12%)3

+10/(1+12%)4+10/(1+12%)5= ₤36.05

General formula of PV of an annuity is:

PVA = 1-1/1+RTR*A

Where R is the discount rate (e.g. interest rate), T is the number of year that is annuity will last, and A is the amount of annual payment. In our example, R=12% and A=110. Then PVa = 36/05

Perpetuities

a perpetuity is a financial instrument which offers the holder a regular sum of identical payments received at internal forever

what is the PV of perpetuity

PV of a perpetuity is the sum of PVs of all future payments

PV and market price

Example

A perpetuity offers the annual payment of ₤10 per year, the payment starts at the end of year one to infinity, and given the interest rate is 12% per annum, what is the PV of this perpetuity.

Illustration (breakdown to each year)

Year FV PV

1 10 10/(1+12%)

2 10 10/(1+12%)2

3 10 10/(1+12%)3

4 10 10/(1+12%)4

5 10 10/(1+12%)5

General formula of PV of a perpetuity is:

PVP = A/R

Where A is the amount of annual payment and R is the discount rate. Therefore, for our example

A is 10 and R is 12%. The present value of this perpetuity

PVP = 10/12%=PVP = ₤83.3

[cg1]Financial Investors:

Risk averse investors: investors only take on increased risk if there is sufficient return to compensate. Such as old people living with pension. In finance, all rational investors are summed to risk averse.

Risk neutral investors: investors who are looking for a certain amount of return and will not be effected by the degree of risk. Such as lottery buyers

Risk lover investors: investors who would choose higher risk opportunities even the expected are the same. Such as gamblers.

Financial instruments or financial claims refer to claims to the payment of a sum of money at some future dates

Characteristics:

Risk, uncertainty of return

Liquidity, the ease and speed at which a financial instrument can be turned into cash without loss

Real value certainty, susceptible to loss due to increase in the general level of price, such as inflation

Expected return, probability of outcome

Term to maturity, time of losing liquidity

Currency denomination, relating to exchange rate risk

Divisibility reflects the degree which the financial instrument can be subdivided into smaller units for transaction purpose.

[cg2]Riskier: equity or debt:

Equity claims are riskier than debt claims t o claim holder

Equity holders are only entitled to receive funds in the form of dividends once debt holders have been paid

Debt holders have legal precedence in instances where the company is placed into liquidation.

The implication to the required rate of return is clear, since equity claims are riskier, the expected rate of return needs to be greater than the expected rate of return on debt.

Role of the financial system

The role is to transfer funds from surplus agents to deficit agents in as an efficient manner possible

Deficient agents may wish to borrow short, medium or long term while surplus agents may wish to lend short, medium or long term.

In general deficit agents tend to wish to be able to recall funds at short notice

Surplus agents are risk averse and therefore require quite a degree of safety for their funds while deficit agents require funds for risk projects.

It is therefore important that finance intermediaries design products that can reconcile the somewhat conflicting needs of these two parties.

Difference between Arbitrageurs, hedgers and speculators

Arbitrageurs:

Exploiting a price anomaly in order to make riskless guaranteed profits. Example if asset X is traded at a higher price in market A than in Market B, then arbitrageurs will buy asset X from Market B and sell it in market A

Hedgers

Buying or selling a financial asset in order to reduce or eliminate an existing risk. Example, using interest rate option to lock into fixed interest rate in the future, in order to avoid the unforeseen rate drop

Speculators

Taking on risk in hoping to make a profit. Example: predicting future interest rate and using interest rate forward in hoping to make a profit.

[cg3]Features used to classify financial markets:

Whether the asset are traded are newly issued or already issued (primary and secondary markets)

Type of asset trade (money and capital markets)

The means of settlement (cash and futures markets)

The obligation to exchange (forward and options market)

The organisational structure of the market (regulated and OTC markets)

The method of sale/pricing (screen based trade, OTC trading and pit trading)